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<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<meta name="Author" content="C. L. Davis">
<title>Electricity - Gauss's Law and Conductors - Physics 299</title>
</head>
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
255);" link="#0000ee" alink="#ff0000" vlink="#551a8b">
<center>
<h1> <img src="ULPhys1.gif" height="50" align="texttop"
width="189"></h1>
</center>
<center>
<h1>Gauss's Law and Conductors<br>
</h1>
</center>
<center><img src="celticbar.gif" height="22" width="576"><br>
<br>
<font color="#ff0000"><i>"</i></font><font color="#ff0000"><i>
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
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."</i></font><br>
Stephen Hawking<br>
</center>
<img src="netbar.gif" height="40" align="middle" width="100%"> <br>
<ul>
<li>In electrostatic conditions - no electric current flow -
Gauss's Law applied to conductors (typically metallic objects)
leads to some important conclusions.</li>
</ul>
<blockquote><img alt="exclamation" src="exclamation-icon.gif"
height="30" width="31"> Note that since a conductor contains
"free" charges if an electric field exists anywhere in the
conductor a current will flow.&nbsp; Thus, in electrostatic
conditions ("static" means all charges are at rest) there can be
no electric field anywhere in the conductor.<br>
</blockquote>
<ul>
<li><b><img alt="elec gauss figure 4" src="elec_gauss_figure3.jpg"
height="166" align="right" width="193">Insulated solid
conductor having a net charge</b></li>
</ul>
<blockquote>Under electrostatic conditions, <b>E</b> = 0 throughout
the object.&nbsp; Applying Gauss's Law to the closed surface A, we
conclude that there can be no charge inside A.&nbsp; But the
conductor has a net charge.&nbsp; The only possibility is that the
charge resides outside the surface A.&nbsp; 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.&nbsp; Therefore, as a consequence of Gauss's Law, any <b>charge
placed in a conductor must reside on its surface.</b><br>
<br>
</blockquote>
<ul>
<li><b>Insulated hollow charged conductor (conducting shell)</b></li>
</ul>
<blockquote>
<p>We now hollow out the conductor, changing nothing else.&nbsp;
Thus, there is no charge inside the hollowed out conductor, so
that <b>E</b> = 0 inside.&nbsp; This fact leads to the
necessity for an antenna to pick up radio signals inside a
car.&nbsp; Radio waves are comprised of electric and magnetic
fields (electromagnetic waves - much more later), which must be
received by the radio.&nbsp; But the car is approximately a
hollow metallic conductor, which means <b>E</b> = 0
inside.&nbsp; Without an antenna the radio waves cannot be
received by the radio.&nbsp; The antenna provides a "shielded
channel" to direct the radio signal into the car.<br>
<br>
</p>
<center><img alt="elec gauss figure 4"
src="elec_gauss_figure4.jpg" height="226" width="700"><br>
</center>
</blockquote>
<center>
<div align="left">
<ul>
<li><b>Faraday Cage</b></li>
</ul>
<blockquote>
<p>A <a
href="http://www.princeton.edu/%7Eachaney/tmve/wiki100k/docs/Faraday_cage.html">Faraday
cage</a> is a metal container, which is used to shield
sensitive electronics from stray electric fields.&nbsp;
Fields outside the container cannot penetrate due to the
above explanation.<br>
<br>
</p>
</blockquote>
<ul>
<li><b>Proof of inverse square nature of Coulomb's Law</b></li>
</ul>
<blockquote>
<p>It can be shown mathematically that if Coulomb's Law is not
exactly of the inverse square form - 1/r<sup>2</sup> then
the electric field inside a closed conductor would not be
exactly zero.&nbsp; 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.<br>
</p>
</blockquote>
</div>
</center>
<br>
<img src="netbar.gif" height="40" width="100%"><br>
<center><span style="font-size: 12pt; font-family: &quot;Times New
Roman&quot;;"><span style="color: rgb(255, 0, 0); font-style:
italic;"></span></span><span style="font-size: 12pt;
font-family: &quot;Times New Roman&quot;;"><span style="color:
rgb(255, 0, 0); font-style: italic;">
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</span></span><br>
<font color="#ff0000"><i>A Simpleton's Guide to Science (stolen
from UK magazine)
<br>
Relativity : Family get-togethers at Christmas
<br>
Gravity : Strength of a glass of beer
<br>
Time travel : Throwing the alarm clock at the wall
<br>
Black holes : What you get in black socks
<br>
Critical mass: A gaggle of film reviewers
<br>
Hyperspace : Where you park at the superstore</i></font><br>
<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>
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