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+ + +

+ +

+
+
+ "All science is either physics or stamp collecting"
+ Ernest Rutherford
+ + +

+ +

Classical Electromagnetism +
- Electricity +
  - Electric Charge
  - Structure of Matter
    +
  - Coulomb's Law
  - Electric Field
  - Gauss' Law
  - Electric Potential
  - Electric Potential + Energy
  - Capacitors
  - Dielectric Materials
  - Conductors and Insulators
  - Electric Current, + Resistance and Power
  - Electric Circuits
  +
- Magnetism
- Maxwell's Equations
- Electromagnetic Oscillations
+
Light and Optics

Reflection
Refraction

Apparent Depth
Total Internal Reflection

Wave (Physical) Optics

+ +

+
+ "Physics is, + hopefully, simple. Physicists are not"
+ Edward Teller +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

wearyellow.com
+

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--- /dev/null +++ b/elec_capacitors.html @@ -0,0 +1,482 @@ + + + + + + + Electricty - Capacitors - Physics 299 + + +

+ +

Capacitors
+

+ +

+
+ " + + I used to wonder how it comes about that the electron is + negative. Negative-positive—these are perfectly symmetric in + physics. There is no reason whatever to prefer one to the + other. Then why is the electron negative? I thought about this + for a long time and at last all I could think was 'It won the + fight!' "
+ Albert Einstein
+ +

+
Calculating Capacitance
+

+ +

A capacitor is a system of two insulated conductors.
+

+ +

The parallel plate capacitor is the + simplest example. When the two conductors have equal but + opposite charge, the E field between the plates can be + found by simple application of Gauss's Law.

Assuming the plates are large enough so that the E + field between them is uniform and directed perpendicular, then + applying Gauss's Law over surface S₁ we find,
+

+
where A is the area of S₁ + perpendicular to the E field and σ is the surface + charge density on the plate (assumed uniform). + Therefore,
+

+
+
everywhere between the plates.
+
+
+
+
+

The potential difference between the plates can be + found from

+
where A and B are points, one on each + plate, and we integrate along an E field line, + d is the plate separation, A the plate area and q the + total charge on either plate.
+
+

The capacitance (capacity) of this capacitor is + defined as,

The expression for C for all capacitors is the + ratio of the magnitude of the total charge (on + either plate) to the magnitude of the potential + difference between the plates.

Units of + C: + Coulomb/Volt = Farad, 1 C/V = + 1 F

Note that since the Coulomb is a + very large unit of charge the Farad is also a very + large unit of capacitance. Typical + capacitors in circuits are measured in μF (10^-6) + or pF (10^-12).
+

Note that the expression for the + capacitance of the parallel plate capacitor + depends on the geometric properties (A and + d). Even though it appears that there is + also a dependence on the charge and potential + difference (q/ΔV), what happens is that whatever + charge you place on the capacitor the pd adjusts + itself so that the ratio q/ΔV remains + constant. This is a general rule for + all capacitors. The capacitance is set by + the construction of the capacitor - not the + charge or voltage applied.

The above expression for the + parallel plate capacitor is strictly only true + for an infinite parallel plate capacitor - in + which "fringing" (see above) does not + occur. However, so long as d is small + compared to the "size" of the plates, the simple + expression above is a good approximation.

The parallel plate capacitor + provides an easy way to "measure" ε₀ +
+

+

+
+

As indicated above the parallel plate + capacitor is the most basic capacitor. + You should also be able to determine the + expressions for the capacitance of spherical + and cylindrical capacitors,

+ + + + elec cap fig2

+
+ divider

+
+
Energy and Capacitors
+
+

One of the most important uses of + capacitors is to store electrical + energy.

If a capacitor is placed in a + circuit with a battery, the potential + difference (voltage) of the battery will + force electric charge to appear on the + plates of the capacitor. The work + done by the battery in charging the + capacitor is stored as electrical + (potential) energy in the capacitor. + This energy can be released at a later + time to perform work.
+
+
+

The work necessary to move a + charge dq onto one of the plates is + given by, dW = Vdq, where V is the + pd (voltage) of the battery (= + q/C). The total work to place + Q on the plate is given by,

+
which is equal to + the stored electrical potential + energy, U.
+
+

The electrical energy actually + resides in the electric field + between the plates of the + capacitor. For a parallel + plate capacitor using C = + Aε₀/d and E = + Q/Aε₀ we may write + the electrical potential energy, +
+

+
(Ad) is the + volume between the plates, + therefore we define the energy + density,
+
+

+
+
+

Although we have + evaluated this + expression for the + energy density for a + parallel plate capacitor + it is actually a general + expression. + Wherever there is an + electric field the + energy density is given + by the above.

+
+
Combinations of + Capacitors
+
+

It is common + to find multiple + combinations of + capacitors in + electrical + circuits. In the + simplest situations + capacitors can be + considered to be + connected in series + or in parallel. + + + + +
+

Capacitors + + + + + in Series

+
When + different capacitors + are connected in + series the charge on + each capacitor is + the same but the + voltage (pd) across + each capacitor is + different
+
+
+

+
+
In + + + + + this + situation, + using the fact + that V = V₁ + + V₂ + +V₃ + + + + + we can show + that, as far + as the voltage + source is + concerned, the + capacitors can + be replaced by + a single + "equivalent" + capacitor C_eq + + + + + given by,
+
+
+

+
+

Capacitors + + + + + in Parallel

+
For + capacitors + connected in + parallel it is + the voltage + which is same + for each + capacitor, the + charge being + different.
+
+

+

+ Using the fact + that Q_Total= + Q₁ + + Q₂ + + Q₃ + we can show + that the + equivalent + capacitor, C_eq + + + + + is given by,
+
+

+
+
+
+
+

+ +

+

+

+ +

+ + At the electric company: "We would be delighted if you + send in your bill. However, if you don't, you will be."
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_charged_particle_motion.jpg b/elec_charged_particle_motion.jpg new file mode 100644 index 0000000..aa88ff1 Binary files /dev/null and b/elec_charged_particle_motion.jpg differ diff --git a/elec_chargemotion.html b/elec_chargemotion.html new file mode 100644 index 0000000..269153a --- /dev/null +++ b/elec_chargemotion.html @@ -0,0 +1,101 @@ + + + + + + + Electricity - Charged Particle Motion in an Electric Field - + Physics 299 + + + +

+ + +

Charged Particle Motion in an Electric Field
+

+ +

+
+ " + + The hardest thing in the world to understand is the income tax"
+ Albert Einstein
+ +

+ +

Having determined the electric field we now want to determine + the behaviour of a point charge, q₀, placed in this + field.

The force on the charge is given by F = q₀E. + + + + But Newton's second law tells us that F = ma, so + that the acceleration of the particle can be written, a + = (q₀/m)E.

Once we have an expression for the acceleration it is usually + possible to determine the trajectory of the particle, although + in the general case this will involve solving differential + equations. However, when E is constant the + acceleration is constant which allows us to use the kinematic + equations describing motion under constant acceleration from the + beginning of the first semester of this course (Physics + 298). Important equations in Physics should never be + forgotten .
+

In two dimensions, with E constant in one direction + and zero in the other, charged particle motion can be treated in + the same way as projectile motion of a particle under the + influence of a (constant) gravitational field.

+ +

+ + +
+ What do you get if you have Avogadro's + number of donkeys? + Answer: molasses (a mole of asses)
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_circuit.jpg b/elec_circuit.jpg new file mode 100644 index 0000000..8be06d8 Binary files /dev/null and b/elec_circuit.jpg differ diff --git a/elec_circuits_RC.html b/elec_circuits_RC.html new file mode 100644 index 0000000..bfc238c --- /dev/null +++ b/elec_circuits_RC.html @@ -0,0 +1,242 @@ + + + + + + + Electricity - RC circuits - Physics 299 + + + + +

+ + +

RC Circuits
+

+ +

+
+ + + + + +

"A fact is a simple + statement that everyone believes. It is innocent, + unless found guilty. A hypothesis is a novel + suggestion that no one wants to believe. It is + guilty, until found effective"
+

+ Edward Teller
+ +

+
+

CHARGING

An example of a series RC circuit is + shown at right. With the emf included in the circuit, + applying the loop theorem we find

+
where q/C is the voltage drop across the + capacitor and i is the current in the circuit.
+
+

Using the fact that i = dq/dt, we obtain

This is a "simple" differential equation the solution + of which can be written

+
or
+

+
+
+

The voltage across the capacitor, V_C = + q/C and the voltage across the resistor, V_R + = iR. Using the equations above we find that + the dependence of these voltages on time is shown + below

+
+

Note that the time on the + horizontal axis is measured in units of τ = RC, + the capacitative time constant.

After one time constant V_C + has reached 63% (1 - e^-1) of its + maximum value and V_R has 37% (1/e) of + its final value.

DISCHARGING

Now + switch the emf out of the circuit and + reapply the loop theorem

+
which gives
+

+
+
which has the solution
+

+
and
+

+
+
+
+
+
where Cε is the + initial charge on the capacitor + and ε/R is the initial voltage + across the capacitor.
+
+
+
+
+
+

The time + dependence of V_C and + V_R (where V_R + is proportional to the current + in the capacitor) are shown at + right.

Once + again the time axis is measured + in units of RC.

After + one time constant V_C + has decreased to 37% (1/e) of + its initial value and |V_R| + has decreased to 37% (1/e) of + its initial value.

+
+
+
+
+

+
+
+
+
+

+ +

+ Q: What did one quantum physicist say + when he wanted to fight another quantum physicist?
+ A: Let me atom.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_circuits_eqn1.jpg b/elec_circuits_eqn1.jpg new file mode 100644 index 0000000..f553172 Binary files /dev/null and b/elec_circuits_eqn1.jpg differ diff --git a/elec_circuits_fig1.jpg.png b/elec_circuits_fig1.jpg.png new file mode 100644 index 0000000..4bf04e5 Binary files /dev/null and b/elec_circuits_fig1.jpg.png differ diff --git a/elec_circuits_fig2.jpg.gif b/elec_circuits_fig2.jpg.gif new file mode 100644 index 0000000..dac2d44 Binary files /dev/null and b/elec_circuits_fig2.jpg.gif differ diff --git a/elec_circuits_fig3.jpg.gif b/elec_circuits_fig3.jpg.gif new file mode 100644 index 0000000..b175111 Binary files /dev/null and b/elec_circuits_fig3.jpg.gif differ diff --git a/elec_circuits_fig4.jpg.gif b/elec_circuits_fig4.jpg.gif new file mode 100644 index 0000000..98e9646 Binary files /dev/null and b/elec_circuits_fig4.jpg.gif differ diff --git a/elec_circuits_fig5.jpg.gif b/elec_circuits_fig5.jpg.gif new file mode 100644 index 0000000..759e057 Binary files /dev/null and b/elec_circuits_fig5.jpg.gif differ diff --git a/elec_circuits_kirchoff.html b/elec_circuits_kirchoff.html new file mode 100644 index 0000000..0958f9f --- /dev/null +++ b/elec_circuits_kirchoff.html @@ -0,0 +1,211 @@ + + + + + + + Electricity - Kirchoff's Laws - Physics 299 + + + + +

+ + +

Kirchhoff's Laws
+

+ +

+
+ + + + + +

"An expert is a man who has made all + the mistakes which can be made, in a narrow field. + "
+

+ Niels Bohr
+ +

+
The most common general method to analyze + electrical circuits is by use of Kirchhoff's Laws.
+

+
Junction Theorem
+

+
At any + junction in a circuit the current entering the junction + must equal the current leaving the junction.
+
+
+
(This is nothing more than a statement of + conservation of charge)
+
+

+
Loop Theorem
+
The sum of the + changes in potential when traversing any complete + loop is zero.
+
+
(This is equivalent to conservation of energy)
+
+

+ +

+
Conventions
+

As usual, in order to ensure consistent results from + application of these laws, we must adhere to several conventions + concerning the currents and potentials in circuits.
+
+ Potentials:
+
+
When a resistive device is traversed in the direction of + current flow the change in potential is -iR. Conversely, + if the resistance is traversed opposite to the direction of + the current the potential change is +iR.
+
When an emf is traversed in the direction of the emf the + change in potential is +ε. Conversely, if the emf is + traversed opposite to the emf direction the change in + potential is -ε.
+
+

+ Currents:
+
+
+
In setting up a problem, the current direction in any + particular circuit element is assigned arbitrarily. + Kitchoff's laws are then applied to the circuit using these + current directions. After solving the resulting + equations if a current is negative that means the "actual" + current direction is opposite the arbitrarily chosen + direction.
+
+
+
+
+

+
+

+
Application of Kirchhoff's Laws
+

+
Kirchhoff's laws can be applied to any circuit to + obtain a set of equations relating the currents, resistances and + emfs in the circuit. These equations can then be solved + for the unknown quantities in the circuit. For any circuit + follow the steps below.
+
+

+
+
Label the current flowing in each part of the circuit, + bearing in mind that current will "split" on reaching a + junction. The direction of the defined direction of the + current does not matter - see current convention above.
+
At each junction in the circuit use the junction theorem to + write down the equations relating the currents entering and + leaving.
+
Define all possible loops in the circuit and label.
+
For each loop choose a starting location then use the loop + theorem to write down the equation relating changes in + potential which must be zero after traversing the complete + loop.
+
Solve the set of equations from 2. and 4. to obtain the + unknown parameters of the circuit.
+
+

+ As an example, consider the circuit below. With the 3 emfs + we cannot use the series/parallel analysis.
+
+
+

Junctions:
+
a: I₁ = I₂ + I₃ +
+ b: I₃ + I₂ = I₃
+
+
+ Loops:
+
1 (including ε₁ starting at a traversing + clockwise): - I₃R₄ - ε₃ - + I₁R₂ + ε₁ - I₁R₁ + = 0
+ 2 (including ε₂ starting at a traversing clockwise): + - I₂R₃ - ε₂ + ε₃ + + I₃R₄ = 0
+ 3 (including ε1 and ε₂ starting at a traversing + clockwise): - I₂R₃ - ε₂ - + I₁R₂ + ε₁ - I₁R₁ + = 0
+
+ Looking at these equations it is clear that the two junction + equations are equivalent, and that loop equation 3 is simply the + sum of loop equations 1 and 2. Therefore there are only 3 + independent equations (a, 1 and 2), which we can solve for, say, + the currents I₁, I₂ and I₃.
+
+ Note that in more complicated circuits there will be + many more junctions and a large number of possible loops. + You only need apply the loop theorem to as many loops to obtain + the number of independent equations necessary to determine the + unknown parameters. That is if you have 3 unknown + quantities, you'll need a total of 3 independent equations.
+

+ +

+ What do you get if you have Avogadro's + number of donkeys?
+ Answer: molasses (a mole of asses)
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_circuits_sp.html b/elec_circuits_sp.html new file mode 100644 index 0000000..5e17902 --- /dev/null +++ b/elec_circuits_sp.html @@ -0,0 +1,140 @@ + + + + + + + Electricity - Series and Parallel Circuits - Physics 299 + + + + +

+ + +

Series and Parallel Circuits
+

+ +

+
+ " + + It would be better for the true physics if there were no + mathematicians on earth."
+ Daniel Bernoulli
+ +

You may already be familiar with the idea of circuits with + resistors in series or parallel or some combination of the two.

+
Series
+

+
The same current flows + in each resistor, the voltages across them are typically + different, where V = V₁ + V₂ + V₃ + which leads to the equivalent resistance formula
+
+
R_eq = R₁ + R₂ + + R₃
+
+
+

+
Parallel
+

+
The potential difference across each resistor is the + same, but the currents through them are typically different, + where I = I₁ + I₂ + I₃. + This lead to the equivalent resistance formula,
+

+
+
Note that both of the diagrams below + represent resistors in parallel.
+
+
+ + +
+
+
+

+
Combinations
+

+
Some circuits can be analysed as combinations of + series and parallel circuits. In the circuit below R₂ + and R₃ are in parallel, their equivalent resistance + is then in series with R₁.
+

+
+
+ Note that it is not possible to represent all + circuits as combinations of series and parallel elements, this + is most obvious in many cases where there is more than one + battery in the circuit, see example below. To analyse this + type of circuit we must use Kirchhoff's Laws.
+
+

+
+

+
+
+

+
+

+ +

+ Got mole problems? Call Avogadro at + 602-1023.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_condins.html b/elec_condins.html new file mode 100644 index 0000000..320942d --- /dev/null +++ b/elec_condins.html @@ -0,0 +1,147 @@ + + + + + + + Electricity - Conductors and Insulators - Physics 299 + + + + +

+ + +

Conductors and Insulators

+ +

+
+"What is the use of a new-born child ?"
+Benjamin Franklin
+(when asked what was the use of a new invention)
+ +

+ +

Moving electric charges constitute what is know as an electric +current. It is the electric currents in semi-conductor devices +which are responsible for the electronic technology in today's society.
+
+

Conductors are materials which allow the free movement +of electric charge. Examples include,

Metals
Some liquids
Gas plasmas
+
+

Insulators (or non conductors) are materials which +provide +significant resistance to the flow of electric charge. Examples +include,

Non metals - plastic, wood, glass, rubber etc.
Gases
+
+

Semi-conductors are materials whose resistance to +current flow +falls between conductors and insulators. There are very few such +materials, but their importance in electronic technology cannot be +emphasized enough. Examples,

Silicon
Germanium
+
+

Mechanisms of conduction:

Metals (solid)

Each atom in the solid is "fixed", forming a lattice.
Outer electrons in a metal are weakly bound to the atomic +nucleus.
When an external electric field is applied these outer +electrons move +through the material creating an electric current.

Liquid conductors and gas plasmas

Conducting liquids and gases are comprised of positive and +negative +ions (charged particles).
Both positive and negative ions move when an external +electric field +is applied, thus creating the current.
A positive charge moving to the right creates the same +current as +an equal negative charge moving to the left.

Insulators

All electrons in these materials are tightly bound to the +atomic nuclei. External electric fields are typically not large +enough to cause any flow of charge.

Semi-conductors

These materials have a small number of weakly bound +electrons, the +number of which is very dependent on the temperature and +potential +difference applied across the material.

It is important to realise that because sustained electric +currents +only occur when a potential difference is maintained in a closed +circuit, +as many charge carriers enter as leave any part of the circuit. +In +other words electric current is not "used up"; it has the same value +everywhere in the circuit.
+
+

+ +

Marilyn Monroe +suggests to Einstein: What do you say, +professor, shouldn't we marry and have a little baby together: what a +baby it +would be - my looks and your intelligence!
+Einstein: I'm +afraid, dear lady, it might be the other way around...
+Albert Einstein
+

+ +

Dr. C. L. Davis
+Physics Department
+University of Louisville
+email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_contdist.html b/elec_contdist.html new file mode 100644 index 0000000..e8e15ac --- /dev/null +++ b/elec_contdist.html @@ -0,0 +1,96 @@ + + + + + + + Electricity - Electric Field Due to Continuous Charge + Distributions - Physics 299 + + + +

+ + +

Electric Field Due Continuous Charge Distribtuions
+

+ +

+
+ " + + Common sense is the collection of prejudices acquired by age + eighteen"
+ Albert Einstein
+ +

+ +

Electric charge is a property of individual particles - + protons, electrons etc. But since these particles are + extremely small it is often convenient to consider charge to be + continuously distributed.
+

These distributions can be over a line (one dimension), an + area (two dimensions) or a volume (three dimensions).

In order to determine the electric field due to a continuous + charge distribution we "sum" the fields due to the individual + "elements" that comprise the distribution, by integrating over + the line, area or volume in question. For example in the + example below charge is distributed uniformly over the rod on + the x axis. To determine the electric field at point P, we + write down the expression for the field at P due to the "point" + charge dq located at "x" as shown, then integrate over x from x + = 0 to x = x.
+

+ +
+

+ +

+ + +
+ Overheard after a student failed a + physics test miserably: + Nuclear, Hydrogen, Atomic, My test- They can all be bombs.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_continchgdist.jpg b/elec_continchgdist.jpg new file mode 100644 index 0000000..c5d04b3 Binary files /dev/null and b/elec_continchgdist.jpg differ diff --git a/elec_coulomb.html b/elec_coulomb.html new file mode 100644 index 0000000..8f69792 --- /dev/null +++ b/elec_coulomb.html @@ -0,0 +1,154 @@ + + + + + + + Electricity - Coulomb's Law - Physics 299 + + + +

+ + +

Coulomb's Law

+ +

+
+"When man wanted to make a machine that would +walk +he created the wheel, which does not resemble a leg"
+Guillaume Apollinaire
+ +

+ +

The magnitude of the force of attraction (or repulsion), F₁₂ +between two point charges q₁ and q₂ is +given by Coulomb's Law.

+
+

where R₁₂ is the distance between the +charges. k is a constant of proportionality known as the Coulomb +constant, having the value 9 x +10⁹ N.m² / C² in a +vacuum.

Note that the Coulomb constant, k, is +often replaced with (1/4π ε₀), where +ε₀is the permittivity of the vacuum (more later).
+

The direction of this force is along the line joining the two +charges +with the sense determined by the relative signs of the charges

Note that the force on each charge has the same magnitude (as +required by Newton's third law of motion).

For two 1 Coulomb charges separated by 1 metre the +magnitude +of the force is given by, +
+F = (9 x 10⁹ x 1 x 1 )/ 1 = 9 x 10⁹ + Newtons +
This is an extremely large force (sufficient to +move Mt. Everest with an acceleration of 1cm/s²). The +Coulomb +is a very large unit. Typical macroscopic charges +are measured in micro-coulombs (10^-6 C).
+
To handle situations with more than one charge, the charges must +be treated in pairs, so that the overall force on one charge will be +the vector sum of the force +due to each of the other charges. For example the force on q₁ +due to all other charges q₂, q₃ , q₄... +would +be +given +by,

F₁ = F₂₁ + +F₃₁ + F₄₁ + ...
+

Notice +the +similarity +of +Coulomb's Law to Newton's Law of Gravitation

+both are "inverse square" laws. Substitute charge for mass and +"k" for "G" and you have Coulomb's law.
+

The relative magnitudes of the Coulomb +constant, k = 9 x 10⁹ and the gravitational constant, G = +6.67 x 10^-11, is an indication of the relative strengths of +the two forces. The electrical force of attraction is much, much +stronger than the gravitational force of attraction.
+

+ +

+"The +wireless +telegraph +is +not +difficult +to +understand. The ordinary telegraph is like a very long cat. You pull +the tail +in New York, +and +it +meows +in +Los Angeles. The wireless is +the same, only without the cat."
+Albert Einstein
+
+

+ +

Dr. C. L. Davis
+Physics Department
+University of Louisville
+email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_coulomb_eqn1.gif b/elec_coulomb_eqn1.gif new file mode 100644 index 0000000..87001de Binary files /dev/null and b/elec_coulomb_eqn1.gif differ diff --git a/elec_current.html b/elec_current.html new file mode 100644 index 0000000..c8b4eba --- /dev/null +++ b/elec_current.html @@ -0,0 +1,391 @@ + + + + + + + Electricity - Electric Current - Physics 299 + + + + +

+ + +

Electric Current, Resistance and Power
+

+ +

+
+ "When I find myself in the company of + scientists, I feel like a shabby curate who has strayed by + mistake into a drawing room full of dukes"
+ W. H. Auden
+ +

+
+

+
Electric Current
+
+

Electric current is equal to the rate at which charge passes + a fixed point in space.

Amperes:

1 + Ampere = 1 Coulomb/second

It is important to realize that the value of the current is + constant, whatever the cross section of the conductor. If + this were not so then charge would "pile up" at points along a + conductor.

When you flip a switch a light bulb turn on instantly. + In fact the current moves at speeds close to the speed of + light. However, the charge carriers, electrons in a + metallic wire, travel at a much slower velocity - the drift velocity.
+ Consider a wire of length l, cross section A, with n conduction + electrons per unit volume. The current in the wire can be + written,

where e is the + charge on the electron and v_d is the drift velocity.
+

Current Density, J + (A/m²) is defined by,

+
+

physically, + J represents charge movement at a particular place within a + conductor, e.g. when A is large J is small, when A is small + J is large.
+ The general relationship between I and J is
+

The current is the flux of + J through a surface.
+
+

Important: +The +current, +I, +is + + + + + + + + + + + + a scalar quantity, whereas J is a vector. I has a + "sense" in that we draw arrows to represent its + "direction", but does not obey the rules of vector + algebra.
+

Historical quirk. + The direction of current flow is defined as the direction in + which a positive charge will move. But in solid metallic + conductors the charge carriers are electrons (negative charges) + which actually move in the opposite direction. Negative + charges moving right to left are exactly equivalent to positive + charges moving left to right.

+
+
Resistance
+
+

+ +

In metallic conductors the electric field and current density + are in the same direction and are found to be proportional to + each other,

+
+

where ρ is the + resistivity of the conductor - characteristic of the + conductor. The conductivity of a conducting material is + defined by, σ = 1/ρ.
+ For a uniform conductor, length l, cross section A, we have E = + V/l and J = i/A, so that
+
+

+
+

The resistance of the conductor + R, is defined by,
+

+ Resistance is measured in ohms (Ω), then resistivity has + units ohm.metre and conductivity (ohm.metre)^-1 +
+

Important: The relationship V = + IR is NOT + Ohm's Law !

Ohm's + Law:
+

"If the ratio of + voltage across a conductor to the current through + it is constant for all voltages then that + conductor obeys Ohm's Law"
+

+ Ohm's law holds for metallic conductors, but not + for devices such as transistors, diodes etc. + The relationship V = IR can always be used to + determine the resistance at some particular I and + V for any device.
+

Even in conductors current will only flow between two points + A and B when

There is a potential difference between A and B (producing + the electric field which forces the charges to move) and,
A and B form part of a complete circuit.
+

Power

Suppose a charge dq moves from point A to point B, where the + potential difference between A and B is V_AB, then the + energy released in time dt is given by

+
+

+
so that the rate at which energy is + transferred (power), P, is given by,
+

+
+
In terms of units we can state that + Amps x Volts = Watts.
+
+
+
+

The form of the energy "released" depends on the + electrical component placed between A and B, for + example,

Motor - mechanical energy (work) released
Battery - chemical energy stored in the battery
Resistance - thermal energy (heat) released
+

+ +

+
+
Electro-motive Force - "emf"
+
+

In discussing electric circuits + you may come across the term "emf" - electro-motive + force. It is important to realize that an "emf" is + NOT a force !

If a device has an "emf" it has the ability to maintain a + potential difference (voltage). Thus, for example, a + battery maintains an emf between its positive and negative + terminals.

The emf of a device can be defined by ε = dW/dq, where dW + is the work done on a positive charge dq in taking it + acrosss the potential difference of the device. In the + case of a simple circuit with a battery (see above) as a + charge traverses the external (to the battery) circuit it + loses energy. In the circuit above the energy appeara + as heat and light in the light bulb. When the + charge returns to the battery the emf of the battery + replenishes its energy.

At this introductory level we can consider the emf of a + "source" (battery, generator etc) to be exactly equivalent + to the voltage provided by the source.

The direction of the emf always represents the direction a + positive charge would move in the external circuit. + See circuit at right. The emf direction is an + important factor when we use Kirchoff's laws to analyze + circuits.

+ +

+
+

+
+
Internal Resistance
+
+

All emfs - batteries, generators etc - and electrical + measuring devices - ammeters, voltmeters etc - have an + "internal resistance".

As far as circuit analysis is + concerned these internal resistances can simply be + considered as resistors in series with the "ideal" + emf/meter.

For ammeters (current measuring devices) the goal is to + have as low an internal resistance as possible so that the + current is not affected.

fig3

For a voltmeter the internal resistance should be as large + as possible.
+

+
+

+ +

Q: Does light have mass?
+ A: Of course not. It's not even Catholic!!!

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_current_eqn1.jpg b/elec_current_eqn1.jpg new file mode 100644 index 0000000..1e32000 Binary files /dev/null and b/elec_current_eqn1.jpg differ diff --git a/elec_current_eqn2.jpg b/elec_current_eqn2.jpg new file mode 100644 index 0000000..b822f8a Binary files /dev/null and b/elec_current_eqn2.jpg differ diff --git a/elec_current_eqn3.jpg b/elec_current_eqn3.jpg new file mode 100644 index 0000000..f4f84d0 Binary files /dev/null and b/elec_current_eqn3.jpg differ diff --git a/elec_current_eqn4.jpg b/elec_current_eqn4.jpg new file mode 100644 index 0000000..3ca857c Binary files /dev/null and b/elec_current_eqn4.jpg differ diff --git a/elec_current_eqn5.jpg b/elec_current_eqn5.jpg new file mode 100644 index 0000000..0b88b7c Binary files /dev/null and b/elec_current_eqn5.jpg differ diff --git a/elec_current_eqn6.jpg b/elec_current_eqn6.jpg new file mode 100644 index 0000000..2007aa2 Binary files /dev/null and b/elec_current_eqn6.jpg differ diff --git a/elec_current_eqn7.png b/elec_current_eqn7.png new file mode 100644 index 0000000..2d0e20c Binary files /dev/null and b/elec_current_eqn7.png differ diff --git a/elec_current_eqn8.png b/elec_current_eqn8.png new file mode 100644 index 0000000..9aca76a Binary files /dev/null and b/elec_current_eqn8.png differ diff --git a/elec_current_eqn9.jpg b/elec_current_eqn9.jpg new file mode 100644 index 0000000..93e5501 Binary files /dev/null and b/elec_current_eqn9.jpg differ diff --git a/elec_current_fig2.jpg b/elec_current_fig2.jpg new file mode 100644 index 0000000..0157dc4 Binary files /dev/null and b/elec_current_fig2.jpg differ diff --git a/elec_current_fig3.jpg.png b/elec_current_fig3.jpg.png new file mode 100644 index 0000000..cad921b Binary files /dev/null and b/elec_current_fig3.jpg.png differ diff --git a/elec_current_fig4.jpg.png b/elec_current_fig4.jpg.png new file mode 100644 index 0000000..786c4b9 Binary files /dev/null and b/elec_current_fig4.jpg.png differ diff --git a/elec_dielec_eqn1.png b/elec_dielec_eqn1.png new file mode 100644 index 0000000..b6dc394 Binary files /dev/null and b/elec_dielec_eqn1.png differ diff --git a/elec_dielec_eqn2.png b/elec_dielec_eqn2.png new file mode 100644 index 0000000..7df4260 Binary files /dev/null and b/elec_dielec_eqn2.png differ diff --git a/elec_dielec_fig1.jpg.png b/elec_dielec_fig1.jpg.png new file mode 100644 index 0000000..038f806 Binary files /dev/null and b/elec_dielec_fig1.jpg.png differ diff --git a/elec_dielec_fig2.jpg b/elec_dielec_fig2.jpg new file mode 100644 index 0000000..27dd3c8 Binary files /dev/null and b/elec_dielec_fig2.jpg differ diff --git a/elec_dielectrics.html b/elec_dielectrics.html new file mode 100644 index 0000000..9e4d350 --- /dev/null +++ b/elec_dielectrics.html @@ -0,0 +1,152 @@ + + + + + + + Electricty - Dielectric Materials - Physics 299 + + +

+ +

Dielectric Materials
+

+ +

+
+ + + +

"Basic research + is like shooting an arrow into the air and, where it lands, + painting a target."
+

+ Homer Burton Adkins
+ +

In all our discussions to date we have implicitly assumed that + our charges have been located in a vacuum or on the surface of + conductors. We now need to consider how to take into + account the presence of non-conducting material in the real + world. Dielectric material is simply another way of saying + non-conducting material.

Imagine a parallel + plate capacitor in which a dielectric material is placed between + the plates (at right below). The dielectric is composed of + atoms/molecules which contain positive and negative + charges. The applied electric field between the plates, E₀, + will cause the positive and negative charges of the constituent + atoms/molecules to move slightly in opposite directions + (right). Electric dipole moments will be "induced" in the + material, as shown. The net effect will be for charge to + appear on the surface of the dielectric material as shown. + The dielectric is said to have been polarized, leading to a + polarization electric field, E_P.
+

+
In + conductors (metals) there are (almost) free electrons which will + move through the material when an electric field is applied, + generating an electric current.
+
+

+ +

The net E field + between the plates has been reduced,
+

+
+

+
where κ is called the dielectric constant or + relative permittivity of the medium.
+
+ Note that for a vacuum, since E_P = 0, κ = 1 + and since E_P < E₀ for all other + materials κ > 1.
+
+

It is easy to show that for the parallel plate capacitor + the voltage (p.d) between the plates and the energy stored + are reduced by a factor κ, whereas the capacitance is + increased by a factor of κ.

By application of Gauss's Law to a parallel plate + capacitor with a dielectric between the plates it can be + shown that to account for the presence of the dielectric + Gauss's Law becomes,

+
As a general rule when dielectric media is + present wherever ε₀ appears it must be replaced + by ε₀κ.
+

+ +

A chemist, a biologist and an + electrical engineer were on death row waiting to go in the + electric chair.

+ +

The chemist was brought forward first. + "Do you have anything you want to say?" asked the + executioner, strapping him in. "No," replied the chemist. + The executioner flicked the switch and nothing happened. + Under this particular State's law, if an execution attempt + fails, the prisoner is to be released, so the chemist was + released.

+ +

Then the biologist was brought + forward. "Do you have anything you want to say?" "No, just + get on with it." The executioner flicked the switch, and + again nothing happened, so the biologist was released.

+ +

Then the electrical engineer was + brought forward. "Do you have anything you want to say?" + asked the executioner. "Yes," replied the engineer. "If you + swap the red and the blue wires over, you might make this + thing work."

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_dip_exte.gif b/elec_dip_exte.gif new file mode 100644 index 0000000..9a105a0 Binary files /dev/null and b/elec_dip_exte.gif differ diff --git a/elec_dipexte.html b/elec_dipexte.html new file mode 100644 index 0000000..21e4bf9 --- /dev/null +++ b/elec_dipexte.html @@ -0,0 +1,117 @@ + + + + + + + Electricity - Electric Dipole in an External Field - Physics + 299 + + + +

+ + +

Electric Dipole in an External Electric Field
+

+ +

+
+ " + + When you look at yourself from a universal standpoint, + something inside always reminds or informs you that there are + bigger and better things to worry about."
+ Albert Einstein
+ +

+ +

We have already considered the electric field created + by an electric dipole. Now we consider the behavior of an + electric dipole placed in a uniform (constant) electric field.

+
+

Note that since the force on each of the charges are equal + in magnitude but opposite in direction there is no net + force on the dipole.

However, since the two forces are not concurrent, there is + a non-zero torque about the center of the dipole given by,

+
+

Using the definition of the work done by a torque + (rotational force), it can be shown that the + electrical potential energy stored by a dipole in an + external field is given by,

A dipole placed in a + uniform electric field will rotate until it is + aligned "-" to "+" along the field - this is the + lowest energy configuration.

If the external + field is not uniform, the net force will not be + zero.
+

+ +

+ + +
+ What is a quantum particle? + The dreams that stuff is made of!
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_dipexte_eqn1.jpg b/elec_dipexte_eqn1.jpg new file mode 100644 index 0000000..5972694 Binary files /dev/null and b/elec_dipexte_eqn1.jpg differ diff --git a/elec_dipexte_eqn2.jpg b/elec_dipexte_eqn2.jpg new file mode 100644 index 0000000..42ae78d Binary files /dev/null and b/elec_dipexte_eqn2.jpg differ diff --git a/elec_dipole.html b/elec_dipole.html new file mode 100644 index 0000000..0c85fee --- /dev/null +++ b/elec_dipole.html @@ -0,0 +1,116 @@ + + + + + + + Electricity - Electric Dipole - Physics 299 + + + +

+ + +

Electric Field due to a Dipole
+

+ +

+
+ " + + To punish me for my contempt for authority, fate made me an + authority myself"
+ Albert Einstein
+ +

+ +

An electric dipole consists of two point charges of equal + magnitude, but opposite sign, separated by a short distance.

The dipole is electrically neutral, but due to the + separation of its charges gives rise to an electric field in its + vicinity.

The electric field at the "field point" is given by + E = E_+q + E_-q. + + + + + Note that in adding the two electric fields the y-component + cancels leaving only an x-component given by,

+
where R is the distance from the centre of + the dipole to the field point and the approximation is + valid when r and R are almost equal. In this case + the dimension of the dipole (a) is small compared to the + field point distance.
+
+

p (=2aq) is called the electric dipole moment. + It's actually a vector pointing from the negative to the + positive charge in the dipole so that,

Many molecules have + charge distributions which can be approximated as an + electric dipole, water being one of the most common.

+ +

+
+ "How many Astronomers does it take to change a light + bulb ?
+ None, astronomers prfeer the dark"
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_dipole.jpg b/elec_dipole.jpg new file mode 100644 index 0000000..d52fe92 Binary files /dev/null and b/elec_dipole.jpg differ diff --git a/elec_dipole_eqn1.jpg b/elec_dipole_eqn1.jpg new file mode 100644 index 0000000..ef69fd4 Binary files /dev/null and b/elec_dipole_eqn1.jpg differ diff --git a/elec_dipole_eqn2.jpg b/elec_dipole_eqn2.jpg new file mode 100644 index 0000000..9e306d7 Binary files /dev/null and b/elec_dipole_eqn2.jpg differ diff --git a/elec_efield.html b/elec_efield.html new file mode 100644 index 0000000..6736e5c --- /dev/null +++ b/elec_efield.html @@ -0,0 +1,166 @@ + + + + + + + Electricity - Electric Field - Physics 299 + + + +

+ + +

Electric Field

+ +

+
+"Discovery consists of seeing what everybody +has +seen and thinking what nobody has thought"
+Albert von Szent-Gyorgyi
+ +

+ +

When two charges exert a force on each other, through what means +is the force transmitted ?

The simplest assumption is "action-at-a-distance". +They just "know" +about each other's presence. If one of the charges moves the +other charge is aware of this immediately. This sounds like +"magic" with today's scientific understanding.
+The mechanism to remove the magic was proposed by +Michael Faraday

+- the electric field. +Every charge creates its own electric field in the space around it +(actually the space around it means all space); other charges then +interact with this field. When a charge moves it creates a +disturbance in its electric field which is propagated away from the +charge at the speed of light.
+
+

In developing his theory of gravitation +Newton was aware of the same "action-at-a-distance" +problem. To solve the problem, in a similar manner, we introduce +the concept of the gravitational field.
+
+

Note that the concept of the electric +field is a convenient construct to describe electromagnetic +phenomena, +but its true existence is neither proven nor essential.

The electric field vector, E, +is defined in the following way. If a charge, q, feels a force F, +then +the +electric field, E, at the location of the charge +is +given by

+
+

Units of electric field are Newtons/Coulomb (N/C) or (as +we shall see later) Volts/metre (V/m).

If the electric field felt by the charge q is due to +a point +charge Q, located a distance R from q, then its magnitude is given by

The electric field due to many point charges is given by the +vector +sum of the fields due to the individual charges

E = E₁ + + +E₂ + E ₃ + +.....

In performing this sum the direction of each E +is +the +same as the force felt by a positive charge.
+

The electric field in a region of space can be represented by +electric field lines otherwise known as "lines of force".

The direction of the electric field line is the same as that of +the force +felt by a positive charge. The density of the field lines +provides a +measure of the magnitude of the field. FIeld lines alway begin on +positive +charges and end on negative charges; they cannot be left 'hanging' in +empty +space.
+

The diagrams above display the electric field lines in the +vicinity of +two equal point charges.

+
+"Two things are +infinite: the universe and human +stupidity; and I'm not sure about the universe."
+Albert Einstein
+
+

+ +

Dr. C. L. Davis
+Physics Department
+University of Louisville
+email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_field_eqn1.gif b/elec_field_eqn1.gif new file mode 100644 index 0000000..c3e8cc3 Binary files /dev/null and b/elec_field_eqn1.gif differ diff --git a/elec_field_eqn2.gif b/elec_field_eqn2.gif new file mode 100644 index 0000000..77abb94 Binary files /dev/null and b/elec_field_eqn2.gif differ diff --git a/elec_gauss.html b/elec_gauss.html new file mode 100644 index 0000000..a2c4337 --- /dev/null +++ b/elec_gauss.html @@ -0,0 +1,227 @@ + + + + + + + Electricity - Gauss's Law - Physics 299 + + + +

+ + +

Gauss's Law
+

+ +

+
+ " + + Equations are just the boring part of mathematics. I attempt + to see things in terms of geometry."
+ Stephen Hawking
+ +

Gauss's Law is the first of Maxwell's equations we + will consider. At first the whole concept of Gauss's Law + will seem to be very abstract and confusing, hopefully at least some of the confusion + will pass as you become more familiar with the idea.

+
+

+ +

At the outset it is important to realize that Gauss's Law + and Coulomb's Law are different statements of the same + physical concept. Which of the two is used in any + particular situation depends on the particular application and + what you are asked to determine.

Before stating Gauss's Law we must first define the concept of + FLUX - in particular the flux of the electric field.

At every point on a + surface we can calculate an "element" of the electric flux + given by

+
so that the total electric flux passing + through a surface, S, is given by,
+
+

+
+
+

Gauss's Law then states that,

+
where the circle on the integral + means that the surface is closed and + q_inside is the net charge inside this + closed surface.
+
+

A closed surface has a definite + inside and outside differentiated by the surface, + e.g. the surface of a sphere.
The dA vector of a closed + surface is always directed from the inside to the + outside of the surface.
The exact location of the charges + inside the closed surface is not important, all + that matters is the net charge.
ε₀ is the "Permittivity + of the Vacuum" a constant whose value is 8.85 x 10^-12 + C²/(N.m²) where the Coulomb + constant, k = 1/(4πε₀). Note that + if the charges are not located in vacuum ε₀ + must be replaced by the permittivity of the medium + in question.
The proof of Gauss's Law is beyond + the scope of this course. Suffice to say the + inverse square dependence on distance of Coulomb's + Law is critical.

Before using Gauss's Law to evaluate electric + fields a brief qualitative discussion is + worthwhile. Consider the situation of two + point charges below. Application of Gauss's + Law over each of the closed surfaces:

+
+
S₁: + At every point on this surface both E and + + + + + + + + + + dA are directed "outwards", such that the + scalar product E·dA = EdAcosθ is always + positive. Thus the integral over the + surface S₁ will be positive, as it + must be if Gauss's Law is to be satisfied, since + the net charge enclosed is positive.
+
S₂ : E is directed + "inwards", dA "outwards", leading to a + negative value for the flux through S₂, + consistent with the fact that the net charge + enclosed is negative.
+
S₃: Some of this surface has + E directed "inwards" the remainder has E + directed "outwards". dA is + "outwards" everywhere on the surface. + Therefore the flux integral has both positive + and negative contributions. Since there is + no net charge enclosed by S₃ by + Gauss's Law the net flux will be zero.
+
S₄: Once again there are negative + and positive contributions to the flux integral, + so that we can write Gauss's Law,
+
+

+

+
+
+
+
+

+ +

Electric flux through a closed box animation.

Coulomb's Law, Electric Field, Electric Flux and Gauss's Law video.
+

+ + +
+ Did you hear about the French post-doc + who went to work at the Fermi Lab, but never went in because + the sign over the door always said it was closed.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_gauss_apps.html b/elec_gauss_apps.html new file mode 100644 index 0000000..f34b597 --- /dev/null +++ b/elec_gauss_apps.html @@ -0,0 +1,517 @@ + + + + + + + Electricity - Quantitative use of Gauss's Law - Physics 299 + + + +

+ + +

Quantitative Use of Gauss's Law
+

+ +

+
+ " + + It has been said that democracy is the worst form of + government except all the others that have been tried."
+ Winston Churchill
+ +

Gauss's Law is valid for any closed surface (a Gaussian + surface) and any distribution of charges. If the electric + field is known at every point on the surface S the integral can + in principle be evaluated and will be seen to be equal to the + sum of the enclosed charges divided by ε₀. + However, only in certain very symmetric situations, + where we can infer a great deal of information about the + electric field, can it be used to actually calculate E. + + + + + + + + + + + + + In such cases Gauss's Law provides a short cut to determining E. + + + + + + + + + + + + + The key is to be able to "extract" the E from the flux + integral.

We will consider three possible geometric situations in which + we can obtain E from Gauss's Law:

Spherical symmetry - three dimensions
Rectangular symmetry - two dimensions
Cylindrical symmetry - one dimension

SPHERICAL + SYMMETRY

+ +

Single Point Charge

Consider a single point charge +Q and a spherical + surface, S, of radius r and center at the location of + +Q. From the symmetry of this situation we can conclude + that, everywhere on the surface S, E has the same value + and is directed radially outwards (normal to the surface). + This is the same as the direction of dA. Therefore,
+

+
so that,
+

+
which is exactly Coulomb's Law !!
+
+ As has already been stated - Gauss's + + + + + + + + + + + + + Law and Coulomb's Law are different statements of + the same physical principle.
+
+
+
+
+
+
+

Spherical Charge Distribution with Uniform + Charge Density

Charge is distributed uniformly + throughout the volume of the sphere (this means that the + sphere must be a non-conductor since as we have seen the + charge on a conductor must reside on the surface) such + that the total charge Q is given by,
+
+

+
+
where ρ is the (volume) charge + density, in units of Coulombs/m³.
+
+ What is the electric field at any point either outside + or inside the sphere ?
+ Due to the symmetry of this configuration we can + conclude that E is directed radially outwards + everywhere and can (at most) depend only on the + (radial) distance from the center of the sphere. + There are two distinct regions to consider:
+
+ Outside the + sphere, r > R
+
+ Applying Gauss's Law over a Gaussian surface (sphere) + of radius r, then,
+

+
+
so that,
+

+
+
In other words, for points + outside the sphere, the sphere behaves as a + point charge located the sphere's center.
+ We saw + exactly the same type of behavior when + considering the gravitational effect of a + spherical mass.
+
+
+
+
+
+ Inside the sphere, r + < R
+
+ Applying Gauss's Law over a Gaussian surface (sphere) + of radius r, then,
+
+

+
Or in terms of Q and R,
+
+

+
+
Note that for r < R only + the charge inside a sphere of radius r + contributes to E. The charge + between r and R has no effect.
+
+ It is important to realize that + without using Gauss's Law, these results could + be obtained via Coulomb's Law, but would + involve considerably more work - setting + up a non-trivial multiple integral to + consider every point charge in the sphere....
+
+

+ CYLINDRICAL + + + + + + + + + + SYMMETRY
+
+
+
+
+
+
+
+
+

Infinite Line Charge + with Linear Charge Density λ

Determine + + + + + + + + + the E field a distance r from the + line charge. (Note that the units of + λ are Coulombs/meter)
+
+ Symmetry tells us that E can only + have a component perpendicular to the line + charge, that is perpendicular to the + cylindrical surface shown.
+
+ Applying Gauss's Law over the cylindrical + Gaussian surface, radius r and length l, + as shown, there will in principle be three + contributions - one from the curved + surface and one from each of the two + ends. However, on the ends E + and dA are perpendicular, so that + E·dA = 0, therefore there is no + contribution to the flux through S. + On the curved surface E and dA + are parallel, thus,
+
+

+
so that,
+

+

+ We can extend this analysis to the + case of a uniformly charged + infinite cylinder in a similar + manner to the extension of the + point charge to the spherical + charge distribution above.
+
+

+ RECTANGULAR + + + + + + + + SYMMETRY
+
+
+
+
+
+

Infinite plane of + charge

Determine the E + field at any distance above or + below an infinite plane with + charge density σ (Coulombs/m²).
+
+ Symmetry dictates the E + must be perpendicular to the + surface everywhere.
+
+ Applying Gauss's Law over the + cylindrical surface shown, + then the curved surface of the + cylinder contributes + nothing to the flux since E + and dA are + perpendicular. But on + the ends E and dA + are parallel. Therefore,
+
+

+
+
so that,
+

+
+
+
+
+

That is the electric + field is constant - it does + not depend on how far the + field point is from the plane + !!
+
+ Note + that this is only true for an + infinite plane of + charge. If the distance + of the field point from the + plane is small compared to the + "size" of the plane, the above + expression is a good + approximation.
+
+

+
+

In all the above + situations the key to + using Gauss's Law is SYMMETRY. + There must be enough + symmetry in the problem + to know the direction of + E everywhere in + the vicinity of the + charge + distribution. + Knowing the direction of + E the trick is + then to choose a + Gaussian surface over + which to apply Gauss's + Law such that E + can be "taken out" of + the flux integral. + So when using Gauss's + Law to determine E + there are three key + steps:

+
State what you are + assuming about E + based on the + symmetry of the + problem.
+
+
State clearly the + Gaussian surface(s) + you will use - often + most easily done by + sketching the + surface(s) on a + diagram.
+
+
Evaluate the + surface (flux) + integral to + determine E. + The symmetry of E + and choice of + Gaussian surface + should allow "E" to + be "taken out" of + the integral and + thus be determined.
+
+

+
+
+

+
+
+

+ +

+
+

+
+

+
+ An engineer + friend of mine told me of a group of scientists that were + nominated for a Nobel prize. Using dental tools, they were + able to sort out the smallest particles that mankind has yet + discovered. The group became known as " the Graders of the + Flossed Quark." + +
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_gauss_cond.html b/elec_gauss_cond.html new file mode 100644 index 0000000..75d38c2 --- /dev/null +++ b/elec_gauss_cond.html @@ -0,0 +1,157 @@ + + + + + + + Electricity - Gauss's Law and Conductors - Physics 299 + + + +

+ + +

Gauss's Law and Conductors
+

+ +

+
+ " + + We shouldn't be surprised that conditions in the universe are + suitable for life, but this is not evidence that the universe + was designed to allow for life."
+ Stephen Hawking
+ +

In electrostatic conditions - no electric current flow - + Gauss's Law applied to conductors (typically metallic objects) + leads to some important conclusions.

Note that since a conductor contains + "free" charges if an electric field exists anywhere in the + conductor a current will flow. Thus, in electrostatic + conditions ("static" means all charges are at rest) there can be + no electric field anywhere in the conductor.
+

Insulated solid + conductor having a net charge

Under electrostatic conditions, E = 0 throughout + the object. Applying Gauss's Law to the closed surface A, we + conclude that there can be no charge inside A. But the + conductor has a net charge. The only possibility is that the + charge resides outside the surface A. If we gradually + increase the size of A, so that eventually it lies just below the + surface of the conductor, the charge must still reside outside + A. Therefore, as a consequence of Gauss's Law, any charge + + + + + + placed in a conductor must reside on its surface.
+
+

Insulated hollow charged conductor (conducting shell)

+
We now hollow out the conductor, changing nothing else. + Thus, there is no charge inside the hollowed out conductor, so + that E = 0 inside. This fact leads to the + necessity for an antenna to pick up radio signals inside a + car. Radio waves are comprised of electric and magnetic + fields (electromagnetic waves - much more later), which must be + received by the radio. But the car is approximately a + hollow metallic conductor, which means E = 0 + inside. Without an antenna the radio waves cannot be + received by the radio. The antenna provides a "shielded + channel" to direct the radio signal into the car.
+
+
+
+ +

+ +

Faraday Cage

+
A Faraday + + + + cage is a metal container, which is used to shield + sensitive electronics from stray electric fields. + Fields outside the container cannot penetrate due to the + above explanation.
+
+
+

Proof of inverse square nature of Coulomb's Law

+
It can be shown mathematically that if Coulomb's Law is not + exactly of the inverse square form - 1/r² then + the electric field inside a closed conductor would not be + exactly zero. All experiments to date have failed to + measure such an electric field, with an accuracy such that + we know that the inverse component of r in Coulomb's Law is + 2 with an accuracy of 16 decimal places.
+
+

+ +
+

+ + +
+ A Simpleton's Guide to Science (stolen + from UK magazine) +
+ Relativity : Family get-togethers at Christmas +
+ Gravity : Strength of a glass of beer +
+ Time travel : Throwing the alarm clock at the wall +
+ Black holes : What you get in black socks +
+ Critical mass: A gaggle of film reviewers +
+ Hyperspace : Where you park at the superstore
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_gauss_eqn1.jpg b/elec_gauss_eqn1.jpg new file mode 100644 index 0000000..2943212 Binary files /dev/null and b/elec_gauss_eqn1.jpg differ diff --git a/elec_gauss_eqn10,jpg.jpg b/elec_gauss_eqn10,jpg.jpg new file mode 100644 index 0000000..f31146c Binary files /dev/null and b/elec_gauss_eqn10,jpg.jpg differ diff --git a/elec_gauss_eqn11.jpg b/elec_gauss_eqn11.jpg new file mode 100644 index 0000000..db23bbe Binary files /dev/null and b/elec_gauss_eqn11.jpg differ diff --git a/elec_gauss_eqn12.jpg b/elec_gauss_eqn12.jpg new file mode 100644 index 0000000..8a1f38b Binary files /dev/null and b/elec_gauss_eqn12.jpg differ diff --git a/elec_gauss_eqn13.jpg b/elec_gauss_eqn13.jpg new file mode 100644 index 0000000..f114e0a Binary files /dev/null and b/elec_gauss_eqn13.jpg differ diff --git a/elec_gauss_eqn2.png b/elec_gauss_eqn2.png new file mode 100644 index 0000000..b4bc104 Binary files /dev/null and b/elec_gauss_eqn2.png differ diff --git a/elec_gauss_eqn3.jpg b/elec_gauss_eqn3.jpg new file mode 100644 index 0000000..8a89454 Binary files /dev/null and b/elec_gauss_eqn3.jpg differ diff --git a/elec_gauss_eqn4.png b/elec_gauss_eqn4.png new file mode 100644 index 0000000..98c7f5f Binary files /dev/null and b/elec_gauss_eqn4.png differ diff --git a/elec_gauss_eqn5.png b/elec_gauss_eqn5.png new file mode 100644 index 0000000..b74e6ca Binary files /dev/null and b/elec_gauss_eqn5.png differ diff --git a/elec_gauss_eqn6.png b/elec_gauss_eqn6.png new file mode 100644 index 0000000..b3a31ff Binary files /dev/null and b/elec_gauss_eqn6.png differ diff --git a/elec_gauss_eqn7.png b/elec_gauss_eqn7.png new file mode 100644 index 0000000..f76d689 Binary files /dev/null and b/elec_gauss_eqn7.png differ diff --git a/elec_gauss_eqn8.jpg b/elec_gauss_eqn8.jpg new file mode 100644 index 0000000..ce38758 Binary files /dev/null and b/elec_gauss_eqn8.jpg differ diff --git a/elec_gauss_eqn9.jpg b/elec_gauss_eqn9.jpg new file mode 100644 index 0000000..3c17142 Binary files /dev/null and b/elec_gauss_eqn9.jpg differ diff --git a/elec_gauss_figure1.jpg b/elec_gauss_figure1.jpg new file mode 100644 index 0000000..ab7c5f1 Binary files /dev/null and b/elec_gauss_figure1.jpg differ diff --git a/elec_gauss_figure2.png b/elec_gauss_figure2.png new file mode 100644 index 0000000..d1d5135 Binary files /dev/null and b/elec_gauss_figure2.png differ diff --git a/elec_gauss_figure3.jpg b/elec_gauss_figure3.jpg new file mode 100644 index 0000000..4a1d96b Binary files /dev/null and b/elec_gauss_figure3.jpg differ diff --git a/elec_gauss_figure4.jpg b/elec_gauss_figure4.jpg new file mode 100644 index 0000000..ad127ff Binary files /dev/null and b/elec_gauss_figure4.jpg differ diff --git a/elec_gauss_figure5.jpg b/elec_gauss_figure5.jpg new file mode 100644 index 0000000..b713061 Binary files /dev/null and b/elec_gauss_figure5.jpg differ diff --git a/elec_gauss_figure6.png b/elec_gauss_figure6.png new file mode 100644 index 0000000..7ca686c Binary files /dev/null and b/elec_gauss_figure6.png differ diff --git a/elec_gauss_figure7.png b/elec_gauss_figure7.png new file mode 100644 index 0000000..3a30b8a Binary files /dev/null and b/elec_gauss_figure7.png differ diff --git a/elec_gauss_figure8.png.jpg b/elec_gauss_figure8.png.jpg new file mode 100644 index 0000000..f87f79f Binary files /dev/null and b/elec_gauss_figure8.png.jpg differ diff --git a/elec_gauss_figure9.jpg b/elec_gauss_figure9.jpg new file mode 100644 index 0000000..b6a3127 Binary files /dev/null and b/elec_gauss_figure9.jpg differ diff --git a/elec_kirch_fig1.gif b/elec_kirch_fig1.gif new file mode 100644 index 0000000..759e057 Binary files /dev/null and b/elec_kirch_fig1.gif differ diff --git a/elec_pot_dip_eqn1.jpg b/elec_pot_dip_eqn1.jpg new file mode 100644 index 0000000..b4cc1ac Binary files /dev/null and b/elec_pot_dip_eqn1.jpg differ diff --git a/elec_pot_dip_eqn2.jpg b/elec_pot_dip_eqn2.jpg new file mode 100644 index 0000000..4eb35d6 Binary files /dev/null and b/elec_pot_dip_eqn2.jpg differ diff --git a/elec_potenergy.html b/elec_potenergy.html new file mode 100644 index 0000000..4b16157 --- /dev/null +++ b/elec_potenergy.html @@ -0,0 +1,108 @@ + + + + + + + Electricty - Electric Potential Energy - Physics 299 + + +

+ +

Electric Potential Energy
+

+ +

+
+ "Atomic power will make electricity too + cheap to meter"
+ Glenn Seaborg
+ +

+
+

It is important to realize that electric potential (potential + difference - measured in Volts) is not the same thing as + electric potential energy (measured in Joules). We already + know how to calculate the pd dues to a system of charges,

eqn2

+
or for a point charge a distance r_A + from the charge
+
+

+
+

What about the Potential Energy, PE ?

+
Imagine two charges Q + and q , with Q at rest. Now gradually bring qfrom + + + infinity towardsQ to point P. Then the work + done by an external agent in performing this task must be equal + to the negative of the work done by the electric field due to Q,
+
+

+
+

+
This work is stored in the two charge system as + Potential Energy, U_E ,
+
+

+
+
For systems of more than 2 charges we must + consider all possible pairings to determine the total + potential energy.
+
+ For U > 0 energy must be provided to + create the system
+ For U < 0 energy must be + provided to break up the system (initially this system is + "bound")
+
+ Don't forget - Change in PE = work + needed to accomplish the change.
+
+
+

+ +

+ + Do you realize if it weren't for Edison we'd be watching TV by + candlelight?
+ Al Boliska
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_potenergy_eqn1.jpg b/elec_potenergy_eqn1.jpg new file mode 100644 index 0000000..87e56fc Binary files /dev/null and b/elec_potenergy_eqn1.jpg differ diff --git a/elec_potenergy_eqn2.jpg b/elec_potenergy_eqn2.jpg new file mode 100644 index 0000000..5605787 Binary files /dev/null and b/elec_potenergy_eqn2.jpg differ diff --git a/elec_potenergy_fig1.gif b/elec_potenergy_fig1.gif new file mode 100644 index 0000000..f11ae87 Binary files /dev/null and b/elec_potenergy_fig1.gif differ diff --git a/elec_potential.html b/elec_potential.html new file mode 100644 index 0000000..e492a56 --- /dev/null +++ b/elec_potential.html @@ -0,0 +1,327 @@ + + + + + + + Electricty - Electric Potential and Potential Difference - + Physics 299 + + +

+ +

Electric Potential and Potential Difference

+ +

+
+ "The outcome of any serious research can + only be to make two questions grow where one question grew + before"
+ Thorstein Veblen
+ +

+ +

The field near a system of charges can + also be described by a scalar quantity known as the "Electric + Potential".
+
+ " A potential difference of one volt exists between two + points when one Joule of work is required to move one + Coulomb of charge from one point to the other"
+
+ Between two points A and B we may write +
+ W_AB = -V_AB q +
where V_AB = V_B + - V_A is the potential difference between A + and B.
+

Note that W_AB + is the work done by the electric field in moving the charge. + The work done by the "external agent" is -W_AB.

Units of potential difference are volts
+ +
1 Volt = 1 Joule/Coulomb (J/C)
+ +
In a region of space where there is an electric field the work + done by the electric field, dW, when a positive point charge, q, + is displaced by ds is + given by,

Therefore,
+

+
+

For a uniform electric field we + obtain,
+

+
+

where an arbitrary path can always be + split into sections along E and sections + perpendicular to E.
+
+

Note that this means that + the electric field can be expressed in the units + V/m. [ 1 N/C = 1V/m ]
+

The + electric field is a conservative field. + hot

+ +

This means that the potential difference between + two points is independent of the path taken. + Every point in space has a single value of V and E.

Food + for thought....
+
+ The gravitational field behaves in exactly the same + way. Changes in gravitational energy are + independent of the path taken. Climbing stairs + from one floor to another involve the same amount of + work against gravity as riding an elevator.
+ Note that in simple gravitational applications we + don't usually define a gravitational potential only + gravitational potential energy (mgh). In this + case the gravitational potential is defined as gh.
+
+

Exactly equivalent to gravity, it + is CHANGES + in potential difference, , + which are defined. To obtain absolute values + of V physicists usually define V = 0 at + infinity. But this is an arbitary definition; + in engineering applications it is often convenient + to define the earth as V = 0.

Potential due to a point + charge
+
+ For a single point charge Q the potential difference + between A and B is given by,

+
+

where + + + + + + + + + E is the field due to a point charge and ds = dr , + so that,
+
+

+ If we assume r_B= ∞ then V_B + = 0 and,
+
+

+
+

Note that the + potential is inversely proportional to r, + rather than r² as in the case of + the electric field.
+

Since V is a scalar the potential due + to multiple point charges is found by + adding the potential due to the + individual charges (taking into account + the sign of the charge).

Continuous Charge + Distributions

+ +

For continuous distributions of + charge we may write,
+

The electric potential due to a + continuous charge distribution can + be calculated in a similar manner to + the electric field due to such a + distribution. For example the + potential at point P due to a + uniform ring of charge (below).
+

Equipotential + Surfaces
+
+ An Equipotential Surface is a + surface in space on which all points + have the same potential. Since + all points have the same potential + it requires no work to move a charge + on such a surface. This means + that there is no component of E in + the plane of the surface, in other + words E must be at right angles to + the surface.

Electric + Field Lines and Equipotential + Surfaces are at right angles
+ (Red dotted lines below)
+ equip2

+ + + + + + + + + equip1

+ +

In the period that Einstein was active as + a professor, one of his students came to him and said: "The + questions of this year's exam are the same as last years!" + "True," Einstein said, "but this year all answers are + different."
+ Albert Einstein
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_potential_dip_figure1.png b/elec_potential_dip_figure1.png new file mode 100644 index 0000000..f46d06d Binary files /dev/null and b/elec_potential_dip_figure1.png differ diff --git a/elec_potential_dipole.html b/elec_potential_dipole.html new file mode 100644 index 0000000..513f4ae --- /dev/null +++ b/elec_potential_dipole.html @@ -0,0 +1,97 @@ + + + + + + + Electricty - Electric Potential due to an Electric Dipole - + Physics 299 + + +

+ +

Electric Potential due to an Electric Dipole
+

+ +

+
+ " + + We will make electricity so cheap that only the rich will burn + candles"
+ Thomas Edison
+ +

+
+

Just as we calculated the electric field due to a dipole it is + possible to calculate the electric potential. However, in + this case it is convenient to use polar co-ordinates.

Assuming no azimuthal variation we may write,
+
+

+
+
When r >> a, then r₁, r₂ + and r are approximately equal and r₂- r₁ + = 2acosθ. Therefore,
+
+

+
+
+
+
+

Note that the dipole potential decreases as 1/r² + whereas the dipole E field decreases as 1/r³ + .

Notice that when θ = 90⁰ V_P + = 0, that is it would require no work to bring a charge from + infinity to the center of the dipole if it moves along the + dipole bisector.
+

+
+

+
+

+ +

+ + "There are three kinds of men. The one that learns by reading. + The few who learn by observation. The rest of them have to pee + on the electric fence for themselves."
+ Will Rogers
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_potential_efromV.html b/elec_potential_efromV.html new file mode 100644 index 0000000..c2cdd50 --- /dev/null +++ b/elec_potential_efromV.html @@ -0,0 +1,114 @@ + + + + + + + Electricty - Electric Field from Electric Potential - Physics + 299 + + +

+ +

Determining the Electric Field from the Electric Potential
+

+ +

+
+ " + + + + I've found out so much about electricity that I've reached the + point where I understand nothing and can explain nothing"
+ [Describing his experiments with the Leyden jar.]
+ Pieter van Musschenbroek
+ +

+
+

Suppose we are given the electric potential, V, as a function + of position. Is it possible to determine the E + field from this V ?

Starting from the definition of the potential difference + in terms of the E field,
+

+
+
then if the path A to B is along the x axis we + obtain,
+

+
+
+
+

This expression can be written in the alternative + form,

+
+

+
If the path A to B is in an arbitrary + direction we obtain the most general expression of "E + from V",
+
+

+
+
+

+
+

+
+

+ +

+ + " + + I am an expert of electricity. My father occupied the chair of + applied electricity at the state prison."
+ W. C. Fields
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_potential_efromV_eqn1.png b/elec_potential_efromV_eqn1.png new file mode 100644 index 0000000..711e93c Binary files /dev/null and b/elec_potential_efromV_eqn1.png differ diff --git a/elec_potential_efromV_eqn2a.jpg b/elec_potential_efromV_eqn2a.jpg new file mode 100644 index 0000000..d049216 Binary files /dev/null and b/elec_potential_efromV_eqn2a.jpg differ diff --git a/elec_potential_efromV_eqn3.png b/elec_potential_efromV_eqn3.png new file mode 100644 index 0000000..65adbc9 Binary files /dev/null and b/elec_potential_efromV_eqn3.png differ diff --git a/elec_potential_eqn1.jpg b/elec_potential_eqn1.jpg new file mode 100644 index 0000000..d47325a Binary files /dev/null and b/elec_potential_eqn1.jpg differ diff --git a/elec_potential_eqn2.jpg b/elec_potential_eqn2.jpg new file mode 100644 index 0000000..161a26e Binary files /dev/null and b/elec_potential_eqn2.jpg differ diff --git a/elec_potential_eqn3b.jpg b/elec_potential_eqn3b.jpg new file mode 100644 index 0000000..8fe3834 Binary files /dev/null and b/elec_potential_eqn3b.jpg differ diff --git a/elec_potential_eqn4.jpg b/elec_potential_eqn4.jpg new file mode 100644 index 0000000..c425a6e Binary files /dev/null and b/elec_potential_eqn4.jpg differ diff --git a/elec_potential_eqn5.jpg b/elec_potential_eqn5.jpg new file mode 100644 index 0000000..bfe01eb Binary files /dev/null and b/elec_potential_eqn5.jpg differ diff --git a/elec_potential_eqn6.jpg b/elec_potential_eqn6.jpg new file mode 100644 index 0000000..6127752 Binary files /dev/null and b/elec_potential_eqn6.jpg differ diff --git a/elec_potential_eqn7.jpg b/elec_potential_eqn7.jpg new file mode 100644 index 0000000..a51e83c Binary files /dev/null and b/elec_potential_eqn7.jpg differ diff --git a/elec_potential_equip1.gif b/elec_potential_equip1.gif new file mode 100644 index 0000000..7524938 Binary files /dev/null and b/elec_potential_equip1.gif differ diff --git a/elec_potential_equip2.gif b/elec_potential_equip2.gif new file mode 100644 index 0000000..a05bdd1 Binary files /dev/null and b/elec_potential_equip2.gif differ diff --git a/elec_potential_fig1.jpg b/elec_potential_fig1.jpg new file mode 100644 index 0000000..b73e4ea Binary files /dev/null and b/elec_potential_fig1.jpg differ diff --git a/elec_potential_fig2.jpg b/elec_potential_fig2.jpg new file mode 100644 index 0000000..8018744 Binary files /dev/null and b/elec_potential_fig2.jpg differ diff --git a/elec_potential_fig3.gif b/elec_potential_fig3.gif new file mode 100644 index 0000000..75417ec Binary files /dev/null and b/elec_potential_fig3.gif differ diff --git a/elec_potential_fig4.jpg b/elec_potential_fig4.jpg new file mode 100644 index 0000000..52c42a9 Binary files /dev/null and b/elec_potential_fig4.jpg differ diff --git a/elec_stat.html b/elec_stat.html new file mode 100644 index 0000000..820a8af --- /dev/null +++ b/elec_stat.html @@ -0,0 +1,164 @@ + + + + + + + Electricity - Static Electricity - Physics 299 + + + +

+ + +

Electric Charge and Matter
+

+ +

+
+ "A new scientific truth does not triumph + by + convincing + its opponents and making them see the light, but rather + because its + opponents + eventually die, and a new generation grows up that is familiar + with it"
+ Max Planck
+ +

In order to feel an electric force an object must possess ELECTRIC + CHARGE.

Electric charge can be either positive (+) or negative (-).

Electric charge is a fundamental property of matter + (similar + to mass).
+ The unit of electric charge is the Coulomb + (C)
+
+ One Coulomb is the amount of charge which flows through a wire + carrying + a current of 1 Ampere in one second.
+
+ Formally, as we will see later in + this + course, the unit of electric current - the Ampere - is the + defined + unit, one of the seven basic units (meters, kilograms, seconds, + amperes, temperature, candela, mole). The Coulomb is then + defined + as Ampere.Seconds. However, in developing the basic theory + of + electricity it is more convenient to "pretend" that the Coulomb + is the + basic unit; the Ampere is then Coulomb/sec.

Electric + charge is "quantized" + in + units of the charge on the electron, e = 1.6 x 10^-19 + C. That is charge always appears in integer multiples of + "e". Unless we are dealing with individual atoms or + sub-atomic + particles, since the value of "e" is so small, this quantization + is not + apparent and need to be considered.

Conservation of charge

"The net electric charge of an isolated system + is + constant"
+
+

However, Note that in calculating + the net charge + the sign of + the charges must be taken into account, e.g. the net charge of a + system + containing objects with +2 C and -1 C is +1 C.

The conservation of charge is a basic physical "law" in the + same + manner as mass, energy and momentum conservation.

The force between two charges can be attractive or repulsive, + depending on the relative signs of the charges. This fact + can be + expressed simply,

"Like charges repel - unlike charges + attract"

The magnitude of the force between charged objects is given + by + Coulomb + 's Law (see later section for detailed description).

Most useful/interesting electrical phenomena occur as electric + charge is transferred from one place to another. Where + possible + electric charge will "flow" to minimize the total energy + of a + system. However, initially, we will discuss static + situations, + where the charges are held in place by some external mechanism.
+

+ +

"If + I + were + as + rich + as + Rockerfeller, I'd be richer than + Rockerfeller"
+ "How's that?"
+ "I'd do a bit of window cleaning on the side"

+ Ronnie Barker
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_strmatt.html b/elec_strmatt.html new file mode 100644 index 0000000..7284ede --- /dev/null +++ b/elec_strmatt.html @@ -0,0 +1,253 @@ + + + + + + + Electricity - Structure of Matter - Physics 299 + + + +

+ + +

Structure of Matter

+ +

+
+ "If I have seen further it is by standing + on the shoulders of giants"
+ Isaac Newton
+ +

It is well known today that all + matter is comprised of atoms. The concept of + atoms was postulated by the ancient + Greeks , but their existence was not confirmed until a + little more than 100 years ago. All atoms consist of a + nucleus made of protons and neutrons around + which "orbits" one or more electrons. +

The basic properties of protons, neutrons, electrons and the + atom as a whole are described in the following table.
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ Particle + +	+ Electric charge + +	+ Mass + +	+ Approximate Size + +
+ electron (e^-) + +	+ - 1.6 x 10^-19 C + +	+ 9.1 x 10^-31 kg + +	+ < 10^-18 m + +
+ proton (p) + +	+ + 1.6 x 10^-19 C + +	+ 1.6 x 10^-27 kg + +	+ 10^-15 m + +
+ neutron (n) + +	+ 0 + +	+ 1.6 x 10^-27 kg + +	+ 10^-15 m + +
+ Atom + +	+ 0 (neutral) + +	+ (N_p + N_n) x + 1.6 x 10^-27 kg + +	+ 10^-10 m + +

+
+ where N_p, N_n are the number of protons and + neutrons, respectively, in the nucleus of the atom.

Other important properties:
+
- Mass of proton (m_p) is approximately 2000 + times the mass of the electron (m_e)
- More than 99% of the volume of an atom is empty space. + If the nucleus of the Hydrogen atom was one inch in + diameter the orbit of the electron would have a radius of + ½ mile.
- Current experiments indicate that the electron has no + structure, it is a true point particle.
- Protons and neutrons are each comprised of quarks. + With the same experimental limit as the electrons, + quarks also have no sub-structure.
- The wavelength of visible light is of order 5 x 10^-7 + m. Atoms are typically more than 1000 times smaller + than this wavelength.
  +
+

The properties of the different elements in nature, e.g. + Hydrogen, Sodium, Uranium etc. are defined by their "atomic + structure". These elements can be arranged in a form + known as the + "periodic table" which illustrates the + similarities and differences between them. Dmitri + Mendeleev is generally + considered the creator of the modern periodic table.
+ Nottingham University has created the Periodic Table of + Videos, which features a short video clip describing the + properties, history, production etc of each element.

Starting with the + Hydrogen atom, which consists of a single proton nucleus + and a single electron, different elements can be created by + adding additional protons to the nucleus while at the same time + adding the same number of electrons to keep the atom neutral. + For light elements (excluding Hydrogen) the number of + neutrons in the nucleus is equal to the number of protons; for + heavier elements a neutron excess develops. For example + the most common + Lead atom comprises 82 protons and 126 neutrons. The + heaviest naturally occuring element is Uranium , having + 92 protons and 146 neutrons. Certain elements with more + protons can be created but undergo radioactive decay with a + lifetime shorter than that of the earth.
+
+

+
+

+ +

For this course, the it is important to + realize that the negatively charged electrons are held in + "orbit" around the positively charged nucleus by the + electric force of attraction. In fact all atomic and + molecular forces of any significance are electrical (or + electromagnetic) in nature. It could be said that + all of Chemistry is due to the electromagnetic + force. In fact virtually all everyday physical + phenomena are electromagnetic in nature, friction, + thermodynamics, elasticity etc etc. Only those + phenomena involving very large masses (where the + gravitational force becomes significant) and certain very + small scale processes (e.g. radioactive decay, fission, + fusion) are not primarily electromagnetic in nature. + Understanding electricity and magnetism - electromagnetism + - is critical to our understanding of nature.
+

+ A + neutron walks into a bar. "I'd like a beer" he says. The + bartender promptly serves up a beer. "How much will that be?" + asks the neutron. "For you?" replies the bartender, "no charge"
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/elec_water-molecule-and-dipole-moment.jpg b/elec_water-molecule-and-dipole-moment.jpg new file mode 100644 index 0000000..958b200 Binary files /dev/null and b/elec_water-molecule-and-dipole-moment.jpg differ diff --git a/exclamation-icon.gif b/exclamation-icon.gif new file mode 100644 index 0000000..2a06a13 Binary files /dev/null and b/exclamation-icon.gif differ diff --git a/faraday.jpg b/faraday.jpg new file mode 100644 index 0000000..11424ed Binary files /dev/null and b/faraday.jpg differ diff --git a/fraunhofer.jpg b/fraunhofer.jpg new file mode 100644 index 0000000..e69de29 diff --git a/fresnel.jpg b/fresnel.jpg new file mode 100644 index 0000000..e69de29 diff --git a/gauss.jpg b/gauss.jpg new file mode 100644 index 0000000..a9a8843 Binary files /dev/null and b/gauss.jpg differ diff --git a/grav_eqn1.jpg b/grav_eqn1.jpg new file mode 100644 index 0000000..13bdbad Binary files /dev/null and b/grav_eqn1.jpg differ diff --git a/hamburger.gif b/hamburger.gif new file mode 100644 index 0000000..e8056af Binary files /dev/null and b/hamburger.gif differ diff --git a/header-index.gif b/header-index.gif new file mode 100644 index 0000000..e212849 Binary files /dev/null and b/header-index.gif differ diff --git a/hot.gif b/hot.gif new file mode 100644 index 0000000..6f4b3c7 Binary files /dev/null and b/hot.gif differ diff --git a/idea2.gif b/idea2.gif new file mode 100644 index 0000000..ba42d4b Binary files /dev/null and b/idea2.gif differ diff --git a/kirchhoff.jpg b/kirchhoff.jpg new file mode 100644 index 0000000..04b25a5 Binary files /dev/null and b/kirchhoff.jpg differ diff --git a/lo_BentStick.jpg b/lo_BentStick.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_EMSpec.gif b/lo_EMSpec.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_Interference_GodAsDeveloper.gif b/lo_Interference_GodAsDeveloper.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_anim_prism_anim.gif b/lo_anim_prism_anim.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_anim_refl2.gif b/lo_anim_refl2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_apparentdepth.jpg b/lo_apparentdepth.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_appdepth.html b/lo_appdepth.html new file mode 100644 index 0000000..ca53a27 --- /dev/null +++ b/lo_appdepth.html @@ -0,0 +1,87 @@ + + + + + + + Light and Optics - Apparent Depth - Physics 299 + + + +

+ + +

Apparent Depth and Distortion

+ +

+
+
+"Give me but one firm spot on which to stand, +and +I will move the earth"
+Archimedes
+ +

+
+
+

The depth of a swimming pool always appears to be less +than it actually is. This effect is due to the refraction of +light rays as they traverse the boundary between water and air.

In the following graphic, the chest appears to be closer to the +surface than it actually is.
+

+

By using Snell's law and simple geometry it can be shown that
+
+
+ +

Spearfishing is particularly difficult due to the apparent depth +phenomenon !!
+

+

+
+
+
+
The discontinuous bending of a stick held partly in and partly +out of water is also a result of light refraction at the air-water +interface.

+
+

+"Physics +is +like sex: sure, it may give some practical results, but that's not why we do it."
+Richard Feynman.
+
+

+ +

Dr. C. L. Davis
+Physics Department
+University of Louisville
+email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_appdepth_eqn1.gif b/lo_appdepth_eqn1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_brewster.html b/lo_brewster.html new file mode 100644 index 0000000..ac78f3d --- /dev/null +++ b/lo_brewster.html @@ -0,0 +1,115 @@ + + + + + + + Light and Optics - Brewster's Law - Physics 299 + + + +

+

+ + +

Brewster's Law
+

+ +

+
+ "If aliens + visit us, the outcome would be much as when Columbus landed in + America, which didn't turn out well for the Native Americans."
+ + + + + Stephen Hawking
+
+ +

+
+

By applying the boundary conditions for electromagnetic waves + striking the boundary between two media it can be shown that the + intensity of the reflected and refracted waves depend on the + polarisation of the incident wave.
+

In particular, for unpolarised light incident on the boundary + at a specific angle, θ_p , the reflected light + contains only one polarisation. When this occurs the + reflected and refracted light rays are at 90⁰ to each + other,
+

Using Snell's law we can show that,

+
This relationship is known as Brewster's + Law.
+
+

+
+
+

For light incident on water (from air) we find that θ_p= + 53⁰. Thus, at this angle the light + reflected from the surface is (linearly) + polarised. If this reflected wave is viewed with + polarised sunglasses (which block this particular + polarisation), no reflective glare is observed - + allowing the observer to see clearly underwater.
+

+ +
+

+ "Outside + of a dog, a book is a man's best friend. Inside of a dog + it's too dark to read."
+ + + Groucho Marx
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_brewster.jpg b/lo_brewster.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_brewster_eqn1.jpg b/lo_brewster_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_brewster_eqn2.jpg b/lo_brewster_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_brewster_fig1.jpg b/lo_brewster_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_colour.gif b/lo_colour.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_coneofdarknessforfish.jpg b/lo_coneofdarknessforfish.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_dispersion.html b/lo_dispersion.html new file mode 100644 index 0000000..2e330aa --- /dev/null +++ b/lo_dispersion.html @@ -0,0 +1,92 @@ + + + + + + + Light and Optics - Dispersion - Physics 299 + + + +

+ + +

Dispersion

+ +

+
+"To err is human but to really foul things up +requires a computer"
+Anonymous
+(Farmers Almanac 1978)
+ +

Without explicitly making the statement we have assumed that the +refractive index of a medium is independent of the frequency of the +light transmitted. That is we have assumed for example that red +light and blue light have the same speed when passing through glass (or +any other medium). This is not exactly true, refractive index is +frequency dependent such that for glass, n_blue > n_red +(blue light is bent more than red light when passing from air to glass) +and the speed of blue light in glass is slightly smaller than the speed +of red light.

This fact may be demonstrated by the production of a spectrum of +colours when white light is incident on a glass prism. [White +light is comprised of all the wavelengths of visible light] Each +constituent of the white light has a slightly different refractive +index and is deflected (according to Snell's law) through a slightly +different angle.
+
+

+

This phenomenon is known as DISPERSION. + White light is dispersed into its constituent +colours.

A rainbow is created by a combination of dispersion and total +internal reflection within water droplets in the atmosphere.
+

+

An object appears a particular colour under white light +illumination because it reflects that colour strongly.
+

+
+For example a red object reflects most of the red wavelength +incident and absorbs most of the other wavelengths. If +such an object is illuminated with blue light it will appear black, +the blue light is absorbed, but there is no red to be reflected.

+
+

+"There +is no Dark Side of the Moon really. Matter of fact it's all dark"
+Pink Floyd
+
+

+ +

Dr. C. L. Davis
+Physics Department
+University of Louisville
+email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_dsdiffraction.html b/lo_dsdiffraction.html new file mode 100644 index 0000000..8269c75 --- /dev/null +++ b/lo_dsdiffraction.html @@ -0,0 +1,194 @@ + + + + + + + Light and Optics - Double Slit Diffraction/Interference - + Physics 299 + + + +

+

+ + +

Double Slit Diffraction/Interference
+

+ +

+
+ " + + All of physics is either impossible or trivial. It is + impossible until you understand it, and then it becomes + trivial. + + "
+ + + + + + + Ernest Rutherford
+ +

+
+
+
+
+
+

+
+
+
+
+
+

Intensity pattern for single slit diffraction:

+ where eqn2

+ +

Intensity pattern for double slit interference:

+ where + eqn4

+
+

+
Note that φ' = φ/2, where φ is defined in the + double slit interference analysis.
+
+
+

Remember that in the double slit interference analysis we + (implicitly) assumed that the two slits were "point" wave + sources. Of course in reality this is impossible, no + sources are true "point" sources. An accurate + description of double slit interference must include the + effect of the finite width of each slit - that is, the + diffraction phenomena from each slit. A detailed + mathematical analysis leads to an intensity pattern at point + P given by,

+
Qualitatively, the interference pattern is + modulated by the diffraction pattern, as indicated below.
+

+
+
+

+
Note + that the slit width "a" must be smaller than the slit + separation "d" (center to center).
+
+

+
The + number of interference maximum underneath the central + maximum of the diffraction envelope depends on the + relative values of a and d.
+
+ Diffraction minima occur at θ = + λ/a , 2λ/a , 3λ/a... [ asinθ + = nλ ]
+ + Interference minima occur at θ = λ/2d , 3λ/2d , + 5λ/2d... [ dsinθ = (n+1/2)λ ]
+
+

In the examples below the first intensity pattern + has d = 3a, whereas the second pattern has d = + (15/2)a
+

+

+

+
+
+

+ +

+
+ + + + + A year after almost failing + her high school physics class, a girl told her older brother, +
+ "You know, my physics teacher was right about + the optical Doppler effect. You see those cars. The lights of + the ones approaching us are white, but the lights of the ones + moving away from us are red."
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_dsdiffraction_eqn1.jpg b/lo_dsdiffraction_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_dsdiffraction_eqn4.jpg b/lo_dsdiffraction_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_dsdiffraction_eqn5.jpg b/lo_dsdiffraction_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_dsdiffraction_fig1.gif b/lo_dsdiffraction_fig1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_dsdiffraction_fig2.jpg b/lo_dsdiffraction_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_dsdiffraction_fig3.jpg b/lo_dsdiffraction_fig3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_e_mag.gif b/lo_e_mag.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_emwave.gif b/lo_emwave.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_emwaves.html b/lo_emwaves.html new file mode 100644 index 0000000..c197b16 --- /dev/null +++ b/lo_emwaves.html @@ -0,0 +1,130 @@ + + + + + + + Light and Optics - Electromagnetic Waves - Physics 299 + + +

+ Electromagnetic Waves +

+ +

+
+ "Basic research is what I am doing when I + don't know what I am doing"
+ Wernher von Braun
+ +

+
+

At the end of the nineteenth century + James Clerk Maxwell was responsible for bringing together + the work of Coulomb, Ampere, Faraday and others, to provide an + elegant theoretical description of electricity and magnetism. + Classical electromagnetism was described by four "simple" + equations known as Maxwell's equations + . These equations provided the "explanation" for + electromagnetic waves.
+
+
An electromagnetic wave is a transverse wave comprised of + oscillating Electric and Magnetic fields. Mathematically + the analysis of EM waves is rather complex. A plane + polarised electromagnetic wave traveling from left to right can + be represented as indicated below.

The "traveling nature of the wave is + represented thus, emwave2

where E represents + + + the electric field and H the magnetic field.
+
+

Visible light is a very small part of the electromagnetic + spectrum. The full EM spectrum extends continuously from + the very low frequency E and B oscillations of + radio waves through microwaves, infra-red, visible light, + ultra-violet, X-rays to very high frequency gamma rays.
+
+

+

The speed of electromagnetic waves (of all frequencies and + wavelengths) in a vacuum is equal to the speed of light, c = 3 x + 10⁸ m/s. Speed, frequency (f) and + wavelength () are related by the usual + relationship
+
+
+
Using Maxwell's equations it can be shown that the speed + of light is given by
+

Using Maxwell's decription of electromagnetic waves it is + possible to explain many of the properties of the interactions + of visible light with matter. The details of such + explanations are technically quite difficult and are + typically covered in senior level Physics courses. In the + following discussion we will investigate some of the + consequences of these properites, for example, the law of + reflection, law of refraction (Snell's law), total internal + reflection, dispersion, interference and diffraction.

The electromagnetic spectrum NASA video.

Maxwell brief biography video.
+

Maxwell's equations and electromagnetic waves video.
+

+ +

"I've heard that the government wants to put + a tax on the mathematically ignorant. Funny, I thought that's + what the lottery was!"
+ Gallagher

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_emwaves_eqn1.jpg b/lo_emwaves_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_emwaves_eqn2.gif b/lo_emwaves_eqn2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_emwaves_eqn2.jpg b/lo_emwaves_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_fiberopticcladdingandfiberbundle.jpg b/lo_fiberopticcladdingandfiberbundle.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference.html b/lo_interference.html new file mode 100644 index 0000000..dcc6f77 --- /dev/null +++ b/lo_interference.html @@ -0,0 +1,591 @@ + + + + + + + Light and Optics - Double Slit Interference - Physics 299 + + + +

+

+ + +

Double Slit Interference

+ +

+
+ "We only have + to look at ourselves to see how intelligent life might + develop into something we wouldn't want to meet."
+ + + Stephen Hawking
+
+ +

+
+

We now begin a discussion of wave (physical) optics in which - + in contrast to geometric optics - we explicitly consider the + wave nature of light. Remember, in geometric optics light + traveled in straight lines (light rays). This is a valid + approximation so long as we do not consider apertures with + dimensions similar to the wavelength of the light or look too + closely at the edges of objects.

So what happens when a wave passes through apertures whose + size is similar to the wavelength of the wave ? First + we'll consider the case of double slit interference, in which a + parallel beam of incident monochromatic (containing a specific + wavelength) light from the left strikes a screen with two slits, + S₁ and S₂ , as below.

+
+ divider

+
+ CONDITIONS for MAXIMA and MINIMA + in DOUBLE SLIT INTERFERENCE
+
+

With L >> d geometric optics predicts that two + bright spots would be observed on the right hand screen + immediately opposite S₁ and S₂ . + The rest of this screen would be in shadow. What is + actually observed on the right hand screen is an + "interference pattern" as indicated below,

+ + + + + + + + + + + + + + double slit interference

The explanation is that each slit acts as a source of + spherical waves, which "interfere" as they move from + left to right as shown above.

In the diagram at the top of the page, light reaching + P from S₁ and S₂ will travel + different distances. Assuming that the light from + the two sources S₁ and S₂ are + initially in phase, then due to the path difference S₁P + - S₂P , at P the two waves will be out of + phase. If the path difference is equal to an + integral number of wavelengths the waves will interfere + constructively, leading to a bright spot on the + screen. Mathematically we can write this condition + + + + + + + + + + + + + + for maximum intensity as,

+
where n can take on integer values, n + = 0, 1, 2, 3... and we have assumed that θ = θ' or in + other words the width of each slit is small compared + to their separation (D >> a above).
+
+ Similarly, the condition for minimum intensity at + + + + + + + + + + + + + + P, when the path difference is a multiple of half + wavelengths, is given by,
+
+

+
where n can again take on integer + value, n = 0, 1, 2, 3...
+
+
+
+

When the distance from slits to screen is much + larger than the distance on the screen, D + >> y above (or L >> x in first + diagram), then the angle θ is "small" and we may + assume tanθ is approximately equal to sinθ which + is approximately equal to θ (in radians) and we + may write,

+
for the position on the screen + for maximum intensity.
+
+
+
+
INTENSITY + DISTRIBUTION in DOUBLE SLIT + INTERFERENCE
+
+
+
+

The interference pattern shown above was + first observed for visible light in 1801 by + Thomas + + + + + + + + + + + + Young , the experiment + is still sometimes called Young's slit + experiment.

In the above description we have + assumed the incident light is + monochromatic. If white light + (containing all the wavelengths in the visible + spectrum) is used, the maxima for the + different wavelengths will occur at slightly + different positions (y) on the screen. + In this case an interference pattern will only + be observed if the maximum - minimum + separation is much larger than the separation + between the maxima of the extreme wavelengths + in white light (red and violet) for the same + "n".
+
+

In the above description we have shown + that at certain locations on the screen + there will be bright spots whereas at other + locations there will be no light - the + interference pattern. But exactly how + does the light intensity vary as a function + of position on the screen ?

In the diagram at the top of this + page the electric field from light originating + at each of the slits S₁ and S₂ + + + + + + + + + + + + can be written,
+
+

+
+
where each slit has the + same maximum E field, E₀ + and φ is the phase difference due to the + path difference S₁P - S₂P. + + + + + + + + + + +
+ Therefore the E field at P can be + written,
+
+

+
+
+
the product of an + amplitude and a sinusoidal time + varying wave. In the case of + light waves the frequency of the time + varying part is so large that our eyes + and most instruments "see" only the + ampliutde part. Actually, what + we observe is the intensity, + which is the square of the + amplitude. The intensity + observed at P is then given by,
+
+

+
+
as shown in the + red shading in the diagram + above. Note that maxima of + the above cosine squared function + occur when φ = 2π n; this leads to + bright spots on the screen.
+
+
+
+
+
+
+
+

As we have seen, when the path + difference is an integer multiple of + wavelengths, the waves from the two + sources interefer constructively. + That is they are in phase, and as we + have seen above, φ must be an + integer multiple of 2π,
+

+
+
+

+
+
Thus for small values + of θ (sinθ = θ), φ and θ are + proportional to each other.
+
+
+
+
COHERENCE
+
+
+
+
+
+
+

Throughout the above + description we have implicitly + assumed that the light waves + from the two slits S₁ + and S₂ are in phase + with each other. This + ensures that any phase + difference in the light from the + two slits is due entirely to the + different path lengths the two + waves travel. If the + relative phase of the + sources S₁ and + S₂ is unknown and + randomly varying with time then + the interference pattern will + also randomly change with a + frequency similar to the + frequency of the light. + Practically this means there + will be no observed interference + pattern.

The difficulty of obtaining + two sources (S₁ and S₂) + emitting waves coherently + (in phase) depends on the + wavelength of the + electromagnetic wave.
+

For long wave radiation + (e.g. radio waves) a single source + illuminating the two slits results + in two coherent sources, since + this type of radiation is + typically produced in a continuous + waveform, as shown at left below.
+
+ For short wavelength radiation + (e.g. light) "waves" are typically + emitted by multiple individual + atoms in a random incoherent + manner (no definite phase between + these multiple "sources". + The radiation is emitted in + "packets" rather than as a + continuous wave. Thus a two + slit configuration, at left below, + will not produce an interference + pattern. In order to observe + an interference pattern with light + the configuration at right below + must be employed. The single + slit to the left of the two slits + ensures that light reaching the + two slits is from the same part of + the source and therefore in phase.
+ Note that a + laser beam produces a coherent + light source and can be used to + create an interference pattern in + the left configuration.
+

+ + + + + + interference fig5

+
+ divider

+
+ QUANTUM LIMIT - DOUBLE + SLIT INTERFERENCE
+
+

Consider + double slit + interference. In the + figure at right there are + locations on the screen + which have zero light + intensity.
Now gradually reduce the + intensity of the incident + light so that instead of a + "continuous" wave impacting + the slits we have individual + "photons" incident. + This is the "quantum limit", + where we treat a source of + light as a source of + discrete "wave packets" or + photons. with + individual photons incident + the same interference + pattern is observed.
+
But with photons incident + one at a time it makes sense + to ask, "which slit did the + photon pass through ?"
Close one of the slits, + but continue illumination + with individual + photons. The intensity + pattern observed on the + screen changes with only one + slit open. But if the + photon passes through the + lower slit, how does it know + whether the upper slit is + open or closed ? For + the interference pattern to + change it must know.
Explanation.... The + photon is an extended + object, so it never really + passes though one + slit. Due to its + extended nature it can + "feel" whether the other + slit is open.
However, perhaps most + intriguing, is the fact that + if the two slits are + illuminated with a beam of + particles, for example + electrons, the same + interference phenomena is + observed. You'd + naturally expect electrons + to go through one slit or + the other, but with both + slits open an interference + pattern similar to that at + left is observed. The + electron is displaying "wave + properties".
This is an example of "wave-particle duality", + an important consequence of + the quantum theory of + matter.
For an accessible + description of what's going + on in the double slit + experiment see what Dr. + Photon has to say....
+

+
+
+

+ + + + + + interefernce cartoon

+
+
+
+

+
+
+
+

+ +

+
+

+ "One morning I shot an elephant in + my pajamas. How he got into my pajamas I'll never know."
+ + Groucho Marx
+ (in the film Animal Crackers)
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_interference_eqn1.jpg b/lo_interference_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_eqn2.jpg b/lo_interference_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_eqn3.jpg b/lo_interference_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_eqn4.jpg b/lo_interference_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_eqn5.jpg b/lo_interference_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_eqn6.jpg b/lo_interference_eqn6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_eqn7.jpg b/lo_interference_eqn7.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_fig1.jpg b/lo_interference_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_fig2.jpg b/lo_interference_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_fig3_inf.gif b/lo_interference_fig3_inf.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_fig4.jpg b/lo_interference_fig4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_fig5.jpg b/lo_interference_fig5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_fig6.jpg b/lo_interference_fig6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_interference_fig7.jpg b/lo_interference_fig7.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_internalreflectiontwodiagrams.jpg b/lo_internalreflectiontwodiagrams.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_intthinfilm.html b/lo_intthinfilm.html new file mode 100644 index 0000000..dc17c5d --- /dev/null +++ b/lo_intthinfilm.html @@ -0,0 +1,326 @@ + + + + + + + Light and Optics - Interference from Thin Films - Physics 299 + + + +

+

+ + +

Interference From Thin Films
+

+ +

+
+ "Everything + + + + we call real is made of things that cannot be regarded as real"
+ + + + + Niels Bohr
+ +

Double slit interference, described on the previous page, is + rarely observed in nature. On the other hand, interference + due to thin films is quite frequently observed - swirling + colours on an oil slick, colours on a soap bubble, the purple + tinge on an expensive camera lens - are all examples of thin + film interference.

+ + + +

+
+

Consider a thin film, + separating two regions of the same refractive index, for example + a soap bubble. Incident light undergoes reflection and + refraction at every interface as shown at right. There + will be multiple "rays" reflected back into the air (only the + first two are shown in the diagram) and multiple "rays" + transmitted through the film (only the first of these is shown).

The reflected rays will interfere with each other, their phase + difference being determined by their path difference.
Similarly the transmitted rays will interfere with each other.

Note that coherence of the interfering rays is + ensured since there is only one source - the incident ray + coloured blue in the diagram at right.

Assuming a monochromatic source and normal incidence, we + can expect that the two reflected rays will interfere + constructively if their path difference is an integer multiple of + wavelengths,
+
+

+
+
where d is the thickness of the film.
+
+
+

First Correction

The path difference 2d is measured inside the film, + but the wavelength is the wavelength in air... Therefore + the condition for a maximum should be,
+
+

+
+ However, we know that,
+
+

+
+
and using the definition of refractive + index,
+
+

+
+
This means the condition for + constructive interference can be written,
+
+

+
+
where n is the refractive index of + the film and λ is the wavelength of the light in + air.
+
+
+
+
+
+
+
+

Second Correction

This result implies that when the film + becomes very thin (d approximately zero), we + should expect constructive interference + (equivalent to m = 0). That is, just before + a soap bubble bursts, as its thickness gets + smaller and smaller, we should expect the swirling + colours to become brighter. Actually the + opposite is observed - bubbles becomes dull just + before they burst - in other words destructive + interference must be taking place.
+
+ The explanation to this apparent conflict is that + the first reflected ray (green in the above + diagram) is phase changed by 180⁰ + by the act of reflection. In + + + the above diagram, only this ray undergoes + such a phase change. In fact the + rule (which can be verified theoretically from + Maxwell's equations) is,
+
+
"A 180⁰ + phase change on reflection + occurs when light incident from a less + dense medium (smaller n) reflects off the + boundary with a more dense (larger n) + medium"
+ +

+ Reflection from more dense to less dense + (large n to small n) causes no phase change + and transmitted rays never undergo phase + changes.
+
+ Incorporating this phase change leads to the + condition for constructive interference, +
+
+

+
and for destructive + interference,
+
+

+
+
+
+
+
+
+

IMPORTANT !!

The second correction + applies specifically to the air-soap-air + configuration, or more generally to the + circumstance of a film with greater refractive + index than the media on either side. This + correction may not be needed for other thin film + configurations; for example, a film of water + on a glass surface, shown at right. In this + case, since n_air < n_water + < n_glass , there is a 180⁰ + phase change for the reflected rays from both + the air-water and water-glass interface. + That is the condition for constructive + interference reverts to
+
+

+
+

+
+
+
+
+
and for destructive interference,
+
+
+
+
+
+

+
+
+
+

+
+
+
+
+
+

All of the above analysis assumes + a single wavelength of light. + With incident white light on a thin + film maxima for different + wavelengths will occur at different + film thicknesses. Thus, in + nature, where a thin film will not + typically have a fixed thickness, we + often observe swirling colours, as + the thickness of the film changes.

Finally, why thin + films ? A thin film implies + path differences (thicknesses) of no + more than a few wavelengths. + Films thicker than this will not + necessarily exhibit this type of + interference due to re-emission and + scattering of light within the film.
+

+
+
+
+
+
+

+
+
+
+
+
+

+

+ " + + Military intelligence is a contradiction in terms."
+ + Groucho Marx
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_lenses.html b/lo_lenses.html new file mode 100644 index 0000000..e69de29 diff --git a/lo_lenses_eqn1.gif b/lo_lenses_eqn1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_malus.jpg b/lo_malus.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_maxeqn.gif b/lo_maxeqn.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_msdiffraction_eqn1.jpg b/lo_msdiffraction_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_msdiffraction_eqn2.jpg b/lo_msdiffraction_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_msdiffraction_fig1.jpg b/lo_msdiffraction_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_msdiffraction_fig2.jpg b/lo_msdiffraction_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_msdiffraction_fig3.jpg b/lo_msdiffraction_fig3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_msdiffraction_fig4.jpg b/lo_msdiffraction_fig4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_msgratings.html b/lo_msgratings.html new file mode 100644 index 0000000..183b86d --- /dev/null +++ b/lo_msgratings.html @@ -0,0 +1,234 @@ + + + + + + + Light and Optics - Multiple Slit Diffraction/Interference - + Diffraction Gratings - Physics 299 + + + +

+

+ + +

Multiple Slit Diffraction/Interference - Diffraction Gratings
+

+ +

+
+ " + + + + Physics is actually too hard for physicists"
+ + + + + + + David Hilbert (Mathematician)
+ +

+
+
+
+
+
+

+
+
+
+
+
+

IMPORTANT: Don't be confused, diffraction + and interference are different aspects of the same phenomenon - + the superposition + of waves.

+
Interference: Superposition of waves + from a finite number of "point" sources.
+
+
Diffraction: Superposition + of waves from an infinite number of "point" sources, + comprising a single large source.
+
+

Having discussed double slit interference/diffraction, the + natural extension is to 3, 4, 5... multiple slits.

+
The diagram at right illustrates a 5 slit configuration, where + the path difference at point P between waves from each of the + slits is dsinθ with a slit separation of "d". Clearly, if + the waves from all five slits are in phase, maximum intensity + will be observed at P when
+
+

+
where n = 0, 1, 2,...
+
+
+

A detailed mathematical analysis yields an intensity pattern + for N slits each of width d given by

+
where β is the same β as in the single slit + diffraction and
+

+
Note that this pattern is comprised of a + diffraction envelope together with the (sin²Nγ)/sin²γ + term. This latter term leads to the existence of principal + maxima predicted by dsinθ = nλ together with much + weaker secondary maxima between the principal + maxima as shown below for a five slit example.
+

+
+
+
DIFFRACTION GRATINGS
+
+
+

The diffraction + grating is an important experimental application + of the multiple slit maximum/minimum phenomenon. + In its simplest form a diffraction grating consistes of + a metal or glass plate with many very finely spaced + grooves or slits.

For a metal grating interference occurs in the + reflected light. For a glass grating reflected or + transmitted light will interfere.

The "slit" spacing, d, is typically defined by + the number of grooves per cm (or inch).

Principal maxima are located at angles θ given by sinθ + = nλ/d. Therefore, the smaller "d" (or the more + grooves per cm) the larger the angle θ.

By examining the exact intensity formula it can be + shown that the smaller "d" the brighter the principal + maxima are compared to the secondary maxima.

When an atom is "excited" the spectrum of light it + emits de-exciting back to its ground state is + characteristic of that particular atom. + Thus, observing the spectrum of light emitted by a star + gives an accurate measure of the elemental compostion of + the star. Since the angle θ depends on the + wavelength λ we can use a diffraction grating to obtain + the spectrum of the light emitted by the star.

For a "white" light source a diffraction grating may + lead to several "orders", corresponding to n = 1, 2, + 3,... Each order will contain the complete spectrum of + colors (see below).
+

+
+ Depending on the value of "d" the various "orders" may + overlap. In other words red light (long + wavelength) in the first order (n=1) could have the + same value of θ as blue light (smaller wavelength) in + the second order (n=2).
+
+ Note that in a diffraction + grating red light is diffracted through a larger angle + than blue light, in contrast to the way in which a + prism separates the rainbow of colors (below).
+

+
+
+

+ +

+
+ + + A little boy refused to run anymore. When his mother asked him + why, he replied, "I heard that the faster you go, the shorter + you become
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_polarisation.html b/lo_polarisation.html new file mode 100644 index 0000000..08004cb --- /dev/null +++ b/lo_polarisation.html @@ -0,0 +1,148 @@ + + + + + + + Light and Optics - Polarisation - Physics 299 + + + +

+

+ + +

Polarisation

+ +

+
+ " + + +

A physicist is just an + atom's way of looking at itself.
+ Read more at http://www.brainyquote.com/quotes/quotes/n/nielsbohr382329.html#urRTQl9BfaJk3yj3.99

+ + + +

A physicist is just an + atom's way of looking at itself.
+ Read more at http://www.brainyquote.com/quotes/quotes/n/nielsbohr382329.html#urRTQl9BfaJk3yj3.99

+ + + +

A physicist is just an + atom's way of looking at itself.
+ Read more at http://www.brainyquote.com/quotes/quotes/n/nielsbohr382329.html#urRTQl9BfaJk3yj3.99

+ A physicist is just an atom's way of + looking at itself"
+ Niels Bohr
+ +

+
+

We have seen that electromagnetic waves may be described by + transverse waves of E and B (at right angles to + each other). However, there is nothing special about any + particular direction for the E or B vectors to + oscillate. In fact an unpolarised wave contains + waves with E vectors in all possible directions (for + each E wave there is a B wave at right + angles). If the wave propagates in the z direction this + wave has E components in all possible directions.

In a polarised wave the E vector oscillates in a + specific direction - the direction of polarisation.

Polarised light does not appear any different to unpolarised + light to our eyes. The difference only becomes apparent + when observing through transparent polarising material,

+ + +

+
+

The intensity of initially unpolarised light which + passes through two polarisers is given by Malus' + Law,

+
where I₀ is the incident + intensity and θ is the angle between the directions of + the two polarisers. Note that for "cross + polarisers" there is no transmitted wave.
+
+

Analog TV and radio + signals are transmitted as polarised waves. When + rotating the direction of an antenna you are + effectively rotating the second polariser, thus + varying the angle θ. Maximum and minimum signal + reception will be obtained with orientations of the + antenna at ninety degrees to each other.
+

+

+

+
+

+ "Alimony + + is like buying hay for a dead horse"
+ Groucho Marx
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_polarisation1.jpg b/lo_polarisation1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_polarisation2.gif b/lo_polarisation2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_polarisation_eqn1.jpg b/lo_polarisation_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_rainbowgirltwodrops.jpg b/lo_rainbowgirltwodrops.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_refl1.gif b/lo_refl1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_refl4.gif b/lo_refl4.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_reflection.html b/lo_reflection.html new file mode 100644 index 0000000..6583f4e --- /dev/null +++ b/lo_reflection.html @@ -0,0 +1,130 @@ + + + + + + + Light and Optics - Reflection - Physics 299 + + + +

+ + +

Reflection

+ +

+
+"We believe a scientist because he can +substantiate his remarks, not because he is eloquent and forcible in +his enunciation. In +fact we distrust him when he seems to be influencing us by his manner"
+I. A Richards
+ +

+Edouard +Manet - A bar at the Folies_Bergere
+Spot the deliberate(?) mistakes
+

A general description of the reflection of electromagnetic waves +is obtained by considering the wave nature of the radiation. + However, when the wavelength of the radiation is small compared +to any apertures or obstacles nearby we may treat the wave as a stream +of "particles" traveling in a straight line. This is the +situation when considering the formation of images by visible light in +mirrors and lenses. In this case the straight lines +in which the visible light waves travel are known as light rays +. The study of the behaviour of light under these conditons +is known as Geometric Optics.

Light rays undergo one of two types of reflection - +diffuse or specular.
+
+
- Diffuse reflection is more common for almost all objects. + The reflected light is emitted in all directions due to +irregularities on the surface of the material.
- Specular reflection occurs if the irregularities of the +surface are small compared to the wavelength of the light. In +this case reflection occurs at a single angle, for example from the +surface of a plane mirror or water.
+

+
+We will consider only specular reflection in +this course
+

The law of reflection.(which can be derived from +Maxwell's equations)
+
+
Angle of incidence = angle of reflection
+
+Angles are measured with respect to the normal to the surface.

+ + + reflection2

Ray Tracing and Image Formation in a plane mirror
+
+Light rays are reflected from a plane mirror according to +the law of reflection. An image is formed on the "other" side of the +mirror, where the reflected rays appear to originate.

Images formed in plane mirrors have the +following properties,
+
+
- Located the same distance behind the mirror as the object is +in front of the mirror.
- Same size as the object.
- Right and left inversion
  +
- Upright
- Virtual
+
+An image is virtual if light rays do not physically pass +through it. Real images are formed if light rays actually pass +through the image.

+
+"The +tides are a fight between the Earth and Moon. All water tends +towards the moon, because there is no water in the moon, and nature +abhors a +vacuum. I forget where the sun joins in this fight."
+Middle School Science Test Answer
+
+

+ +

Dr. C. L. Davis
+Physics Department
+University of Louisville
+email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_reflpic.jpg b/lo_reflpic.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_refracpic.jpg b/lo_refracpic.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_refraction.html b/lo_refraction.html new file mode 100644 index 0000000..da81b99 --- /dev/null +++ b/lo_refraction.html @@ -0,0 +1,137 @@ + + + + + + + Light and Optics - Refraction - Physics 299 + + + +

+ + +

Refraction

+ +

+
+ "Technology...the knack of so arranging + the world so that we need not experience it"
+ Max Frisch
+ +

+
+

Refraction may be defined as the "bending" of light + (or any EM wave) as it passes from one medium to another. + The bending is caused by differing speeds of the wave in + the two media.

Refractive Index
+ The refractive index, n, of a medium is defined as the ratio of + the speed of light in a vacuum to the speed of light in the + medium
+
+
+ +
+
Snell + 's Law (Law of Refraction), describes exactly how much + the light is bent when passing from one medium to another.
+

$Refraction + picture$
+

Important points

+ +

Light is bent towards the normal when moving into a + medium of larger refractive index.

Angles of incidence, reflection and refraction are all + measured with respect to the normal.
+

As a general rule the refractive index increases with + the density of the medium. For example, the + refractive index of glass (1.5) is greater than that of + water (1.33) - glass is more dense than water.

Light incident normally is not deflected.

Light rays are "reversible". In other + words the refracted ray in the above diagram can act as + an incident ray and the incident ray will represent the + direction of the refracted ray.

The refractive index of a medium depends on the + wavelength of light, e.g. in glass, blue light travels + more slowly than red light. This phenomena is + called "dispersion".
+

+ +

What is π?
+ Mathematician: "π is + the ratio of the circumference of a circle to its diameter."
+ Engineer: "π + is about 22/7."
+ Physicist: "π is 3.14159 plus or minus 0.000005."
+ Computer Programmer: "π is 3.141592653589 in double + precision."
+ Nutritionist: "You one track math-minded fellows, Pie is + a healthy and delicious dessert!"

+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_refraction_eqn1.gif b/lo_refraction_eqn1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_anim.gif b/lo_sm_anim.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_anim2.gif b/lo_sm_anim2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_anim3.gif b/lo_sm_anim3.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_anim4.gif b/lo_sm_anim4.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_anim5.gif b/lo_sm_anim5.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_cc.gif b/lo_sm_cc.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_convex.gif b/lo_sm_convex.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_defs.gif b/lo_sm_defs.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_objatF.gif b/lo_sm_objatF.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_sm_parallel.gif b/lo_sm_parallel.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_snellslaw.gif b/lo_snellslaw.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_spearfishing.jpg b/lo_spearfishing.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_speculardiffuse.jpg b/lo_speculardiffuse.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_spmirror.html b/lo_spmirror.html new file mode 100644 index 0000000..d3fbcb0 --- /dev/null +++ b/lo_spmirror.html @@ -0,0 +1,473 @@ + + + + + + + Light and Optics - Spherical Mirrors - Physics 299 + + + +

+ + +

Spherical Mirrors

+ +

+
+
+"A modern compter hovers between the +obsolescent and the non existent"
+Sydney Brenner
+ +

+
+

There are two kinds of spherical mirrors, concave +and convex.
The focal point (F) of a concave mirror is +the point at which a parallel beam of light is "focussed" after +reflection in the mirror. For a convex mirror the focal point is +the point from which light appears to have originated after reflection +from the mirror. The centre of curvature (C) is the centre of the +circle (sphere) of which the mirror is an arc.
+
+
The focal length (f) and radius of curvature +(R) are defined in the diagram at the right. It can be shown that R = +2f. "A" in the diagram is known as the "vertex" (often +labeled V).
+
+

Image formation in spherical mirrors is defined by +certain +"characteristic" rays whose behaviour is governed by the law +of reflection.

Rays parallel to the principal axis are reflected through the +focal point - concave (or as if they came from the focal point +- convex ).
Rays passing through the focal point are reflected parallel to +the principal axis - concave (for convex mirrors a ray +that would have passed through the focal point is reflected parallel to +the axis).
Rays passing through the centre of curvature are reflected back +along their original path -concave (or a ray which would have +passed through the centre of curvature is reflected back along itself - + convex )

Concave mirror. In +the animation the first two rays from the object are examples of the +first two characteristic rays described above. Only two rays are +needed to define the position of the image. The paths of the +other rays in the animation are +defined since the image position is already known.
+The general characteristics of the image depend on the location of the +object with respect to the centre of +curvature and the focal point. Animations of image formation +in a concave mirror for the five possible object positions can be +observed by choosing from the following options.
+
- Object beyond C
- Object at C
- Object between C and F
- Object at F
- Object between F and the vertex
  +
+
Convex mirror. The general characteristics +of images in convex mirrors are independent of the location of the +object. Three examples are shown below. +

+

Note that for the convex mirror the reflected rays DIVERGE +(this is also the case for the concave mirror when the object is closer +than the focal point to the mirror). In these cases the image +formed is virtual - light rays do not pass though it, but to an +observer " appear" to come from it.

Perhaps the most common everyday experience of a convex mirror is +the passenger side rear-view mirror in your car. As can be seen +from the above ray diagrams, the image you see in a convex mirror +is always smaller than the object. You "know" the typical size of +a car or truck, so much so that the "size" it appears tells you how far +away it is (if you see a tiny car in the mirror you "know" it is far +away). Thus, seeing a vehicle "looking smaller" due to the convex +mirror, will make you think the vehicle is further away from the mirror +than it actually is, hence the warning, "objects mirror are +closer than they appear".
+

Mirror equation. For objects placed close to +the +principle axis the distance of the object from the vertex of the mirror +(p), the distance of the image from the vertex of the mirror (q) and +the focal length (f) are related by the following equation,
+
+

+ +

+
+
+
Magnification. The magnification (m) is +defined by,
+
+

+
+

Sign Conventions. In order to make use of the +above formulae the following sign conventions must be followed.
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ SIGN + +	+ + + +	+ - + +
+ f - focal length + +	+ Concave + +	+ Convex + +
+ p - object distance + +	+ Real + +	+ Virtual + +
+ q - image distance + +	+ Real + +	+ Virtual + +
+ m - magnification + +	+ Upright image + +	+ Inverted image + +

+ +

Image properties. There are four basic properties, +dependent on the position of the object, as indicated in the table +below. These properties can be verified either graphically or by +using the mirror +equation and the definition of magnification.
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ Mirror + +	+ Object location + +	+ Image location + +	+ Type + +	+ Orientation + +	+ Relative size + +
+ CONCAVE + +	+ At infinity + +	+ At F + +	+ Real + +	+ Inverted + +	+ Smaller + +
+ CONCAVE + +	+ Beyond C + +	+ Between F and C + +	+ Real + +	+ Inverted + +	+ Smaller + +
+ CONCAVE + +	+ At C + +	+ At C + +	+ Real + +	+ Inverted + +	+ Same size + +
+ CONCAVE + +	+ Between C and F + +	+ Beyond C + +	+ Real + +	+ Inverted + +	+ Larger + +
+ CONCAVE + +	+ At F + +	+ At infinity + +	+ No image + +	+ No image + +	+ No image + +
+ CONCAVE + +	+ Closer than F + +	+ Behind the mirror + +	+ Virtual + +	+ Upright + +	+ Larger + +
+ + +
+ CONVEX + +	+ Anywhere + +	+ Behind the mirror + +	+ Virtual + +	+ Upright + +	+ Smaller + +

+ +

+What's +a light-year?
+One-third less +calories than a regular year.
+(Very Punny)
+
+

+ +

Dr. C. L. Davis
+Physics Department
+University of Louisville
+email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_spmirror_eqn1.gif b/lo_spmirror_eqn1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_spmirror_eqn2.gif b/lo_spmirror_eqn2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction.html b/lo_ssdiffraction.html new file mode 100644 index 0000000..9263a5f --- /dev/null +++ b/lo_ssdiffraction.html @@ -0,0 +1,251 @@ + + + + + + + Light and Optics - Single Slit Diffraction - Physics 299 + + + +

+

+ + +

Single Slit Diffraction
+

+ +

+
+ " + + + + Physics is really nothing + more than a search for ultimate simplicity, but so far all we + have is a kind of elegant messiness.”
+ Bill Bryson, A Short History of Nearly Everything
+ +

+
+
+
+
+
+

+
+
+
+
+
+

Diffraction may be thought of as the "spreading out" of waves + as they pass through or by an aperture or edge. We now + investigate this phenomenon more closely for a single slit of + width "a".

By considering point sources in pairs across the width of the + slit we can use the ideas of double slit interference to show + that minimum intensity is observed at point P on a screen when

+
+

+ + +

However, in order + to obtain the intensity profile as a function of θ we must + perform a more complex analysis. Considering each + point in the slit as a point source, for electromagnetic + waves the electric field at a point P on the screen at right + can be written,

where ω is the angular frequency of the wave and + Δφ is the phase angle. The relationship between + phase angle and path difference Δs is given by
+

+
+
From the diagram at right the path + difference Δs, relative to the center, is given by + ysinθ. In this case
+

+
+
so that the total electric field + at a point on the screen is obtained by + integration over the slit
+
+

+
+
Performing this integration we + obtain
+

+
where
+
+
+
+
+
+
+
+
+
+

+ +

The intensity observed is proportional to the square of the + electric field
+

Using the intensity function above the minima condition is + given by sinβ = 0 ( β ≠ 0 ), which means β = nπ where + n = 1,2,3... Using the definition of β above + gives the condition for minima

+
as expected.
+
+
+

For n = 0 above, θ = 0, but + the intensity function leads to the central maximum.
Note that the width of the + central maximum - 2λ/a - is double that of secondary + maxima - λ/a. This is in contrast to the double + slit interference pattern where all maxima have the same + width.
The location of the secondary + maxima are given approximately by

+
The exact position of these maxima is + shifted slightly towards smaller θ.
+
+

In the above analysis we have (implicitly) assumed + that the source and observation screen are + infinitely far from the single slit (on opposite + sides of the slit). This allows us to use the + plane wave approximation leading to the intensity + expression above. This is described as Fraunhofer diffraction. + Practically we can approximate a Fraunhofer + situation by using converging lenses to produce + parallel rays.

Without assuming plane waves we must resort to a + more complex analysis known as Fresnel + + + + + + + diffraction.
+

+ +

+
+

+
+ + + + + + + + + The Official Unabashed Scientific Dictionary defines a + transistor as a nun who's had a sex change
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/lo_ssdiffraction_eqn1.jpg b/lo_ssdiffraction_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn2.jpg b/lo_ssdiffraction_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn3.jpg b/lo_ssdiffraction_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn4.jpg b/lo_ssdiffraction_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn5.jpg b/lo_ssdiffraction_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn6.jpg b/lo_ssdiffraction_eqn6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn7.jpg b/lo_ssdiffraction_eqn7.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn8.jpg b/lo_ssdiffraction_eqn8.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_eqn9.jpg b/lo_ssdiffraction_eqn9.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_fig1.gif b/lo_ssdiffraction_fig1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_fig2.jpg b/lo_ssdiffraction_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_fig4.gif b/lo_ssdiffraction_fig4.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_ssdiffraction_fig5.jpg b/lo_ssdiffraction_fig5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilm_fig1.jpg b/lo_thinfilm_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_eqn1.png b/lo_thinfilms_eqn1.png new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_eqn2.png b/lo_thinfilms_eqn2.png new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_eqn3.png b/lo_thinfilms_eqn3.png new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_eqn4.png b/lo_thinfilms_eqn4.png new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_eqn5.png b/lo_thinfilms_eqn5.png new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_eqn6.jpg b/lo_thinfilms_eqn6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_eqn7.jpg b/lo_thinfilms_eqn7.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_fig2.jpg b/lo_thinfilms_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_fig3.jpg b/lo_thinfilms_fig3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_fig4.jpg b/lo_thinfilms_fig4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_thinfilms_fig5.jpg b/lo_thinfilms_fig5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_tir.html b/lo_tir.html new file mode 100644 index 0000000..351163d --- /dev/null +++ b/lo_tir.html @@ -0,0 +1,120 @@ + + + + + + + Light and Optics - Total Internal Reflection - Physics 299 + + + +

+ + +

Total Internal Reflection

+ +

+
+ "One machine can do the work of fifty + ordinary men. No machine can do the work of one + extraordinary man"
+ Elbert Hubbard
+ +

When light passes from a medium with refractive index n₁ + to a medium with refractive index n₂, where n₁ + > n₂, if the incident angle is greater than some + critical angle , the light will undergo + total internal reflection (TIR).

The diagram below represents a light source underwater with + light rays striking the water-air interface. Rays 1, 2 and + 3 are refracted at the interface according to Snell's law, the + refracted ray bending away from the normal such that > . When = 90^o + the refracted ray is directed along the surface of the water and + is called the critical angle . For incident angles greater than + there is no refracted ray, the light + undergoes total internal reflection back into the water.

Note that even when TIR does not take + place there will always be a reflected wave (back into the water), + in this case, of low intensity (about 4% of the total energy is + reflected). In other words, at an interface where the + incident angle is less than the critical angle, part of the + incident energy is transmitted and part is reflected.
+

At the critical angle
+

+
+
+ For light passing into air from water the critical angle + is equal to about 49^o.

Thus a fish-eye's view is of the world in a 98^o + cone. Outside this cone all is darkness...[Actually this + is not true due to the scattering of light in water]
+

+
+

Total Internal Reflection is the mechanism by which fibre + optic cables work. Signal losses along such cables is + extremely small since ALL the incident energy is + reflected.
+
+

+

+ "I know that this defies the law of gravity, + but, you see, I never studied law."
+ Bugs Bunny
+
+

+
+ Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu
+ +

+ +

+ + diff --git a/lo_tir_eqn1.gif b/lo_tir_eqn1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tir_eqn2.gif b/lo_tir_eqn2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tir_eqn3.gif b/lo_tir_eqn3.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tir_eqn4.gif b/lo_tir_eqn4.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_conimg1.gif b/lo_tl_conimg1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_conimg2.gif b/lo_tl_conimg2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_conv2.gif b/lo_tl_conv2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_conv3.gif b/lo_tl_conv3.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_div2.gif b/lo_tl_div2.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_div3.gif b/lo_tl_div3.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_divimg1.gif b/lo_tl_divimg1.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_lens_anim.gif b/lo_tl_lens_anim.gif new file mode 100644 index 0000000..e69de29 diff --git a/lo_tl_typelens.jpg b/lo_tl_typelens.jpg new file mode 100644 index 0000000..e69de29 diff --git a/lo_young.jpg b/lo_young.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR.html b/mag_LR.html new file mode 100644 index 0000000..a650724 --- /dev/null +++ b/mag_LR.html @@ -0,0 +1,208 @@ + + + + + + + Magnetism - LR Circuits - Physics 299 + + + + +

+ + +

LR Circuits
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

As we have seen, due to Faraday's Law, an induced emf will + appear in any loop/coil/circuit in which the current (and + therefore the magnetic field) changes with time. Certain + circuit elements have a larger (self) inductance than others - + the solenoid is the most obvious example of a circuit element + with a large inductance.

An ideal inductance (L) has no resistance and is represented + by the following symbol + .

Placing an inductance (L) and a + resistance (R) in a simple circuit gives us the "LR" circuit, + at right. When the switch is closed to include the power + supply in the circuit we can apply Kirchoff's loop theorem to + obtain the following equation,

+
Note + that in applying the loop theorem we make use of the fact + that the induced emf across the inductance opposes the + changing emf that causes it.
+
+

The solution of this + differential equation is given by,

+
shown at right, where I_max is + ε/R . Also shown is the time dependence of + the voltage across the inductance.
+
+

The time constant of the inductance, given by + is a measure of the time + needed for the current in the circuit to reach 63% of + its maximum value.

+ +

Taking the + power supply out of the circuit leads to an even + simpler differential equation
+

+
the solution of which is
+

+
shown at right. In this figure I₀ + = ε/R.
+
+
+

+ +

+

+

+ +

+ This girl said she recognized me from + the vegetarian club, but I'd never met herbivore.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_LR_eqn1.jpg b/mag_LR_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_eqn2.jpg b/mag_LR_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_eqn3.jpg b/mag_LR_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_eqn4.jpg b/mag_LR_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_eqn5.jpg b/mag_LR_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_fig1.jpg b/mag_LR_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_fig2.jpg b/mag_LR_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_fig3.jpg b/mag_LR_fig3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_LR_fig4.jpg b/mag_LR_fig4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere.html b/mag_ampere.html new file mode 100644 index 0000000..bcea834 --- /dev/null +++ b/mag_ampere.html @@ -0,0 +1,243 @@ + + + + + + + Magnetism - Ampere's Law - Physics 299 + + + + +

+ + +

Ampere's Law
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

We have just seen that + the Biot-Savart Law is in some sense the magnetic equivalent of + Coulomb's Law. Is there a magnetic equivalent of Gauss's + Law ? The answer is (of course) yes - Ampere's Law.
+

+
where ds is an element of length + around an arbitrary closed loop "C", called an Amperian loop + and the summation is over all currents passing through + the loop.
+
+ Currents passing "out of" the loop are defined + as positive, currents passing into the loop are negative, + whereas current which do not pass through the loop are not + included in the summation.
+
+ Ampere's Law forms part of the second of + Maxwell's equations. We will shortly adjust it + slightly (following Maxwell), to complete the second of + Maxwell's equations. Remember, Gauss's Law was the first + of Maxwell's equations.
+
+

As a reminder, Gauss's Law appears below,
+

+
Note that + Gauss's Law involves a surface integral + of E over a closed Gaussian surface "S". + Ampere's Law involves a line integral + around a closed Amperian loop "C".
+
+ Gauss's Law is valid for any arbitrary closed + Gaussian surface. Similarly Ampere's Law is valid for + any closed (Amperian) loop.
+
+

Although Ampere's Law is true for any closed loop "C", it + is only useful to calculate B for some very + symmetric cases, where we already know (from symmetry) some + of the properties of B.

Simple Applications

B due to an infinite straight current carrying + wire.
+
- Symmetry argument: +
  Since the wire is infinite, we know from the + Biot-Savart Law that B is perpendicular to dl + and r and thus lines of B must form + concentric circles around the current. Also, B + can, at most, depend only on the distance from the + wire, r.
  +
  +
- Choice of Amperian Loop: +
  The Amperian loop is chosen so that B is + constant on the loop and in the same direction as ds + - that is a circle whose plane is perpendicular to the + wire and centered on the wire. This allows us to + take B "out of the integral".
  +
- Evaluation of B: +
  With the Amperian loop above we have
  +
  +
  
  +
  so that
  +
  
  +
  +
  directed "circumferentially" + around the loop, with the sense given by the + right-hand-rule described under the Biot-Savart + law.
  +
  +
  +
  +
+

+
+
+

B due to + an infinite solenoid +
- Symmetry argument: +
  Since the solenoid is infinite, we conclude that B + is directed along the axis of the solenoid. + Also, B can, at most, depend only on the + distance from the axis of the solenoid. For an + infinite solenoid B = 0 outside the solenoid.
  +
  +
- Choice of Amperian Loop: +
  The rectangular Amperian loop (at right) is chosen + so that B is constant on the two sides + parallel to the solenoid axis and perpendicular to the + ds on the other two sides. This allows us to + take B "out of the integral".
  +
- Evaluation of B: +
  With the Amperian loop above we have
  +
  +
  
  +
  so that
  +
  
  +
  +
  where n is the number of turns + per unit length and the field is directed along + the solenoid axis as shown. (Use + right-hand-rule)
  +
  +
  +
  +
+ Note that, the above analysis is + true only for an infinite solenoid. For + a real solenoid it is a good approximation inside, away from + the ends. The B field outside is not zero, but + much smaller than the field inside.

The shape of the B field due + to a solenoid is the same as that of a bar magnet and a + magnetic dipole.
+

+
+

+ +

+ What does a clock do when it's hungry ? + It goes back four seconds.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_ampere_eqn1.jpg b/mag_ampere_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_eqn2.jpg b/mag_ampere_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_eqn3.jpg b/mag_ampere_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_eqn4.jpg b/mag_ampere_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_eqn5.jpg b/mag_ampere_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_fig1.jpg b/mag_ampere_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_fig2.jpg b/mag_ampere_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_fig3.gif b/mag_ampere_fig3.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_fig4.gif b/mag_ampere_fig4.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_fig5.jpg b/mag_ampere_fig5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_ampere_fig6.gif b/mag_ampere_fig6.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_biotsavart.html b/mag_biotsavart.html new file mode 100644 index 0000000..2a87074 --- /dev/null +++ b/mag_biotsavart.html @@ -0,0 +1,259 @@ + + + + + + + Magnetism - Biot-Savart Law - Physics 299 + + + + +

+ + +

The Law of Biot-Savart
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

We have seen that a magnetic field exerts + a force on a moving charge or current, just + as an electric field exerts a force on a + charge.

+ and +

+
+

In the electric case Coulomb's Law + gives us a method of determining E + from an arbitrary distribution of + charges. For a point charge we + have
+

+
where is a unit + vector from the point charge to + location at which the E field + is to be determined.
+
+
+

The Biot-Savart Law + provides a general method of + determining the B field from + an arbitrary current distribution.

+
+

+
where μ₀ + is the permeability of the vacuum + (free space) = 4π x 10^-7 + T.m/A, dl is a "current element" + directed along the current in the + wire and is a unit + vector from dl to where + the B field is to be + calculated as in the diagram at + right.
+
+

There are a number of + important points to be aware of:

The law + must be written in differential + form since there is no such thing + as a "point current". Note + that a moving point charge is + equivalent to a current and a + stationary point charge does not + create a magnetic field.
+
+ + Due to the cross product dB + is at right angles to both dl + and . + You can't avoid considering 3 + dimensions.
+
+ The "sense" of dB + (into or out of the plane in the + above diagram) is determined by + the basic definition of a vector + cross product or equivalently + another "right-hand-rule" + shown at right.
+
+ (μ₀/4π) + + + plays a similar role to the + Coulomb constant, k (= 1/4πε₀). + + But compare the values of μ₀ + and k; this is an indication of + the relative strengths of the + electric and magnetic interactions + of charges.
+
+ + Similar to our initial statement + of Coulomb's Law, the above + expression of the Biot-Savart Law + gives dB due to a current + element in a vacuum. For + real world applications wheres the + current is not in a vacuum a + slight adjustment must be made to + take into account the magnetic + properties of the medium. + This can be done in a similar + manner to the adjustment of + Coulomb's Law in a dielectric + + + medium, but is beyond the + scope of this course.
+
+

Needless to say determining + the magnetic field is typically + significantly more complicated + than the electric field.
+

+

+

+ +

+ Energizer bunny arrested. Charged + with battery.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_biotsavart_eqn1.jpg b/mag_biotsavart_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_biotsavart_eqn2.jpg b/mag_biotsavart_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_biotsavart_eqn3.jpg b/mag_biotsavart_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_biotsavart_eqn4.jpg b/mag_biotsavart_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_biotsavart_fig1.jpg b/mag_biotsavart_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_biotsavart_fig2.jpg b/mag_biotsavart_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole.html b/mag_dipole.html new file mode 100644 index 0000000..f19a1bc --- /dev/null +++ b/mag_dipole.html @@ -0,0 +1,171 @@ + + + + + + + Magnetism - Dipoles - Physics 299 + + + + +

+ + +

Magnetic Dipoles
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

Shown below is a rectangular current loop sides a and b placed + in a region of space with uniform magnetic field (B).
+

+
+

Application of the expression for the force on a current + carrying wire to the top and bottom sides of the rectangle + leads to cancellation of forces as shown.

The forces on the other two sides (length a) are also + equal and opposite, as shown in (b) above, . Although the net force + in this case is zero, because the forces are not co-linear, + there is a net torque on the current loop, + given by

+
The magnitude of this torque is given by
+

+
+
where A = ab is the cross section area + of the coil.
+
+
+
+

The magnitude of the magnetic dipole moment of the + loop with N turns is defined by,

+
μ is a vector quantity + whose direction is perpendicular to the loop with + a sense defined by (another) Right Hand Rule.
+
+

With this definition of μ the torque on the + current loop is given by

Without proof, the potential energy of a + magnetic dipole in an external magnetic + field is given by

+
+

Note that the + above expressions for the torque and + potential energy of a magnetic dipole in an + external magnetic field are identical in + form to those obtained for an electric + dipole in an external electric field.
+
+

+ + and

+

+

+ +

+ I stayed up all night to see where the + sun went. Then it dawned on me.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_dipole_eqn1.jpg b/mag_dipole_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_eqn2.jpg b/mag_dipole_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_eqn3.jpg b/mag_dipole_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_eqn4.jpg b/mag_dipole_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_eqn5.jpg b/mag_dipole_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_eqn6.jpg b/mag_dipole_eqn6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_fig1.jpg b/mag_dipole_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_fig2.jpg b/mag_dipole_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_dipole_fig3.jpg b/mag_dipole_fig3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement.html b/mag_displacement.html new file mode 100644 index 0000000..2f2103f --- /dev/null +++ b/mag_displacement.html @@ -0,0 +1,287 @@ + + + + + + + Magnetism - Magnetic Energy - Physics 299 + + + + +

+ + +

Displacement Current
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

Having discussed Gauss' Law for Magnetism, we now have four + equations describing electromagnetism,

Gauss' Law: elecgausseqn3

+
+

Ampere's Law: magampereeqn1

+
+

Faraday's Law: magfaradayeqn6

+
+ Nobody's Law:

+
+

Looking carefully at these equations, the two flux + equations are now consistent with our physical understanding + of electric and magnetic charges.
+

The line integrals are a different matter. The right + hand side of Ampere's Law has a summation over electric + currents. Naively we would expect a similar sum over + "magnetic currents" on the right hand side of Faraday's + Law. But since there are no magnetic charges, + "magnetic currents" do not exist and the necessity for such + an additional term disappears.

However, in words, Faraday's Law states that

+
"A changing magnetic field ( ) gives rise to an + electric field ( )"
+
+
For a more complete correspondence between E + and B we would expect a term added to the right + hand side of Ampere's Law which indicates,
+
+
"A changing electric field ( ) gives rise to a + magnetic field ( )"
+
+

Maxwell proposed this addition, the existence of which + is now physically verified. Furthermore, Maxwell + showed that this additional term, known as the + displacement current, is essential for the description + of electromagnetic waves.

The form of the displacement current term can be + obtained by the argument described below.

We have seen that current and current density are + related by the following equation

+
Suppose we consider a closed surface, + then charge conservation tells us that this flux + integral must be zero. Charge cannot be created + or destroyed inside the closed surface, therefore,
+

+
This equation can be considered as a + formal statement of conservation of charge.
+
+
+
+

Consider a parallel + plate capacitor (at right). The closed surface + over which we will apply the above integral is S₁ + and S₂. Current I passes in though + S₁, but since S₂ is between + the capacitor plates, no current passes out of the + closed surface. As it stands, we have violated + conservation of charge... What to do ? + Propose that there is an equal current passing out + of the closed surface through S₂ - the + "displacement current".

+
+

+
Therefore, if we define
+

+
as the displacement current, + by writing
+

+
we can ensure charge is + conserved.
+
+
+
+
+
+

Therefore, including the displacement + current, Ampere's Law becomes,

+ +

+

+

+ +

+ This girl said she recognized me from + the vegetarian club, but I'd never met herbivore.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_displacement_eqn1.jpg b/mag_displacement_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn2.jpg b/mag_displacement_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn3.jpg b/mag_displacement_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn4.jpg b/mag_displacement_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn5.jpg b/mag_displacement_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn6.jpg b/mag_displacement_eqn6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn7.jpg b/mag_displacement_eqn7.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn8.jpg b/mag_displacement_eqn8.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_eqn9.jpg b/mag_displacement_eqn9.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_displacement_fig1.jpg b/mag_displacement_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_energy.html b/mag_energy.html new file mode 100644 index 0000000..3e552a2 --- /dev/null +++ b/mag_energy.html @@ -0,0 +1,203 @@ + + + + + + + Magnetism - Magnetic Energy - Physics 299 + + + + +

+ + +

Magnetic Energy
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

Let's take a second + look at the differential equation for the simple LR circuit

+
Multiplying throughout by the current I gives
+

+
This is now an energy conservation + equation,
+
+
Rate of thermal heating + (I²R) + + Rate at which energy is stored in the + inductance (LI dI/dt) = Rate at which + energy is supplied (εI)
+
+
+
+
+

The energy stored in the inductance is associated + with the magnetic field of the inductance, U_B. + Therefore,

+
which upon integration gives
+

+
+
equivalent to the electrical + case of energy stored in a capacitor U_E + = q²/2C = (1/2)CV².
+
+
+
+

Exactly as in the electric field case, we + can determine a general expression for the + energy density (u_B) stored in a + magnetic field,

+
+
+

+
+
+

+ +

+

+

+ +

+ This girl said she recognized me from + the vegetarian club, but I'd never met herbivore.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_energy_eqn1.jpg b/mag_energy_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_energy_eqn2.jpg b/mag_energy_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_energy_eqn3.jpg b/mag_energy_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_energy_eqn4.jpg b/mag_energy_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_energy_eqn5.jpg b/mag_energy_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_energy_fig1.gif b/mag_energy_fig1.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday.html b/mag_faraday.html new file mode 100644 index 0000000..82e70ec --- /dev/null +++ b/mag_faraday.html @@ -0,0 +1,440 @@ + + + + + + + Magnetism - Faraday's Law of Induction - Physics 299 + + + + +

+ + +

Faraday's Law of Induction
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

So far we have treated electricity and magnetism as almost + separate subjects. We now begin to discuss phenomena which + show that electricity and magnetism are inextricably connected, + hence the term electromagnetism. The first + of these properties is known as Faraday's Law of + Induction.

Formally, time independent + electrical and magnetic properties can be described by considering + electricity and magnetism as largely separate phenomena. + However, when time dependence becomes part of the "equation" + we find that electrical and magnetic properties become + inextricably linked - electromagnetism.
+

+ +

This law is conveniently written in terms of magnetic flux, + which is defined in the same way as electric flux.

+
where S is the surface over which the flux is + evaluated.
+
+ For constant B, perpendicular to the surface, Φ_B + = BA where A is the surface area of S.
+
+ The magnetic flux, Φ_B, is so + important it has its own unit the Weber - 1 Weber + = 1 T.m² . In the early days of + electromagnetism it was common to measure the magnetic (B) + field in Weber/m² .
+
+

In term of the magnetic flux Faraday's Law of Induction is + given by,

+
The induced electromotive force (emf) + in a circuit is equal to the rate of change of magnetic + flux through the circuit.
+
+ An emf is not a force, + rather it can be considered as the voltage induced + in a closed circuit.
+
+ Faraday experimentally + determined his law in the form presented above.
+
+

+
+

One of the easiest ways to change the magnetic flux + through a circuit is to move a permanent (bar) magnet + towards or away from the circuit as shown in the + diagrams below.

+
(a) Magnetic flux passes through the + circuit, but does not change with time, so there is no + induced emf and so no induced current.
+
+ (b) The flux through the circuit increases with + time causing an induced emf and current.
+
+ (c) As the magnet moves faster the rate of + change of flux with time is increased causing a larger + emf and current.
+
+ (d) When the magnet moves away from the circuit + the flux decreases with time so the induced emf + and current are reversed.
+
+

+
+
+

The origin of the changing magnetic flux (field) + is not limited to permanent magnets. The + magnetic field due to a second circuit can produce a + similar effect, as described in the examples + below.
+

+
In the diagram at + right the current in the left circuit is constant, + but the flux through the other circuit increases + as the two circuits get closer.
+
+
+
+
+ In the situation at + left both circuits are stationary. The + current in the left circuit is initially zero, but + rapidly increases to a constant value when the + switch is closed. As the current reaches its + final (constant) value the flux through the right + circuit is increasing with time, thus by Faraday's + Law, causing a brief pulse of induced + current in the second circuit. When the + switch is opened the flux in the right circuit + rapidly decreases causing a short induced current + pulse in the opposite direction.
+
+
+

Important ! In both the + above examples a magnetic field (B) + changing with time results in a changing + magnetic flux. But it is possible to have + a changing flux with a constant B if the + cross sectional area - dA - can be made + to change with time as in the case of the + (electric) generator.
+

+ +

+
+
LENZ'S LAW
+
+

Mathematically the negative sign in + Faraday's Law tells us about the + direction of the induced (emf) + current. Practically we use Lenz's + Law to determine the direction in + specific cases.
+

+
"The induced + current will appear in such a + direction that it opposes the change + that produced it" +
+
+ Confusing ? Yes !
+
+
+

+ + + + magfaradayfig7

+ +

The induced (flux) + magnetic field (associated with the + induced current) does not necessarily + oppose the field which causes the change + in flux, rather it opposes the CHANGE + in this field.
+

Lenz's Law always ensures + that there is a force resisting the + motion of the magnet. It is the + work done against this force which + appears as the energy of the moving + charges of the induced current.
+

magfaradayfig6

+ +

+
+ FARADAY'S + LAW = MAXWELL + EQUATION
+

Whenever there is an induced + electric current there must also be + an induced electric field, E. + + + + + + The work dW done by this induced + field moving a charge q₀ + a distance ds around a loop + is given by,

+
where dε is the + potential difference in ds.
+
+ Therefore,
+

+
So that the emf + + + + + around the whole loop is
+

+
+
Equating + this emf to that + given by Faraday's Law we + obtain the integral form + of Faraday's Law, the + third of Maxwell's + equations we have + encountered so far,
+

+
+
+ Note that the line + integral of E + must be round a closed + loop (circuit).
+
+
+
+
+
+
+
+

Written in the + above form the + relationship between + the E and B + fields is clear

"A + + + + + magnetic field + changing with + time induces + an electric + field"
+

+
Shortly + + + + + we will see that the + reverse of this + statement is also + true.
+
+

+

+

+ +

+ They told me I had type A blood, but it + was a Type O.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_faraday_eqn1.jpg b/mag_faraday_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_eqn2.jpg b/mag_faraday_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_eqn3.jpg b/mag_faraday_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_eqn4.jpg b/mag_faraday_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_eqn5.jpg b/mag_faraday_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_eqn6.jpg b/mag_faraday_eqn6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_fig1.jpg b/mag_faraday_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_fig2.jpg b/mag_faraday_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_fig3.jpg b/mag_faraday_fig3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_fig4.jpg b/mag_faraday_fig4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_fig5.jpg b/mag_faraday_fig5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_fig6.jpg b/mag_faraday_fig6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_faraday_fig7.jpg b/mag_faraday_fig7.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_2wires.html b/mag_force_2wires.html new file mode 100644 index 0000000..689e378 --- /dev/null +++ b/mag_force_2wires.html @@ -0,0 +1,181 @@ + + + + + + + Magnetism - Force Between Parallel Wires: Ampere Definition - + Physics 299 + + + + +

+ + +

Force Between Two Parallel Wires: Ampere Definition
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

We have just seen that a long straight wire carrying current + i₁ produces a B field which forms + concentric circles around the wire whose magnitude a distance + "d" from the wire is given by
+

+
with direction given by "the" right-hand-rule.
+
+

If a second parallel wire carrying a current + i₂ is placed a distance "d" from the first, it + will feel a force due to the presense of B₁ . + + The force felt by a length l₂ of this + second wire is

+
so that
+

+
+
with a direction such that i₂ + is attracted towards i₁ as shown at right.
+ Then the force per unit length on i₂ is + given by
+

+
+
+
+
+

Note that if we reverse + the roles of i₁ and i₂ we + obtain the same expression for F₁/l₁ + . That is, i₁ exerts a force + on i₂ and i₂ + exerts an equal, but opposite, force on i₁ + + + as expected from Newton's Third Law ("Action equals + Reaction").

The above analysis applies for parallel currents - + the two wires are attracted to each other. If + one of the currents is reversed, so that the + currents are "anti-parallel", the force per unit + length is unchanged, but the force acting on each + wire is reversed. In other words the wires are + now repelled from each other.

"Like + + + currents are attractive, unlike currents are + repelled". Note that this is + opposite to the behavior of point electric charges.
+
+

Definition + + + of the Ampere

+
The unit of electric current, the Ampere, is + defined using the force between parallel wires + carrying current.
+
+
"The Ampere is + that current which when flowing in two + infinite parallel wires one + metre apart produces a force between them of 2 + x 10^-7 + N/m"
+
+
+
Proof:
+
+
+

+ +

+ What do you call a dinosaur with an + extensive vocabulary ? A thesaurus.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_force_2wires_eqn1.jpg b/mag_force_2wires_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_2wires_eqn2.jpg b/mag_force_2wires_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_2wires_eqn3.jpg b/mag_force_2wires_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_2wires_eqn4.jpg b/mag_force_2wires_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_2wires_eqn5.jpg b/mag_force_2wires_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_2wires_fig1.jpg b/mag_force_2wires_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_charge.html b/mag_force_charge.html new file mode 100644 index 0000000..c066f27 --- /dev/null +++ b/mag_force_charge.html @@ -0,0 +1,296 @@ + + + + + + + Magnetism - Force on Charges - Physics 299 + + + + +

+ + +

Magnetic Forces on Charged Particles
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

Proceeding under the assumption that magnetic fields exist - + created by an as yet not described mechanism - the magnetic + force on a positively charged particle is found + experimentally to be given by +
+

+
where q is the charge (positive) of the particle, v its + + + + + + + + + + + + + velocity, F_B the force it experiences and B + the magnetic field causing the force.
+
+

+
+
Note + that this equation is the magnetic equivalent of the + electric expression F_E = qE
+
+

The expression for the magnetic force is written in terms of + a vector (cross) product, which means, like it or not, you + have to work in three dimensions. Several important + facts emerge from this equation.
+

If v = 0 there is no force. Electric + charges at rest in a magnetic field do not feel a magnetic + force.

The magnitude of F_B is given by +
+
+ where φ is the angle between v and B. +
+
- So that, when v is parallel to B (φ + = 0) or antiparallel to B (φ = 180^o) + then sinφ = 0 and F_B = 0. + Therefore, charged particles moving along magnetic + field lines experience no magnetic force.
+
- When v and B are at 90^o + F_B has its maximum value, F_B + = qvB.
+

F_B is at right angles to v + and B. The "sense" is given by the usual + rules for the vector (cross) product, sometimes called + (the) "Right Hand Rule". +

+
+
+ This leads to circular (or spiral) motion around the B + field lines.
+
+

+
+
+
+
Don't + + + + + forget that the direction of the magnetic force + obtained above is for a positive charge. + For a negative charge the direction of F_B + is reversed.
+
+
+

The work done by the magnetic force when a charged + particle is displaced by ds is given by,

where θ is the angle between F_B_{+
+
+
+
+
+
+
+
+
+
+
+
+
+}and ds.
+

The displacement ds and the + velocity of the particle, v, are in the same + direction, so θ is also the angle between F_B_{+
+
+
+
+
+
+
+
+
+
+
+
+
+}and v. But from the form of the + magnetic force we know F_Band + + + + + + + + + + + + + v are perpendicular (θ = 90^o) therefore + dW is always zero. In other words the magnetic + + + + + + + + + + + + + force does no work, which means, unlike the + electric force, it cannot give a charged particle energy + (increase or decrease its kinteic energy). The effect of a + magnetic force is to change the direction not the kinetic + energy.

If a charged particle feels both a magnetic and electric + field the resultant force is given by

+
+

+
this is known as the Lorentz Force Law.
+
+

+
+
+
+

UNITS

+
From the form of the magnetic force we see that the units + of B are N/(C.m/s) = N/(A.m). This + combination of basic units is defined as the Tesla.
+
+
+
+
The Tesla is a very large unit of magnetic field. + For this reason you may occasionally come across the + smaller unit of magnteic field, the Gauss; where 1 + Tesla = 10⁴ Gauss.
+
+

+

+

+ +

+ Q: What did one quantum physicist say + when he wanted to fight another quantum physicist?
+ A: Let me atom.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_force_charge_eqn1.jpg b/mag_force_charge_eqn1.jpg new file mode 100644 index 0000000..6f83db3 Binary files /dev/null and b/mag_force_charge_eqn1.jpg differ diff --git a/mag_force_charge_eqn2.jpg b/mag_force_charge_eqn2.jpg new file mode 100644 index 0000000..43ba48d Binary files /dev/null and b/mag_force_charge_eqn2.jpg differ diff --git a/mag_force_charge_eqn3.jpg b/mag_force_charge_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_charge_eqn4.jpg b/mag_force_charge_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_charge_eqn5.jpg b/mag_force_charge_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_charge_fig1.jpg b/mag_force_charge_fig1.jpg new file mode 100644 index 0000000..41e2c56 Binary files /dev/null and b/mag_force_charge_fig1.jpg differ diff --git a/mag_force_charge_fig2.jpg b/mag_force_charge_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_charge_fig3.jpg b/mag_force_charge_fig3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_current.html b/mag_force_current.html new file mode 100644 index 0000000..b7a0c22 --- /dev/null +++ b/mag_force_current.html @@ -0,0 +1,124 @@ + + + + + + + Magnetism - Force on Currents - Physics 299 + + + + +

+ + +

Magnetic Forces on Electric Currents
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

An electric current is simply a collection of charges moving + along a wire with velocity v_d , known as the + drift velocity. We have already seen that the drift + velocity and current density are related by

+
+

+
Considering the magnetic force on a single + charge (e) we find
+

+
+
Now the total force on a wire comprised of + (nAl) charge carriers each with charge e is given by
+
+

+
+
Defining a vector l along the + wire in the same direction as J and using |JA| + + + = i (electric current) we find for the total force on + the wire
+
+

+
+ + +
+
+
Note that for a given current + negative and positive charge carriers move in + opposite directions. This leads to a + force on the wire in the same direction (see + above), whether the charge carriers are positive + or negative.
+
+
+
+
+
+
+
+

+ +

+ When chemists die, they barium.
+
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_force_current_eqn1.jpg b/mag_force_current_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_current_eqn2.jpg b/mag_force_current_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_current_eqn3.jpg b/mag_force_current_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_current_fig1.jpg b/mag_force_current_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_force_current_fig2.jpg b/mag_force_current_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_intro.html b/mag_intro.html new file mode 100644 index 0000000..3de1575 --- /dev/null +++ b/mag_intro.html @@ -0,0 +1,135 @@ + + + + + + + Magnetism - Introduction - Physics 299 + + + + +

+ + +

Introduction to Magnetism
+

+ +

+
+ + + + + +

"Physics Is + Imagination In A Straight Jacket"
+

+ John Moffat
+ +

+ +

As we will see shortly, Electricity and Magnetism are + different aspects of the same basic physical phenomenon - hence + the description Electromagnetism.

However, initially it is convenient to treat magnetism in a + separate, but similar, manner to electricity. In other + words we will define, magnetic forces, magnetic fields and + magnetic dipoles exactly as we did the electric variables.

After this initial description we will develop the + relationship between magnetism and electricity through Faraday's + Law of Induction and the Displacement Current, leading finally + to a complete description of (classical) electromagnetism in the + form of Maxwell's + equations.

So our starting point in describing magnetism will be the + assumption of the existence of a magnetic field, B, the + origin of which will be described later.

Exactly as for the electric field E, + we will assume that the B field can be represented by + field lines where,

the tangent to a field line gives the direction of B + at that point and

the number of field lines per unit cross sectional area is + proportional to the strength of B.

It is important to realize immediately that unlike + electric field lines, magnetic field lines DO NOT + represent the direction of the force acting on a charged + particle.

The magnetic phenomenon most + familiar to most people is that of permanent magnetism - + refrigerator magnets etc. As it happens, permanent magnetism + is not a simple topic to explain. In fact a complete + description requires a detailed knowledge of the quantum behavior + of materials. For this reason we will barely mention + permanent magnets in this course.
+
+

+
+

+ +

+ + + Q: What is the name of the first electricity detective?
+ A: Sherlock Ohms
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_intro_fig1.jpg b/mag_intro_fig1.jpg new file mode 100644 index 0000000..e5285a1 Binary files /dev/null and b/mag_intro_fig1.jpg differ diff --git a/mag_intro_fig2.jpg b/mag_intro_fig2.jpg new file mode 100644 index 0000000..a16c132 Binary files /dev/null and b/mag_intro_fig2.jpg differ diff --git a/mag_intro_fig3.jpg.png b/mag_intro_fig3.jpg.png new file mode 100644 index 0000000..34bc350 Binary files /dev/null and b/mag_intro_fig3.jpg.png differ diff --git a/mag_monopole_fig1.gif b/mag_monopole_fig1.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_monopole_fig2.jpg b/mag_monopole_fig2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_monopole_fig3.gif b/mag_monopole_fig3.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_monopole_fig4.jpg b/mag_monopole_fig4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_monopole_fig5.jpg b/mag_monopole_fig5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_monopole_fig7.gif b/mag_monopole_fig7.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_monopoles.html b/mag_monopoles.html new file mode 100644 index 0000000..122957f --- /dev/null +++ b/mag_monopoles.html @@ -0,0 +1,292 @@ + + + + + + + Magnetism - Magnetic Energy - Physics 299 + + + + +

+ + +

Magnetic Monopoles & Gauss' Law for Magnetism
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

+ +

Magnetic + + + Monopoles

In our initial discussion of magnetism we made the point that + we were going to treat magnetism in a similar way to + electricity. However, whereas our discussion of + electricity began with electric charges and the electric field + associated with these charges, the magnetic discussion started + with the existence of the magnetic field. No mention was + made of "magnetic charges", which would play the same role in + magnetism as electric charges in electricity. This is + because individual magnetic charges - magnetic monopoles + - are apparently impossible to isolate.

The simplest magnetic object we have been able to isolate is + the magnetic dipole. + Current loops, bar magnets and solenoids all produce + dipole fields with a characteristic magnetic dipole moment.

+ + + + +

The bar magnetic may be considered to be a combination of two + magnetic monopoles, usually labelled North and South. This + is similar to the electric dipole comprised of equal but + opposite electric charges.

+ + + magintrofig3

+
+

Whereas with the + electric dipole it is possible to isolate the positive and + negative charges, experimentally it is not possible to + separate the North and South poles of a bar magnet. + Break a magnet in two and you get two magnets, each with a + North and South pole. Continuing this splitting + process down to the atomic level we find that even + elementary particles behave as magnetic dipoles, each with a + North and South pole. It appears that nature does not + allow us to create magnetic monopoles in this way.

However, theoreticians + developing unified quantum theories of the Universe, + so-called "Theories of Everything", are almost unanimous in + the necessity for magnetic monopoles as elementary particles + created shortly after the birth of the Universe.

+
The belief is that shortly after their creation, magnetic + monopoles were "frozen out" - meaning that their + interactions with the rest of the matter in the Universe is + highly suppressed. This does not prevent physicists + from searching for evidence for the existence of magnetic + monopoles.
+
+

+
+
+

+
+

+
Gauss' Law for Magnetism
+
+

So far we have discussed three basic equations + describing electromagnetic phenomena - the first three + of Maxwell's equations.

+
Gauss' Law:
+
+
+
Ampere's Law:
+
+
+
Faraday's Law:
+
+

Gauss' Law involves the flux integral for the + electric field. To complete the correspondence + between electricity and magnetism we expect a fourth + equation involving the magnetic flux - "Gauss' Law + for Magnetism".

The right hand side of Gauss' Law includes a + summation over electric charges. Therefore, + for magnetism, we expect a summation over "magnetic + charges". But magnetic charges, North and + South poles (equivalent to positive and negative + electric charges) always exist in pairs, the net + "magnetic charge" is thus always zero. Gauss' + Law for Magnetism must therefore take the form,

+
the flux of B through a + closed surface is zero.
+
+ Note that the fact that + the surface is closed is very important ! A + magnetic flux integral appears in Faraday's + Law - in this case the surface is generally not + closed.
+
+ Electric field lines begin + (positive) and end (negative) on charges. + Since there are no magnetic charges magnetic field + lines form closed loops.
+
+
+

+
+
+

+ +

+

+

+ +

+ This girl said she recognized me from + the vegetarian club, but I'd never met herbivore.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_motionch.html b/mag_motionch.html new file mode 100644 index 0000000..c0b5b7c --- /dev/null +++ b/mag_motionch.html @@ -0,0 +1,239 @@ + + + + + + + Magnetism - Motion of Charged Particles in B and E - Physics + 299 + + + + +

+ + +

Motion of Charged Particles in Magnetic and Electric Fields
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

MAGNETIC + + + FIELDS

Return now to the case of a "point" charge + moving with velocity v in a region + of constant magnetic field (B). + We previously stated (without proof) that + such a particle would move in a circle or + helix. Now let's prove it.

Consider + + + the positive charge (e) at the top of the + figure at right. With the directions + of v and B indicated the + right-hand-rule leads to a downwards force + as shown. This force changes the + direction of v but does not change + the magnitude of v, as shown.

Quantitatively we find

+
Assuming that this force + causes circular motion, F_B + is the centripetal force so that
+
+

+
which leads to a + radius
+
+
+
+

+
The period (time taken to + perform one revolution) is given by
+
+

+
The frequency, f, is
+

+
+
+
+
+

Notice that this frequency + is independent of the velocity. + That is fast particles will move in + large radius circles, slow + particles will have smaller radii. + This phenomenon is the basis for the + cyclotron one of the earliest charged + particle accelerators.

If the velocity of + the particle has a component along B + this will be unchanged and the resultant + trajectory will be helical.

+
+ MAGNETIC + and ELECTRIC FIELDS
+

There are many useful applications in + which B and E fields are + applied simultaneously. Perhaps + the simplest application is the + "crossed" B and E + fields.

+ +

+
For this configuration the electric and + magnetic forces are in opposite + directions. If a charged particle + moves through this region of space with + no deflection then
+

+
+
so that
+
+

+

+
+
+
+
+

Other applications include + mass spectrometers and particle + accelerators. (EXPAND + ?)
+

+ +

+ I'm reading a book about + anti-gravity. I can't put it down.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_motionch_eqn1.jpg b/mag_motionch_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_motionch_eqn2.jpg b/mag_motionch_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_motionch_eqn3.jpg b/mag_motionch_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_motionch_eqn4.jpg b/mag_motionch_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_motionch_eqn5.jpg b/mag_motionch_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_motionch_eqn6.jpg b/mag_motionch_eqn6.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_motionch_eqn7.jpg b/mag_motionch_eqn7.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_motionch_fig1.gif b/mag_motionch_fig1.gif new file mode 100644 index 0000000..e69de29 diff --git a/mag_mutualind.html b/mag_mutualind.html new file mode 100644 index 0000000..d8fd7b6 --- /dev/null +++ b/mag_mutualind.html @@ -0,0 +1,210 @@ + + + + + + + Magnetism - Mutual Induction - Physics 299 + + + + +

+ + +

Mutual Induction
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

As we have seen, Faraday's Law of Induction tells us that a + changing magnetic flux through a circuit will induce an emf and + therefore an "induced current". Consider the situation of + two nearby circuits (below) where the flux through circuit 2 + changes due to the changing current in circuit 1.

With N₂ turns in circuit 2 the emf is given by

+
but the total flux through circuit 2 is + proportional to the current in circuit 1, where the + proportionality constant is called the mutual inductance + of the coils, M₂₁,
+
+

+
Combining these two equations gives
+
+
+
+

+
In other words the emf in circuit 2 is + proportional to the rate of change of current in + circuit 1. As we will see shortly, the mutual + inductance M₂₁ depends only on the + geometric configuration of the two circuits.
+
+
+
+

If the roles of the two circuits are reversed - + that is a changing current in circuit 2 induces a + current in circuit 1 - then

It is "easy" to show that M₂₁ + = M₁₂ . In other words given + two circuits in a particular configuration it + doesn't matter in which circuit the current is + induced the mutual inductance is the same.

UNITS: Inductance is measured in + Henrys
+

+
The concept of inductance is + related to the magnetic field in a similar way + that capacitance is related to the electric + field.
+
+

In order to calculate mutual inductance + you will typically follow the steps below:

+
+
Determine B due to one circuit + at the location of the other using + Ampere's Law or the Biot-Savart Law.
+
Using this B calculate the + magnetic flux through the 'other' circuit.
+
Then use the equation N₂Φ₂ + = MI₁ to obtain M.
+
+ You will always find that M depends + only on the geometric parameters of the + two circuits and the number of turns in + each circuit.
+
+
+

+

+

+ +

+ This girl said she recognized me from + the vegetarian club, but I'd never met herbivore.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_mutualind_eqn1.jpg b/mag_mutualind_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_mutualind_eqn2.jpg b/mag_mutualind_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_mutualind_eqn3.jpg b/mag_mutualind_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_mutualind_eqn4.jpg b/mag_mutualind_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_mutualind_eqn5.jpg b/mag_mutualind_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_mutualind_fig1.jpg b/mag_mutualind_fig1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_selfind.html b/mag_selfind.html new file mode 100644 index 0000000..4019dfe --- /dev/null +++ b/mag_selfind.html @@ -0,0 +1,172 @@ + + + + + + + Magnetism - Self Inductance - Physics 299 + + + + +

+ + +

Self Inductance
+

+ +

+
+ + + + + +

+ Edward Teller
+ +

Consider now a single + coil/circuit/loop with N turns. As the current in the loop + changes the magnetic field and hence the magnetic flux through + the loop changes. This changing "self flux" through + Faraday's Law leads to and induced emf in the circuit,

In the same manner as mutual inductance we define the self + inductance of the circuit, L, as follows

+
so that the induced emf - sometimes called + a "back emf" - is given by
+

+
This "back emf" always opposes the + primary emf (due to Lenz's Law), as shown in the + diagram at right.
+
+
+
+

From above, magselfindeqn4

which can be compared to the similar + equation for capacitance magselfindeqn5

.
+

Calculating self inductance proceeds by the same steps + as mutual inductance - Calculate B, calculate + magnetic flux, then use the second equation above to + determine L.
+

+ +

+

+

+ +

+ This girl said she recognized me from + the vegetarian club, but I'd never met herbivore.
+
+

+ +

Dr. C. L. Davis
+ Physics Department
+ University of Louisville
+ email: c.l.davis@louisville.edu +
+

+ +

+ + diff --git a/mag_selfind_eqn1.jpg b/mag_selfind_eqn1.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_selfind_eqn2.jpg b/mag_selfind_eqn2.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_selfind_eqn3.jpg b/mag_selfind_eqn3.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_selfind_eqn4.jpg b/mag_selfind_eqn4.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_selfind_eqn5.jpg b/mag_selfind_eqn5.jpg new file mode 100644 index 0000000..e69de29 diff --git a/mag_selfind_fig1.gif b/mag_selfind_fig1.gif new file mode 100644 index 0000000..e69de29 diff --git a/mendeleev.gif b/mendeleev.gif new file mode 100644 index 0000000..f62891b Binary files /dev/null and b/mendeleev.gif differ diff --git a/misc1.gif b/misc1.gif new file mode 100644 index 0000000..20b461a Binary files /dev/null and b/misc1.gif differ diff --git a/netbar.gif b/netbar.gif new file mode 100644 index 0000000..eab8b38 Binary files /dev/null and b/netbar.gif differ diff --git a/question_mark.gif b/question_mark.gif new file mode 100644 index 0000000..e69de29 diff --git a/sadface.jpg b/sadface.jpg new file mode 100644 index 0000000..9e38adc Binary files /dev/null and b/sadface.jpg differ diff --git a/science.gif b/science.gif new file mode 100644 index 0000000..8581323 Binary files /dev/null and b/science.gif differ diff --git a/tickred1.gif b/tickred1.gif new file mode 100644 index 0000000..6dca2af Binary files /dev/null and b/tickred1.gif differ

CONTENTS

Capacitors +

Calculating Capacitance

Energy and Capacitors

Combinations of + Capacitors

Charged Particle Motion in an Electric Field +

RC Circuits +

CHARGING

DISCHARGING

Kirchhoff's Laws +

Junction Theorem

Loop Theorem

Conventions

Application of Kirchhoff's Laws

Series and Parallel Circuits +

Series

Parallel

Combinations

Conductors and Insulators

Electric Field Due Continuous Charge Distribtuions +

Coulomb's Law

Electric Current, Resistance and Power +

Electric Current +

Resistance

Power

Electro-motive Force - "emf"

Internal Resistance

Dielectric Materials +

Electric Dipole in an External Electric Field +

Electric Field due to a Dipole +

Electric Field

Gauss's Law +

Quantitative Use of Gauss's Law +

State what you are + assuming about E + based on the + symmetry of the + problem.

State clearly the + Gaussian surface(s) + you will use - often + most easily done by + sketching the + surface(s) on a + diagram.

Evaluate the + surface (flux) + integral to + determine E. + The symmetry of E + and choice of + Gaussian surface + should allow "E" to + be "taken out" of + the integral and + thus be determined. +

Gauss's Law and Conductors +

Electric Potential Energy +

Electric Potential and Potential Difference

Electric Potential due to an Electric Dipole +

Determining the Electric Field from the Electric Potential +

Electric Charge and Matter +

Structure of Matter

Apparent Depth and Distortion

+

Brewster's Law +

Dispersion

+

Double Slit Diffraction/Interference +

+ Electromagnetic Waves +

+

Double Slit Interference

+

Interference From Thin Films +

+

Multiple Slit Diffraction/Interference - Diffraction Gratings +

DIFFRACTION GRATINGS

+

Polarisation

Reflection

Refraction

Spherical Mirrors

+

Single Slit Diffraction +

Total Internal Reflection

LR Circuits +

Ampere's Law +

Simple Applications

The Law of Biot-Savart +

Magnetic Dipoles +

Displacement Current +

Magnetic Energy +

Faraday's Law of Induction +

LENZ'S LAW

Force Between Two Parallel Wires: Ampere Definition +

Magnetic Forces on Charged Particles +

Magnetic Forces on Electric Currents +

Introduction to Magnetism +

Magnetic Monopoles & Gauss' Law for Magnetism +

Magnetic + + + Monopoles

Capacitors
+

Charged Particle Motion in an Electric Field
+

RC Circuits
+

Kirchhoff's Laws
+

Series and Parallel Circuits
+

Electric Field Due Continuous Charge Distribtuions
+

Electric Current, Resistance and Power
+

Electric Current
+

Dielectric Materials
+

Electric Dipole in an External Electric Field
+

Electric Field due to a Dipole
+

Gauss's Law
+

Quantitative Use of Gauss's Law
+

Evaluate the + surface (flux) + integral to + determine E. + The symmetry of E + and choice of + Gaussian surface + should allow "E" to + be "taken out" of + the integral and + thus be determined.
+

Gauss's Law and Conductors
+

Electric Potential Energy
+

Electric Potential due to an Electric Dipole
+

Determining the Electric Field from the Electric Potential
+

Electric Charge and Matter
+

Brewster's Law
+

Double Slit Diffraction/Interference
+

Interference From Thin Films
+

Multiple Slit Diffraction/Interference - Diffraction Gratings
+

Single Slit Diffraction
+

LR Circuits
+

Ampere's Law
+

The Law of Biot-Savart
+

Magnetic Dipoles
+

Displacement Current
+

Magnetic Energy
+

Faraday's Law of Induction
+

Force Between Two Parallel Wires: Ampere Definition
+

Magnetic Forces on Charged Particles
+

Magnetic Forces on Electric Currents
+

Introduction to Magnetism
+

Magnetic Monopoles & Gauss' Law for Magnetism
+

Motion of Charged Particles in Magnetic and Electric Fields
+

Mutual Induction
+

Self Inductance
+