davisnotes/mag_energy.html

204 lines
7.5 KiB
HTML

<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0
alpha) [Netscape]">
<meta name="Author" content="C. L. Davis">
<title>Magnetism - Magnetic Energy - Physics 299</title>
<meta content="C. L. Davis" name="author">
</head>
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
255);" link="#0000ee" vlink="#551a8b" alink="#ff0000">
<center>
<h1> <img src="ULPhys1.gif" height="50" width="189"
align="texttop"></h1>
</center>
<center>
<h1>Magnetic Energy<br>
</h1>
</center>
<center><img src="celticbar.gif" height="22" width="576"><br>
<br>
<font color="#ff0000"><i>
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</i></font><font color="#ff0000"><i>
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</i></font>
<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>
</div>
<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
</center>
<img src="netbar.gif" height="40" width="100%" align="middle">
<blockquote> </blockquote>
<ul>
<li> <img alt="magenergyfig1" src="mag_energy_fig1.gif"
height="117" width="245" align="right">Let's take a second
look at the differential equation for the simple LR circuit</li>
</ul>
<div align="center"><img alt="magenergyeqn1"
src="mag_energy_eqn1.jpg" height="84" width="158"><br>
<blockquote>
<div align="left">Multiplying throughout by the current I gives<br>
<div align="center"><img alt="magenergyeqn2"
src="mag_energy_eqn2.jpg" height="84" width="198"><br>
<div align="left">This is now an energy conservation
equation,<br>
<br>
<div align="center"> <big><i><b>Rate of thermal heating
(I</b></i><i><b><sup>2</sup></b></i><i><b>R)&nbsp;
+&nbsp; Rate at which energy is stored in the
inductance (LI dI/dt)&nbsp; =&nbsp; Rate at which
energy is supplied&nbsp; (&#949;I) <br>
</b></i></big></div>
</div>
</div>
</div>
</blockquote>
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<ul>
<li>The energy stored in the inductance is associated
with the magnetic field of the inductance, U<sub>B</sub>.&nbsp;
Therefore,</li>
</ul>
<div align="center"><img alt="magenergyeqn3"
src="mag_energy_eqn3.jpg" height="77" width="144"><br>
<blockquote>
<div align="left">which upon integration gives<br>
<div align="center"><img alt="magenergyeqn4"
src="mag_energy_eqn4.jpg" height="40"
width="122"><br>
<br>
<div align="left">equivalent to the electrical
case of energy stored in a capacitor U<sub>E</sub>
= q<sup>2</sup>/2C = (1/2)CV<sup>2</sup>.<br>
</div>
</div>
</div>
</blockquote>
<div align="left">
<div align="center">
<div align="left">
<ul>
<li>Exactly as in the electric field case, we
can determine a general expression for the
energy density (u<sub>B</sub>) stored in a
magnetic field,</li>
</ul>
<div align="center"><img alt="magenergyeqn5"
src="mag_energy_eqn5.jpg" height="76"
width="102"></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<blockquote>
<div align="left">
<div align="center">
<div align="left"> </div>
</div>
</div>
</blockquote>
</div>
<ol>
</ol>
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left"> </div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<blockquote>
<div align="left"> </div>
</blockquote>
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="center">
<div>
<div align="left">
<div align="center">
<div align="left"> </div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<blockquote>
<div align="left"> </div>
</blockquote>
</div>
</div>
<blockquote> </blockquote>
</div>
<div align="center"><img src="netbar.gif" height="40" width="100%"></div>
<div align="center">
<div align="center"> </div>
<center>
<p style="color: rgb(255, 0, 0); font-style: italic;"
class="MsoNormal">
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</p>
<font color="#ff0000"><i>This girl said she recognized me from
the vegetarian club, but I'd never met herbivore. </i></font><br>
<br>
&nbsp;<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>
<blockquote> </blockquote>
</div>
</body>
</html>