204 lines
7.5 KiB
HTML
204 lines
7.5 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>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" vlink="#551a8b" alink="#ff0000">
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<center>
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<h1> <img src="ULPhys1.gif" height="50" width="189"
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align="texttop"></h1>
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</center>
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<center>
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<h1>Magnetic Energy<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" width="100%" align="middle">
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<blockquote> </blockquote>
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<ul>
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<li> <img alt="magenergyfig1" src="mag_energy_fig1.gif"
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height="117" width="245" align="right">Let's take a second
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look at the differential equation for the simple LR circuit</li>
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</ul>
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<div align="center"><img alt="magenergyeqn1"
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src="mag_energy_eqn1.jpg" height="84" width="158"><br>
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<blockquote>
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<div align="left">Multiplying throughout by the current I gives<br>
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<div align="center"><img alt="magenergyeqn2"
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src="mag_energy_eqn2.jpg" height="84" width="198"><br>
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<div align="left">This is now an energy conservation
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equation,<br>
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<br>
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<div align="center"> <big><i><b>Rate of thermal heating
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(I</b></i><i><b><sup>2</sup></b></i><i><b>R)
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+ Rate at which energy is stored in the
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inductance (LI dI/dt) = Rate at which
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energy is supplied (εI) <br>
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</b></i></big></div>
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</div>
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</div>
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</div>
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</blockquote>
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<div align="left">
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left">
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<ul>
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<li>The energy stored in the inductance is associated
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with the magnetic field of the inductance, U<sub>B</sub>.
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Therefore,</li>
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</ul>
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<div align="center"><img alt="magenergyeqn3"
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src="mag_energy_eqn3.jpg" height="77" width="144"><br>
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<blockquote>
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<div align="left">which upon integration gives<br>
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<div align="center"><img alt="magenergyeqn4"
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src="mag_energy_eqn4.jpg" height="40"
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width="122"><br>
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<br>
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<div align="left">equivalent to the electrical
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case of energy stored in a capacitor U<sub>E</sub>
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= q<sup>2</sup>/2C = (1/2)CV<sup>2</sup>.<br>
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</div>
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</div>
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</div>
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</blockquote>
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<div align="left">
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<div align="center">
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<div align="left">
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<ul>
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<li>Exactly as in the electric field case, we
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can determine a general expression for the
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energy density (u<sub>B</sub>) stored in a
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magnetic field,</li>
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</ul>
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<div align="center"><img alt="magenergyeqn5"
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src="mag_energy_eqn5.jpg" height="76"
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width="102"></div>
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</div>
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</div>
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</div>
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<blockquote>
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<div align="left"> </div>
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</div>
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</div>
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</blockquote>
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</div>
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<ol>
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</ol>
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<div align="center">
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<blockquote>
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<div align="left"> </div>
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<blockquote>
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<div align="left"> </div>
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</blockquote>
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</div>
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</div>
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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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