172 lines
7.3 KiB
HTML
172 lines
7.3 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 - Dipoles - Physics 299</title>
|
|
<meta content="C. L. Davis" name="author">
|
|
</head>
|
|
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
|
|
255);" alink="#ff0000" link="#0000ee" vlink="#551a8b">
|
|
<center>
|
|
<h1> <img src="ULPhys1.gif" align="texttop" height="50"
|
|
width="189"></h1>
|
|
</center>
|
|
<center>
|
|
<h1>Magnetic Dipoles <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. It is innocent,
|
|
unless found guilty. A hypothesis is a novel
|
|
suggestion that no one wants to believe. 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" align="middle" height="40" width="100%">
|
|
<blockquote> </blockquote>
|
|
<ul>
|
|
<li>Shown below is a rectangular current loop sides a and b placed
|
|
in a region of space with uniform magnetic field (<b>B</b>).<br>
|
|
</li>
|
|
</ul>
|
|
<div align="center"><img alt="magdipfig1" src="mag_dipole_fig1.jpg"
|
|
height="368" width="328">
|
|
<img
|
|
alt="magdipfig2" src="mag_dipole_fig2.jpg" height="346"
|
|
width="309"><br>
|
|
<br>
|
|
<div align="left">
|
|
<ul>
|
|
<li>Application of the expression for the force on a current
|
|
carrying wire to the top and bottom sides of the rectangle
|
|
leads to cancellation of forces as shown.</li>
|
|
</ul>
|
|
<ul>
|
|
<li>The forces on the other two sides (length a) are also
|
|
equal and opposite, as shown in (b) above, <img
|
|
alt="magdipeqn3" src="mag_dipole_eqn3.jpg" align="middle"
|
|
height="42" width="117">. Although the net <i><b>force</b></i>
|
|
in this case is zero, because the forces are not co-linear,
|
|
there is a net <i><b>torque</b></i> on the current loop,
|
|
given by</li>
|
|
</ul>
|
|
<div align="center"><img alt="magdipeqn1"
|
|
src="mag_dipole_eqn1.jpg" height="37" width="279"><br>
|
|
<blockquote>
|
|
<div align="left">The magnitude of this torque is given by<br>
|
|
<div align="center"><img alt="magdipeqn2"
|
|
src="mag_dipole_eqn2.jpg" height="49" width="423"><br>
|
|
<br>
|
|
<div align="left">where A = ab is the cross section area
|
|
of the coil.<br>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</blockquote>
|
|
<div align="left">
|
|
<div align="center">
|
|
<div align="left">
|
|
<ul>
|
|
<li>The magnitude of the magnetic dipole moment of the
|
|
loop with N turns is defined by,</li>
|
|
</ul>
|
|
<div align="center"><img alt="magdipeqn4"
|
|
src="mag_dipole_eqn4.jpg" height="42" width="99"><br>
|
|
<blockquote>
|
|
<div align="left"><img alt="magdipfig3"
|
|
src="mag_dipole_fig3.jpg" align="right"
|
|
height="149" width="234">μ is a vector quantity
|
|
whose direction is perpendicular to the loop with
|
|
a sense defined by (another) <b>Right Hand Rule</b>.<br>
|
|
</div>
|
|
</blockquote>
|
|
<div align="left">
|
|
<ul>
|
|
<li>With this definition of μ the torque on the
|
|
current loop is given by</li>
|
|
</ul>
|
|
<div align="center"> <img alt="magdipeqn5"
|
|
src="mag_dipole_eqn5.jpg" height="33" width="99"><br>
|
|
<div align="left">
|
|
<ul>
|
|
<li>Without proof, the potential energy of a
|
|
magnetic dipole in an external magnetic
|
|
field is given by</li>
|
|
</ul>
|
|
<div align="center"><img alt="magdipeqn6"
|
|
src="mag_dipole_eqn6.jpg" height="33"
|
|
width="117"><br>
|
|
<br>
|
|
<div align="left"><img alt="hot" src="hot.gif"
|
|
height="43" width="79"> Note that the
|
|
above expressions for the torque and
|
|
potential energy of a magnetic dipole in an
|
|
external magnetic field are identical in
|
|
form to those obtained for an electric
|
|
dipole in an external electric field.<br>
|
|
<br>
|
|
<div align="center"><img alt="elecdipext"
|
|
src="elec_dipexte_eqn1.jpg" height="45"
|
|
width="117">
|
|
|
|
and <img
|
|
alt="elecdipextf2"
|
|
src="elec_dipexte_eqn2.jpg" height="41"
|
|
width="117"><br>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<blockquote>
|
|
<div align="left"> </div>
|
|
</blockquote>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<img src="netbar.gif" height="40" width="100%">
|
|
<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>I stayed up all night to see where the
|
|
sun went. Then it dawned on me.</i></font><br>
|
|
<br>
|
|
<img src="celticbar.gif" height="22" width="576"> <br>
|
|
|
|
<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>
|
|
</p>
|
|
<p><img src="header-index.gif" height="51" width="92"> </p>
|
|
</center>
|
|
<p><br>
|
|
</p>
|
|
</body>
|
|
</html>
|