211 lines
8.8 KiB
HTML
211 lines
8.8 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 - Mutual Induction - 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>Mutual Induction<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> As we have seen, Faraday's Law of Induction tells us that a
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changing magnetic flux through a circuit will induce an emf and
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therefore an "induced current". Consider the situation of
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two nearby circuits (below) where the flux through circuit 2
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changes due to the changing current in circuit 1.</li>
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</ul>
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<div align="center"><img alt="magmutualindfig1"
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src="mag_mutualind_fig1.jpg" height="261" width="411"><br>
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<div align="left">
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<ul>
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<li>With N<sub>2</sub> turns in circuit 2 the emf is given by</li>
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</ul>
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<div align="center"><img alt="magmutualindeqn1"
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src="mag_mutualind_eqn1.jpg" height="60" width="122"><br>
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<blockquote>
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<div align="left">but the total flux through circuit 2 is
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proportional to the current in circuit 1, where the
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proportionality constant is called the mutual inductance
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of the coils, M<sub>21</sub>,<br>
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<br>
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<div align="center"><img alt="magmutualindeqn2"
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src="mag_mutualind_eqn2.jpg" height="38" width="162"><br>
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<div align="left">Combining these two equations gives<br>
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<br>
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</div>
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</div>
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<div align="center"><img alt="magmutualindeqn3"
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src="mag_mutualind_eqn3.jpg" height="81" width="159"><br>
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<div align="left">In other words the emf in circuit 2 is
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proportional to the rate of change of current in
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circuit 1. As we will see shortly, the mutual
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inductance M<sub>21</sub> depends only on the
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geometric configuration of the two circuits.<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>If the roles of the two circuits are reversed -
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that is a changing current in circuit 2 induces a
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current in circuit 1 - then</li>
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</ul>
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<div align="center"><img alt="magmutualindeqn4"
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src="mag_mutualind_eqn4.jpg" height="81" width="423"><br>
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<div align="left">
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<ul>
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<li>It is "easy" to show that M<sub>21</sub>
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= M<sub>12</sub> . In other words given
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two circuits in a particular configuration it
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doesn't matter in which circuit the current is
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induced the mutual inductance is the same.</li>
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</ul>
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<ul>
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<li><b>UNITS: </b>Inductance is measured in
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Henrys <img alt="Henry" src="Henry.jpg"
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height="135" width="105" align="middle"><br>
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</li>
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</ul>
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<div align="center"><img alt="magmutualindeqn5"
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src="mag_mutualind_eqn5.jpg" height="39"
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width="308"><br>
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<blockquote>
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<div align="left"><img alt="exclamation"
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src="exclamation-icon.gif" height="30"
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width="31"> The concept of inductance is
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related to the magnetic field in a similar way
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that capacitance is related to the electric
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field.<br>
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</div>
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</blockquote>
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<div align="left">
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<ul>
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<li>In order to calculate mutual inductance
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you will typically follow the steps below:</li>
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</ul>
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<blockquote>
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<ol>
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<li>Determine <b>B</b> due to one circuit
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at the location of the other using
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Ampere's Law or the Biot-Savart Law.</li>
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<li>Using this <b>B</b> calculate the
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magnetic flux through the 'other' circuit.</li>
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<li>Then use the equation N<sub>2</sub>Φ<sub>2</sub>
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= MI<sub>1</sub> to obtain M.</li>
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</ol>
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You will always find that <i><b>M depends
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only on the geometric parameters of the
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two circuits and the number of turns in
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each circuit.</b></i><br>
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<ol>
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</ol>
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</blockquote>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</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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</blockquote>
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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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<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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<div align="center">
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<div align="center">
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<div>
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<div align="left">
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<div align="center">
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<div align="left"> </div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</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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</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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