158 lines
6.3 KiB
HTML
158 lines
6.3 KiB
HTML
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<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html;
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charset=windows-1252">
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<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0
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alpha) [Netscape]">
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<meta name="Author" content="C. L. Davis">
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<title>Electricity - Gauss's Law and Conductors - Physics 299</title>
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</head>
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<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
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255);" link="#0000ee" alink="#ff0000" vlink="#551a8b">
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<center>
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<h1> <img src="ULPhys1.gif" height="50" align="texttop"
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width="189"></h1>
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</center>
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<center>
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<h1>Gauss's Law and Conductors<br>
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</h1>
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</center>
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<center><img src="celticbar.gif" height="22" width="576"><br>
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<br>
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<font color="#ff0000"><i>"</i></font><font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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We shouldn't be surprised that conditions in the universe are
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suitable for life, but this is not evidence that the universe
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was designed to allow for life."</i></font><br>
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Stephen Hawking<br>
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</center>
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<img src="netbar.gif" height="40" align="middle" width="100%"> <br>
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<ul>
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<li>In electrostatic conditions - no electric current flow -
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Gauss's Law applied to conductors (typically metallic objects)
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leads to some important conclusions.</li>
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</ul>
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<blockquote><img alt="exclamation" src="exclamation-icon.gif"
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height="30" width="31"> Note that since a conductor contains
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"free" charges if an electric field exists anywhere in the
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conductor a current will flow. Thus, in electrostatic
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conditions ("static" means all charges are at rest) there can be
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no electric field anywhere in the conductor.<br>
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</blockquote>
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<ul>
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<li><b><img alt="elec gauss figure 4" src="elec_gauss_figure3.jpg"
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height="166" align="right" width="193">Insulated solid
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conductor having a net charge</b></li>
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</ul>
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<blockquote>Under electrostatic conditions, <b>E</b> = 0 throughout
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the object. Applying Gauss's Law to the closed surface A, we
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conclude that there can be no charge inside A. But the
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conductor has a net charge. The only possibility is that the
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charge resides outside the surface A. If we gradually
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increase the size of A, so that eventually it lies just below the
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surface of the conductor, the charge must still reside outside
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A. Therefore, as a consequence of Gauss's Law, any <b>charge
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placed in a conductor must reside on its surface.</b><br>
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<br>
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</blockquote>
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<ul>
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<li><b>Insulated hollow charged conductor (conducting shell)</b></li>
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</ul>
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<blockquote>
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<p>We now hollow out the conductor, changing nothing else.
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Thus, there is no charge inside the hollowed out conductor, so
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that <b>E</b> = 0 inside. This fact leads to the
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necessity for an antenna to pick up radio signals inside a
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car. Radio waves are comprised of electric and magnetic
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fields (electromagnetic waves - much more later), which must be
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received by the radio. But the car is approximately a
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hollow metallic conductor, which means <b>E</b> = 0
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inside. Without an antenna the radio waves cannot be
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received by the radio. The antenna provides a "shielded
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channel" to direct the radio signal into the car.<br>
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<br>
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</p>
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<center><img alt="elec gauss figure 4"
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src="elec_gauss_figure4.jpg" height="226" width="700"><br>
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</center>
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</blockquote>
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<center>
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<div align="left">
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<ul>
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<li><b>Faraday Cage</b></li>
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</ul>
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<blockquote>
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<p>A <a
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href="http://www.princeton.edu/%7Eachaney/tmve/wiki100k/docs/Faraday_cage.html">Faraday
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cage</a> is a metal container, which is used to shield
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sensitive electronics from stray electric fields.
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Fields outside the container cannot penetrate due to the
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above explanation.<br>
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<br>
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</p>
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</blockquote>
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<ul>
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<li><b>Proof of inverse square nature of Coulomb's Law</b></li>
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</ul>
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<blockquote>
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<p>It can be shown mathematically that if Coulomb's Law is not
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exactly of the inverse square form - 1/r<sup>2</sup> then
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the electric field inside a closed conductor would not be
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exactly zero. All experiments to date have failed to
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measure such an electric field, with an accuracy such that
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we know that the inverse component of r in Coulomb's Law is
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2 with an accuracy of 16 decimal places.<br>
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</p>
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</blockquote>
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</div>
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</center>
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<br>
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<img src="netbar.gif" height="40" width="100%"><br>
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<center><span style="font-size: 12pt; font-family: "Times New
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Roman";"><span style="color: rgb(255, 0, 0); font-style:
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italic;"></span></span><span style="font-size: 12pt;
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font-family: "Times New Roman";"><span style="color:
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rgb(255, 0, 0); font-style: italic;">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</span></span><br>
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<font color="#ff0000"><i>A Simpleton's Guide to Science (stolen
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from UK magazine)
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<br>
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Relativity : Family get-togethers at Christmas
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<br>
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Gravity : Strength of a glass of beer
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<br>
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Time travel : Throwing the alarm clock at the wall
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<br>
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Black holes : What you get in black socks
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<br>
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Critical mass: A gaggle of film reviewers
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<br>
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Hyperspace : Where you park at the superstore</i></font><br>
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<br>
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<img src="celticbar.gif" height="22" width="576"> <br>
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<p><i>Dr. C. L. Davis</i> <br>
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<i>Physics Department</i> <br>
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<i>University of Louisville</i> <br>
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<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
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<br>
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</p>
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<p><img src="header-index.gif" height="51" width="92"> </p>
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</center>
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<p><br>
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</p>
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</body>
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</html>
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