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<title>Magnetism - Magnetic Energy - Physics 299</title>
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<h1> <img src="ULPhys1.gif" height="50" align="texttop"
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<h1>Magnetic Monopoles &amp; Gauss' Law for Magnetism<br>
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<div class="copy-paste-block"><font color="#ff0000"><i><span
class="bqQuoteLink">"A</span></i></font><font
color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
statement that everyone believes.&nbsp; It is innocent,
unless found guilty.&nbsp; A hypothesis is a novel
suggestion that no one wants to believe.&nbsp; It is
guilty, until found effective</span></i><span></span>"</font><br>
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<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
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<h2><img alt="questionmark" src="question_mark.gif" height="54"
align="middle" width="64">&nbsp;&nbsp;&nbsp;&nbsp; <u>Magnetic
Monopoles</u>&nbsp;&nbsp;&nbsp; <img alt="questionmark"
src="question_mark.gif" height="54" align="middle" width="64"></h2>
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<ul>
<li>In our initial discussion of magnetism we made the point that
we were going to treat magnetism in a similar way to
electricity.&nbsp; However, whereas our discussion of
electricity began with electric charges and the electric field
associated with these charges, the magnetic discussion started
with the existence of the magnetic field.&nbsp; No mention was
made of "magnetic charges", which would play the same role in
magnetism as electric charges in electricity.&nbsp; This is
because individual magnetic charges - <b>magnetic monopoles</b>
- are apparently impossible to isolate.</li>
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<ul>
<li>The simplest magnetic object we have been able to isolate is
the <a href="mag_dipole.html">magnetic dipole</a>.&nbsp;
Current loops, bar&nbsp; magnets and solenoids all produce
dipole fields with a characteristic magnetic dipole moment.</li>
</ul>
<div align="center"><img alt="magmonopolefig2"
src="mag_monopole_fig2.jpg" height="170" width="297">&nbsp;&nbsp;&nbsp;
<img alt="magmonopolefig3" src="mag_monopole_fig3.gif"
height="174" width="243"></div>
<ul>
<li>The bar magnetic may be considered to be a combination of two
magnetic monopoles, usually labelled North and South.&nbsp; This
is similar to the electric dipole comprised of equal but
opposite electric charges.</li>
</ul>
<p><br>
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<div align="center"><img alt="mag_monopole_fig1"
src="mag_monopole_fig1.gif" height="233" width="238"> &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; <img alt="magintrofig3" src="mag_intro_fig3.jpg"
height="217" width="290"><br>
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<li><img alt="magmonopolefig4" src="mag_monopole_fig4.jpg"
height="313" align="right" width="243">Whereas with the
electric dipole it is possible to isolate the positive and
negative charges, experimentally it is not possible to
separate the North and South poles of a bar magnet.&nbsp;
Break a magnet in two and you get two magnets, each with a
North and South pole.&nbsp; Continuing this splitting
process down to the atomic level we find that even
elementary particles behave as magnetic dipoles, each with a
North and South pole.&nbsp; It appears that nature does not
allow us to create magnetic monopoles in this way.</li>
</ul>
<ul>
<li><img alt="exclamation" src="exclamation-icon.gif"
height="30" width="31">&nbsp; However, theoreticians
developing unified quantum theories of the Universe,&nbsp;
so-called "Theories of Everything", are almost unanimous in
the necessity for magnetic monopoles as elementary particles
created shortly after the birth of the Universe.</li>
</ul>
<blockquote>
<p>The belief is that shortly after their creation, magnetic
monopoles were "frozen out" - meaning that their
interactions with the rest of the matter in the Universe is
highly suppressed.&nbsp; This does not prevent physicists
from searching for evidence for the <a
href="http://moedal.web.cern.ch/">existence of magnetic
monopoles</a>. <br>
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<div align="center"><img alt="divider"
src="divider_ornbarblu.gif" height="64" width="393"><br>
<h2><u>Gauss' Law for Magnetism</u></h2>
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<li>So far we have discussed three basic equations
describing electromagnetic phenomena - the first three
of Maxwell's equations.</li>
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<div align="center">Gauss' Law: &nbsp; <img
alt="elecgausseqn3" src="elec_gauss_eqn3.jpg"
height="84" align="middle" width="233"><br>
<br>
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<div align="center">Ampere's Law:&nbsp; <img
alt="magampereeqn1" src="mag_ampere_eqn1.jpg"
height="60" align="middle" width="180"><br>
<br>
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<div align="center">Faraday's Law:&nbsp; <img
alt="magfaradayeqn6" src="mag_faraday_eqn6.jpg"
height="58" align="middle" width="297"><br>
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<ul>
<li>Gauss' Law involves the flux integral for the
electric field.&nbsp; To complete the correspondence
between electricity and magnetism we expect a fourth
equation involving the magnetic flux - "Gauss' Law
for Magnetism".</li>
</ul>
<ul>
<li>The right hand side of Gauss' Law includes a
summation over electric charges.&nbsp; Therefore,
for magnetism, we expect a summation over "magnetic
charges".&nbsp; But magnetic charges, North and
South poles (equivalent to positive and negative
electric charges) always exist in pairs, the net
"magnetic charge" is thus always zero.&nbsp; Gauss'
Law for Magnetism must therefore take the form,</li>
</ul>
<div align="center"><img alt="magmonopolefig5"
src="mag_monopole_fig5.jpg" height="48" width="171"><br>
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<div align="left">the flux of <b>B</b> through a
closed surface is zero.<br>
<br>
<img alt="exclamation" src="exclamation-icon.gif"
height="30" width="31"> Note that the fact that
the surface is closed is very important !&nbsp; A
magnetic flux integral&nbsp; appears in Faraday's
Law - in this case the surface is generally <b>not</b>
closed.<br>
<br>
<img alt="hot" src="hot.gif" height="43"
width="79"> Electric field lines begin
(positive) and end (negative) on charges.&nbsp;
Since there are no magnetic charges magnetic field
lines form closed loops.<br>
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<div align="center"><img alt="magmonopolefig7"
src="mag_monopole_fig7.gif" height="206"
width="260"><br>
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<font color="#ff0000"><i>This girl said she recognized me from
the vegetarian club, but I'd never met herbivore. </i></font><br>
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&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>
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