davisnotes/elec_potential_dipole.html

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<title>Electricty - Electric Potential due to an Electric Dipole -
Physics 299</title>
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<h1>Electric Potential due to an Electric Dipole<br>
</h1>
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<center><img src="celticbar.gif" height="22" width="576"><br>
<br>
<font color="#ff0000"><i>"</i></font><font color="#ff0000"><i>
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charset=windows-1252">
We will make electricity so cheap that only the rich will burn
candles"</i></font><br>
Thomas Edison<br>
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<ul>
<li>Just as we calculated the electric field due to a dipole it is
possible to calculate the electric potential.&nbsp; However, in
this case it is convenient to use polar co-ordinates.&nbsp; </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 &gt;&gt; a, then r<sub>1</sub>, r<sub>2</sub>
and r are approximately equal and r<sub>2</sub>- r<sub>1</sub>
= 2acos&#952;.&nbsp; Therefore,<br>
<br>
<div align="center"><img alt="elec pot dip eqn2"
src="elec_pot_dip_eqn2.jpg" height="58" width="356"><br>
<br>
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</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 &#952; = 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>
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<div align="left"> </div>
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"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>
&nbsp;
<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>
&nbsp; </p>
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