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<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>
&nbsp;
<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&nbsp;</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>&nbsp; is the distance between the
charges.&nbsp; k is a constant of proportionality known as the Coulomb
constant, having the value 9 x
10<sup>9</sup>&nbsp; N.m<sup>2</sup> / C<sup>2</sup>&nbsp; in a
vacuum.&nbsp;</p>
<p><img style="width: 31px; height: 30px;" alt="exclamation"
src="exclamation-icon.gif"> Note that the Coulomb constant, k, is
often replaced with (1/4&#960; &#949;<sub>0</sub>), where
&#949;<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>
&nbsp;
<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>&nbsp; x 1 x 1 )/ 1&nbsp; =&nbsp; 9 x 10<sup>9</sup>
&nbsp; 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>).&nbsp; The
Coulomb
is a <b><i>very large</i></b> unit.&nbsp; 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.&nbsp; 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.&nbsp; 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.&nbsp; 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: &quot;Times New Roman&quot;; 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: &quot;Times New Roman&quot;;">New York</span></st1:place></st1:state><span
style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; 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: &quot;Times New Roman&quot;;">Los Angeles</span></st1:place></st1:city><span
style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;"><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>
&nbsp;
<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>
&nbsp; </p>
<p><img src="header-index.gif" height="51" width="92">
</p>
</center>
<p><br>
</p>
</body>
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