davisnotes/mag_mutualind.html

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<title>Magnetism - Mutual Induction - Physics 299</title>
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<h1>Mutual Induction<br>
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<div class="copy-paste-block"><font color="#ff0000"><i><span
class="bqQuoteLink">"A</span></i></font><font
color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
statement that everyone believes.&nbsp; It is innocent,
unless found guilty.&nbsp; A hypothesis is a novel
suggestion that no one wants to believe.&nbsp; It is
guilty, until found effective</span></i><span></span>"</font><br>
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<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
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<li> 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".&nbsp; Consider the situation of
two nearby circuits (below) where the flux through circuit 2
changes due to the changing current in circuit 1.</li>
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<div align="center"><img alt="magmutualindfig1"
src="mag_mutualind_fig1.jpg" height="261" width="411"><br>
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<li>With N<sub>2</sub> turns in circuit 2 the emf is given by</li>
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<div align="center"><img alt="magmutualindeqn1"
src="mag_mutualind_eqn1.jpg" height="60" width="122"><br>
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<div align="left">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, M<sub>21</sub>,<br>
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<div align="center"><img alt="magmutualindeqn2"
src="mag_mutualind_eqn2.jpg" height="38" width="162"><br>
<div align="left">Combining these two equations gives<br>
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<div align="center"><img alt="magmutualindeqn3"
src="mag_mutualind_eqn3.jpg" height="81" width="159"><br>
<div align="left">In other words the emf in circuit 2 is
proportional to the rate of change of current in
circuit 1.&nbsp; As we will see shortly, the mutual
inductance M<sub>21</sub> depends only on the
geometric configuration of the two circuits.<br>
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<li>If the roles of the two circuits are reversed -
that is a changing current in circuit 2 induces a
current in circuit 1 - then</li>
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<div align="center"><img alt="magmutualindeqn4"
src="mag_mutualind_eqn4.jpg" height="81" width="423"><br>
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<li>It is "easy" to show that&nbsp; M<sub>21</sub>
= M<sub>12</sub> .&nbsp; 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.</li>
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<li><b>UNITS: </b>Inductance is measured in
Henrys <img alt="Henry" src="Henry.jpg"
height="135" width="105" align="middle"><br>
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<div align="center"><img alt="magmutualindeqn5"
src="mag_mutualind_eqn5.jpg" height="39"
width="308"><br>
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<div align="left"><img alt="exclamation"
src="exclamation-icon.gif" height="30"
width="31"> The concept of inductance is
related to the magnetic field in a similar way
that capacitance is related to the electric
field.<br>
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<li>In order to calculate mutual inductance
you will typically follow the steps below:</li>
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<li>Determine <b>B</b> due to one circuit
at the location of the other using
Ampere's Law or the Biot-Savart Law.</li>
<li>Using this <b>B</b> calculate the
magnetic flux through the 'other' circuit.</li>
<li>Then use the equation N<sub>2</sub>&#934;<sub>2</sub>
= MI<sub>1</sub> to obtain M.</li>
</ol>
You will always find that <i><b>M depends
only on the geometric parameters of the
two circuits and the number of turns in
each circuit.</b></i><br>
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<font color="#ff0000"><i>This girl said she recognized me from
the vegetarian club, but I'd never met herbivore. </i></font><br>
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<p><i>Dr. C. L. Davis</i> <br>
<i>Physics Department</i> <br>
<i>University of Louisville</i> <br>
<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
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