98 lines
3.8 KiB
HTML
98 lines
3.8 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>Electricty - Electric Potential due to an Electric Dipole -
|
||
|
|
Physics 299</title>
|
||
|
|
</head>
|
||
|
|
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
|
||
|
|
255);" link="#0000ee" alink="#ff0000" vlink="#551a8b">
|
||
|
|
<center><img src="ULPhys1.gif" height="50" align="texttop"
|
||
|
|
width="189"></center>
|
||
|
|
<center>
|
||
|
|
<h1>Electric Potential due to an Electric Dipole<br>
|
||
|
|
</h1>
|
||
|
|
</center>
|
||
|
|
<center><img src="celticbar.gif" height="22" width="576"><br>
|
||
|
|
<br>
|
||
|
|
<font color="#ff0000"><i>"</i></font><font color="#ff0000"><i>
|
||
|
|
<meta http-equiv="content-type" content="text/html;
|
||
|
|
charset=windows-1252">
|
||
|
|
We will make electricity so cheap that only the rich will burn
|
||
|
|
candles"</i></font><br>
|
||
|
|
Thomas Edison<br>
|
||
|
|
</center>
|
||
|
|
<img src="netbar.gif" height="40" align="middle" width="100%"> <br>
|
||
|
|
<br>
|
||
|
|
<ul>
|
||
|
|
<li>Just as we calculated the electric field due to a dipole it is
|
||
|
|
possible to calculate the electric potential. However, in
|
||
|
|
this case it is convenient to use polar co-ordinates. </li>
|
||
|
|
</ul>
|
||
|
|
<blockquote><img alt="elec dip pot fig1"
|
||
|
|
src="elec_potential_dip_figure1.png" height="446" align="right"
|
||
|
|
width="319">Assuming no azimuthal variation we may write,<br>
|
||
|
|
<br>
|
||
|
|
<div align="center"><img alt="elec pot dip eqn1"
|
||
|
|
src="elec_pot_dip_eqn1.jpg" height="66" width="377"><br>
|
||
|
|
<br>
|
||
|
|
<div align="left">When r >> a, then r<sub>1</sub>, r<sub>2</sub>
|
||
|
|
and r are approximately equal and r<sub>2</sub>- r<sub>1</sub>
|
||
|
|
= 2acosθ. Therefore,<br>
|
||
|
|
<br>
|
||
|
|
<div align="center"><img alt="elec pot dip eqn2"
|
||
|
|
src="elec_pot_dip_eqn2.jpg" height="58" width="356"><br>
|
||
|
|
<br>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</blockquote>
|
||
|
|
<ul>
|
||
|
|
<li><img alt="exclamation" src="exclamation-icon.gif" height="30"
|
||
|
|
width="31"> Note that the dipole potential decreases as 1/r<sup>2</sup>
|
||
|
|
whereas the dipole <b>E</b> field decreases as 1/r<sup>3</sup>
|
||
|
|
.</li>
|
||
|
|
</ul>
|
||
|
|
<ul>
|
||
|
|
<li><img alt="exclamation" src="exclamation-icon.gif" height="30"
|
||
|
|
width="31"> Notice that when θ = 90<sup>0</sup> V<sub>P</sub>
|
||
|
|
= 0, that is it would require no work to bring a charge from
|
||
|
|
infinity to the center of the dipole if it moves along the
|
||
|
|
dipole bisector.<br>
|
||
|
|
</li>
|
||
|
|
</ul>
|
||
|
|
<blockquote>
|
||
|
|
<div align="center">
|
||
|
|
<div align="left"> </div>
|
||
|
|
</div>
|
||
|
|
</blockquote>
|
||
|
|
<img src="netbar.gif" height="40" width="100%">
|
||
|
|
<center>
|
||
|
|
<p class="MsoNormal"><span style="color: rgb(255, 0, 0);
|
||
|
|
font-style: italic;">
|
||
|
|
<meta http-equiv="content-type" content="text/html;
|
||
|
|
charset=windows-1252">
|
||
|
|
"There are three kinds of men. The one that learns by reading.
|
||
|
|
The few who learn by observation. The rest of them have to pee
|
||
|
|
on the electric fence for themselves."</span><br>
|
||
|
|
Will Rogers<br>
|
||
|
|
</p>
|
||
|
|
<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>
|