98 lines
3.8 KiB
HTML
98 lines
3.8 KiB
HTML
<!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>Electricty - Electric Potential due to an Electric Dipole -
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Physics 299</title>
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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" alink="#ff0000" vlink="#551a8b">
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<center><img src="ULPhys1.gif" height="50" align="texttop"
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width="189"></center>
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<center>
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<h1>Electric Potential due to an Electric Dipole<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>"</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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We will make electricity so cheap that only the rich will burn
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candles"</i></font><br>
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Thomas Edison<br>
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</center>
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<img src="netbar.gif" height="40" align="middle" width="100%"> <br>
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<br>
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<ul>
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<li>Just as we calculated the electric field due to a dipole it is
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possible to calculate the electric potential. However, in
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this case it is convenient to use polar co-ordinates. </li>
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</ul>
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<blockquote><img alt="elec dip pot fig1"
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src="elec_potential_dip_figure1.png" height="446" align="right"
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width="319">Assuming no azimuthal variation we may write,<br>
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<br>
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<div align="center"><img alt="elec pot dip eqn1"
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src="elec_pot_dip_eqn1.jpg" height="66" width="377"><br>
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<br>
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<div align="left">When r >> a, then r<sub>1</sub>, r<sub>2</sub>
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and r are approximately equal and r<sub>2</sub>- r<sub>1</sub>
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= 2acosθ. Therefore,<br>
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<br>
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<div align="center"><img alt="elec pot dip eqn2"
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src="elec_pot_dip_eqn2.jpg" height="58" width="356"><br>
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<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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<ul>
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<li><img alt="exclamation" src="exclamation-icon.gif" height="30"
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width="31"> Note that the dipole potential decreases as 1/r<sup>2</sup>
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whereas the dipole <b>E</b> field decreases as 1/r<sup>3</sup>
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.</li>
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</ul>
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<ul>
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<li><img alt="exclamation" src="exclamation-icon.gif" height="30"
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width="31"> Notice that when θ = 90<sup>0</sup> V<sub>P</sub>
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= 0, that is it would require no work to bring a charge from
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infinity to the center of the dipole if it moves along the
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dipole bisector.<br>
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</li>
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</ul>
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<blockquote>
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<div align="center">
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<div align="left"> </div>
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</div>
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</blockquote>
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<img src="netbar.gif" height="40" width="100%">
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<center>
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<p class="MsoNormal"><span style="color: rgb(255, 0, 0);
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font-style: italic;">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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"There are three kinds of men. The one that learns by reading.
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The few who learn by observation. The rest of them have to pee
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on the electric fence for themselves."</span><br>
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Will Rogers<br>
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</p>
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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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