172 lines
7.3 KiB
HTML
172 lines
7.3 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 - Dipoles - 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);" alink="#ff0000" link="#0000ee" vlink="#551a8b">
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<center>
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<h1> <img src="ULPhys1.gif" align="texttop" height="50"
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width="189"></h1>
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</center>
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<center>
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<h1>Magnetic Dipoles <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" align="middle" height="40" width="100%">
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<blockquote> </blockquote>
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<ul>
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<li>Shown below is a rectangular current loop sides a and b placed
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in a region of space with uniform magnetic field (<b>B</b>).<br>
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</li>
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</ul>
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<div align="center"><img alt="magdipfig1" src="mag_dipole_fig1.jpg"
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height="368" width="328">
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<img
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alt="magdipfig2" src="mag_dipole_fig2.jpg" height="346"
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width="309"><br>
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<br>
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<div align="left">
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<ul>
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<li>Application of the expression for the force on a current
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carrying wire to the top and bottom sides of the rectangle
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leads to cancellation of forces as shown.</li>
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</ul>
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<ul>
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<li>The forces on the other two sides (length a) are also
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equal and opposite, as shown in (b) above, <img
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alt="magdipeqn3" src="mag_dipole_eqn3.jpg" align="middle"
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height="42" width="117">. Although the net <i><b>force</b></i>
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in this case is zero, because the forces are not co-linear,
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there is a net <i><b>torque</b></i> on the current loop,
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given by</li>
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</ul>
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<div align="center"><img alt="magdipeqn1"
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src="mag_dipole_eqn1.jpg" height="37" width="279"><br>
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<blockquote>
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<div align="left">The magnitude of this torque is given by<br>
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<div align="center"><img alt="magdipeqn2"
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src="mag_dipole_eqn2.jpg" height="49" width="423"><br>
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<br>
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<div align="left">where A = ab is the cross section area
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of the coil.<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>The magnitude of the magnetic dipole moment of the
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loop with N turns is defined by,</li>
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</ul>
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<div align="center"><img alt="magdipeqn4"
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src="mag_dipole_eqn4.jpg" height="42" width="99"><br>
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<blockquote>
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<div align="left"><img alt="magdipfig3"
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src="mag_dipole_fig3.jpg" align="right"
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height="149" width="234">μ is a vector quantity
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whose direction is perpendicular to the loop with
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a sense defined by (another) <b>Right Hand Rule</b>.<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>With this definition of μ the torque on the
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current loop is given by</li>
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</ul>
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<div align="center"> <img alt="magdipeqn5"
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src="mag_dipole_eqn5.jpg" height="33" width="99"><br>
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<div align="left">
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<ul>
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<li>Without proof, the potential energy of a
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magnetic dipole in an external magnetic
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field is given by</li>
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</ul>
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<div align="center"><img alt="magdipeqn6"
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src="mag_dipole_eqn6.jpg" height="33"
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width="117"><br>
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<br>
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<div align="left"><img alt="hot" src="hot.gif"
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height="43" width="79"> Note that the
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above expressions for the torque and
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potential energy of a magnetic dipole in an
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external magnetic field are identical in
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form to those obtained for an electric
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dipole in an external electric field.<br>
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<br>
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<div align="center"><img alt="elecdipext"
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src="elec_dipexte_eqn1.jpg" height="45"
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width="117">
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and <img
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alt="elecdipextf2"
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src="elec_dipexte_eqn2.jpg" height="41"
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width="117"><br>
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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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</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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<img src="netbar.gif" height="40" width="100%">
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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>I stayed up all night to see where the
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sun went. Then it dawned on me.</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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</body>
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</html>
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