davisnotes/elec_potential_efromV.html

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<title>Electricty - Electric Field from Electric Potential - Physics
299</title>
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<center><img src="ULPhys1.gif" align="texttop" height="50"
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<h1>Determining the Electric Field from the Electric Potential<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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</i></font><font color="#ff0000"><i>
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I've found out so much about electricity that I've reached the
point where I understand nothing and can explain nothing"<br>
<i>[Describing his experiments with the Leyden jar.]</i></i></font><br>
Pieter van Musschenbroek<br>
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<ul>
<li>Suppose we are given the electric potential, V, as a function
of position.&nbsp; Is it possible to determine the <b>E</b>
field from this V ?</li>
</ul>
<blockquote>Starting from the definition of the potential difference
in terms of the <b>E</b> field,<br>
<div align="center"><img alt="elec pot eqn2"
src="elec_potential_eqn2.jpg" height="75" width="519"><br>
<br>
<div align="left">then if the path A to B is along the x axis we
obtain,<br>
<div align="center"><img alt="elec pot efromV eqn1"
src="elec_potential_efromV_eqn1.png" height="43"
width="152"><br>
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</blockquote>
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<ul>
<li>This expression can be written in the alternative
form,</li>
</ul>
<div align="center"><img alt="eqn2"
src="elec_potential_efromV_eqn2a.jpg" height="55"
width="92"><br>
<br>
<blockquote>
<div align="left">If the path A to B is in an arbitrary
direction we obtain the most general expression of "E
from V",<br>
<br>
<div align="center"><img alt="elec pot efromV eqn3"
src="elec_potential_efromV_eqn3.png" height="66"
width="507"><br>
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</blockquote>
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"</span><span style="color: rgb(255, 0, 0); font-style:
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I am an expert of electricity. My father occupied the chair of
applied electricity at the state prison."</span><br>
W. C. Fields<br>
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<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>
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