davisnotes/mag_energy.html

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<title>Magnetism - Magnetic Energy - Physics 299</title>
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<h1>Magnetic Energy<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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<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>
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<div align="center"><img alt="magenergyeqn1"
src="mag_energy_eqn1.jpg" height="84" width="158"><br>
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<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>
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<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>
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<li>The energy stored in the inductance is associated
with the magnetic field of the inductance, U<sub>B</sub>.&nbsp;
Therefore,</li>
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<div align="center"><img alt="magenergyeqn3"
src="mag_energy_eqn3.jpg" height="77" width="144"><br>
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<div align="left">which upon integration gives<br>
<div align="center"><img alt="magenergyeqn4"
src="mag_energy_eqn4.jpg" height="40"
width="122"><br>
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<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>
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<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>
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<div align="center"><img alt="magenergyeqn5"
src="mag_energy_eqn5.jpg" height="76"
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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>
<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>
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