293 lines
12 KiB
HTML
293 lines
12 KiB
HTML
<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<meta http-equiv="Content-Type" content="text/html;
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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>Magnetism - Magnetic Energy - Physics 299</title>
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<meta content="C. L. Davis" name="author">
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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>Magnetic Monopoles & Gauss' Law for Magnetism<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>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</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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</i></font>
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<div class="copy-paste-block"><font color="#ff0000"><i><span
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class="bqQuoteLink">"A</span></i></font><font
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color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
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statement that everyone believes. It is innocent,
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unless found guilty. A hypothesis is a novel
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suggestion that no one wants to believe. It is
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guilty, until found effective</span></i><span></span>"</font><br>
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</div>
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<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
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</center>
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<img src="netbar.gif" height="40" align="middle" width="100%">
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<blockquote> </blockquote>
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<ul>
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</ul>
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<div align="center">
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<h2><img alt="questionmark" src="question_mark.gif" height="54"
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align="middle" width="64"> <u>Magnetic
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Monopoles</u> <img alt="questionmark"
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src="question_mark.gif" height="54" align="middle" width="64"></h2>
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</div>
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<ul>
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<li>In our initial discussion of magnetism we made the point that
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we were going to treat magnetism in a similar way to
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electricity. However, whereas our discussion of
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electricity began with electric charges and the electric field
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associated with these charges, the magnetic discussion started
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with the existence of the magnetic field. No mention was
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made of "magnetic charges", which would play the same role in
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magnetism as electric charges in electricity. This is
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because individual magnetic charges - <b>magnetic monopoles</b>
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- are apparently impossible to isolate.</li>
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</ul>
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<ul>
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<li>The simplest magnetic object we have been able to isolate is
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the <a href="mag_dipole.html">magnetic dipole</a>.
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Current loops, bar magnets and solenoids all produce
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dipole fields with a characteristic magnetic dipole moment.</li>
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</ul>
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<div align="center"><img alt="magmonopolefig2"
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src="mag_monopole_fig2.jpg" height="170" width="297">
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<img alt="magmonopolefig3" src="mag_monopole_fig3.gif"
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height="174" width="243"></div>
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<ul>
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<li>The bar magnetic may be considered to be a combination of two
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magnetic monopoles, usually labelled North and South. This
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is similar to the electric dipole comprised of equal but
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opposite electric charges.</li>
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</ul>
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<p><br>
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</p>
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<div align="center"><img alt="mag_monopole_fig1"
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src="mag_monopole_fig1.gif" height="233" width="238">
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<img alt="magintrofig3" src="mag_intro_fig3.jpg"
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height="217" width="290"><br>
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<br>
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<div align="left">
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<ul>
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<li><img alt="magmonopolefig4" src="mag_monopole_fig4.jpg"
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height="313" align="right" width="243">Whereas with the
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electric dipole it is possible to isolate the positive and
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negative charges, experimentally it is not possible to
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separate the North and South poles of a bar magnet.
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Break a magnet in two and you get two magnets, each with a
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North and South pole. Continuing this splitting
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process down to the atomic level we find that even
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elementary particles behave as magnetic dipoles, each with a
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North and South pole. It appears that nature does not
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allow us to create magnetic monopoles in this way.</li>
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</ul>
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<ul>
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<li><img alt="exclamation" src="exclamation-icon.gif"
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height="30" width="31"> However, theoreticians
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developing unified quantum theories of the Universe,
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so-called "Theories of Everything", are almost unanimous in
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the necessity for magnetic monopoles as elementary particles
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created shortly after the birth of the Universe.</li>
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</ul>
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<blockquote>
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<p>The belief is that shortly after their creation, magnetic
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monopoles were "frozen out" - meaning that their
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interactions with the rest of the matter in the Universe is
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highly suppressed. This does not prevent physicists
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from searching for evidence for the <a
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href="http://moedal.web.cern.ch/">existence of magnetic
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monopoles</a>. <br>
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</p>
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<p><br>
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<br>
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</p>
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<p><br>
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</p>
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<div align="center"><img alt="divider"
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src="divider_ornbarblu.gif" height="64" width="393"><br>
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<h2><u>Gauss' Law for Magnetism</u></h2>
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</div>
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</blockquote>
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<div align="center">
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<div align="left">
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<ul>
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<li>So far we have discussed three basic equations
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describing electromagnetic phenomena - the first three
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of Maxwell's equations.</li>
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</ul>
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<blockquote>
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<div align="center">Gauss' Law: <img
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alt="elecgausseqn3" src="elec_gauss_eqn3.jpg"
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height="84" align="middle" width="233"><br>
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<br>
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</div>
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<div align="center">Ampere's Law: <img
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alt="magampereeqn1" src="mag_ampere_eqn1.jpg"
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height="60" align="middle" width="180"><br>
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<br>
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</div>
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<div align="center">Faraday's Law: <img
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alt="magfaradayeqn6" src="mag_faraday_eqn6.jpg"
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height="58" align="middle" width="297"><br>
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</div>
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</blockquote>
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<div align="center">
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<div align="left">
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<ul>
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<li>Gauss' Law involves the flux integral for the
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electric field. To complete the correspondence
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between electricity and magnetism we expect a fourth
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equation involving the magnetic flux - "Gauss' Law
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for Magnetism".</li>
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</ul>
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<ul>
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<li>The right hand side of Gauss' Law includes a
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summation over electric charges. Therefore,
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for magnetism, we expect a summation over "magnetic
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charges". But magnetic charges, North and
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South poles (equivalent to positive and negative
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electric charges) always exist in pairs, the net
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"magnetic charge" is thus always zero. Gauss'
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Law for Magnetism must therefore take the form,</li>
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</ul>
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<div align="center"><img alt="magmonopolefig5"
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src="mag_monopole_fig5.jpg" height="48" width="171"><br>
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<blockquote>
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<div align="left">the flux of <b>B</b> through a
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closed surface is zero.<br>
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<br>
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<img alt="exclamation" src="exclamation-icon.gif"
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height="30" width="31"> Note that the fact that
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the surface is closed is very important ! A
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magnetic flux integral appears in Faraday's
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Law - in this case the surface is generally <b>not</b>
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closed.<br>
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<br>
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<img alt="hot" src="hot.gif" height="43"
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width="79"> Electric field lines begin
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(positive) and end (negative) on charges.
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Since there are no magnetic charges magnetic field
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lines form closed loops.<br>
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<br>
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<br>
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<div align="center"><img alt="magmonopolefig7"
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src="mag_monopole_fig7.gif" height="206"
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width="260"><br>
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</div>
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</div>
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</blockquote>
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</div>
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<blockquote>
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<blockquote> </blockquote>
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</div>
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<div align="center"><img src="netbar.gif" height="40" width="100%"></div>
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<div align="center">
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<div align="center"> </div>
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<center>
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<p style="color: rgb(255, 0, 0); font-style: italic;"
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class="MsoNormal">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</p>
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<font color="#ff0000"><i>This girl said she recognized me from
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the vegetarian club, but I'd never met herbivore. </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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<blockquote> </blockquote>
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</div>
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</body>
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</html>
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