155 lines
5.6 KiB
HTML
155 lines
5.6 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//w3c//dtd html 4.0 transitional//en">
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type"
|
|
content="text/html; charset=ISO-8859-1">
|
|
<meta name="GENERATOR"
|
|
content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0 alpha) [Netscape]">
|
|
<meta name="Author" content="C. L. Davis">
|
|
<title>Electricity - Coulomb's Law - Physics 299</title>
|
|
</head>
|
|
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);"
|
|
alink="#ff0000" link="#0000ee" vlink="#551a8b">
|
|
<center>
|
|
<h1> <img src="ULPhys1.gif" align="texttop" height="50" width="189"></h1>
|
|
</center>
|
|
<center>
|
|
<h1>Coulomb's Law</h1>
|
|
</center>
|
|
<center><img src="celticbar.gif" height="22" width="576"><br>
|
|
<br>
|
|
<font color="#ff0000"><i>"When man wanted to make a machine that would
|
|
walk
|
|
he created the wheel, which does not resemble a leg"</i></font><br>
|
|
Guillaume Apollinaire<br>
|
|
</center>
|
|
<img src="netbar.gif" align="middle" height="40" width="100%"> <br>
|
|
|
|
<ul>
|
|
<li> The magnitude of the force of attraction (or repulsion), F<sub>12</sub>
|
|
between two point charges q<sub>1</sub> and q<sub> 2 </sub> is
|
|
given by Coulomb's Law.</li>
|
|
<center>
|
|
<p><br>
|
|
<img alt="" src="elec_coulomb_eqn1.gif"
|
|
style="width: 80px; height: 47px;"> <br>
|
|
</p>
|
|
</center>
|
|
<p>where R<sub>12</sub> is the distance between the
|
|
charges. k is a constant of proportionality known as the Coulomb
|
|
constant, having the value 9 x
|
|
10<sup>9</sup> N.m<sup>2</sup> / C<sup>2</sup> in a
|
|
vacuum. </p>
|
|
<p><img style="width: 31px; height: 30px;" alt="exclamation"
|
|
src="exclamation-icon.gif"> Note that the Coulomb constant, k, is
|
|
often replaced with (1/4π ε<sub>0</sub>), where
|
|
ε<sub>0</sub>is the permittivity of the vacuum (more later).<br>
|
|
</p>
|
|
<li> The direction of this force is along the line joining the two
|
|
charges
|
|
with the sense determined by the relative signs of the charges</li>
|
|
<p><br>
|
|
</p>
|
|
<center>
|
|
<p><img src="coulaw1.gif" height="112" width="182"> </p>
|
|
</center>
|
|
<li> Note that the force on each charge has the same magnitude (as
|
|
required by Newton's third law of motion).</li>
|
|
<br>
|
|
|
|
<li> For two 1 Coulomb charges separated by 1 metre the
|
|
magnitude
|
|
of the force is given by,
|
|
<center> <br>
|
|
F = (9 x 10<sup>9</sup> x 1 x 1 )/ 1 = 9 x 10<sup>9</sup>
|
|
Newtons</center>
|
|
<p>This is an <b><i>extremely large</i></b> force (sufficient to
|
|
move Mt. Everest with an acceleration of 1cm/s<sup>2</sup>). The
|
|
Coulomb
|
|
is a <b><i>very large</i></b> unit. Typical macroscopic charges
|
|
are measured in micro-coulombs (10<sup>-6</sup> C). </p>
|
|
</li>
|
|
<li>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 <span style="font-weight: bold;">vector</span> sum of the force
|
|
due to each of the other charges. For example the force on q<sub>1</sub>
|
|
due to all other charges q<sub>2</sub>, q<sub>3</sub> , q<sub>4</sub>...
|
|
would
|
|
be
|
|
given
|
|
by,</li>
|
|
</ul>
|
|
<div style="text-align: center;"><span style="font-weight: bold;">F</span><sub
|
|
style="font-weight: bold;">1</sub><span style="font-weight: bold;"> = F</span><sub
|
|
style="font-weight: bold;">21</sub><span style="font-weight: bold;"> +
|
|
F</span><sub style="font-weight: bold;">31</sub><span
|
|
style="font-weight: bold;"> + F</span><sub style="font-weight: bold;">41</sub><span
|
|
style="font-weight: bold;"> + ...</span><br>
|
|
<div style="text-align: left;">
|
|
<ul>
|
|
<li><img style="width: 79px; height: 43px;" alt="hot" src="hot.gif">Notice
|
|
the
|
|
similarity
|
|
of
|
|
Coulomb's Law to Newton's Law of Gravitation</li>
|
|
</ul>
|
|
<div style="text-align: center;"><img
|
|
style="border: 0px solid ; width: 114px; height: 62px;" alt="eqn1"
|
|
src="grav_eqn1.jpg"><br>
|
|
<div style="text-align: left; margin-left: 40px;"><br>
|
|
both are "inverse square" laws. Substitute charge for mass and
|
|
"k" for "G" and you have Coulomb's law.<br>
|
|
<img style="width: 31px; height: 30px;" alt="exclamation"
|
|
src="exclamation-icon.gif"> The relative magnitudes of the Coulomb
|
|
constant, k = 9 x 10<sup>9</sup> and the gravitational constant, G =
|
|
6.67 x 10<sup>-11</sup>, 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.<br>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<ul>
|
|
</ul>
|
|
<p><br>
|
|
<img src="netbar.gif" height="40" width="100%"> </p>
|
|
<center><span
|
|
style="font-size: 12pt; font-family: "Times New Roman"; color: rgb(255, 0, 0); font-style: italic;">"The
|
|
wireless
|
|
telegraph
|
|
is
|
|
not
|
|
difficult
|
|
to
|
|
understand. The ordinary telegraph is like a very long cat. You pull
|
|
the tail
|
|
in </span><st1:state style="color: rgb(255, 0, 0); font-style: italic;"><st1:place><span
|
|
style="font-size: 12pt; font-family: "Times New Roman";">New York</span></st1:place></st1:state><span
|
|
style="font-size: 12pt; font-family: "Times New Roman"; color: rgb(255, 0, 0); font-style: italic;">,
|
|
and
|
|
it
|
|
meows
|
|
in
|
|
</span><st1:city style="color: rgb(255, 0, 0); font-style: italic;"><st1:place><span
|
|
style="font-size: 12pt; font-family: "Times New Roman";">Los Angeles</span></st1:place></st1:city><span
|
|
style="font-size: 12pt; font-family: "Times New Roman";"><span
|
|
style="color: rgb(255, 0, 0); font-style: italic;">. The wireless is
|
|
the same, only without the cat."</span><br>
|
|
Albert Einstein<br>
|
|
</span><br>
|
|
<img src="celticbar.gif" height="22" width="576"> <br>
|
|
|
|
<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>
|
|
<br>
|
|
</p>
|
|
<p><img src="header-index.gif" height="51" width="92">
|
|
</p>
|
|
</center>
|
|
<p><br>
|
|
</p>
|
|
</body>
|
|
</html>
|