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<!DOCTYPE HTML PUBLIC "-//w3c//dtd html 4.0 transitional//en">
<html>
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<meta http-equiv="Content-Type"
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<meta name="GENERATOR"
content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0 alpha) [Netscape]">
<meta name="Author" content="C. L. Davis">
<title>Electricity - Electric Field - Physics 299</title>
</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>Electric Field</h1>
</center>
<center><img src="celticbar.gif" height="22" width="576"><br>
<br>
<font color="#ff0000"><i>"Discovery consists of seeing what everybody
has
seen and thinking what nobody has thought"</i></font><br>
Albert von Szent-Gyorgyi<br>
</center>
<img src="netbar.gif" align="middle" height="40" width="100%"> <br>
&nbsp;
<ul>
<li>When two charges exert a force on each other, through what means
is the force transmitted ?</li>
</ul>
<div style="margin-left: 40px;">The simplest assumption is "<span
style="font-style: italic; font-weight: bold;">action-at-a-distance</span>".&nbsp;
They just "<span style="font-weight: bold; font-style: italic;">know</span>"
about each other's presence.&nbsp; If one of the charges moves the
other charge is aware of this immediately.&nbsp; This sounds like
"magic" with today's scientific understanding.&nbsp; <br>
The mechanism to remove the magic was proposed by <a
href="http://www.bbc.co.uk/history/historic_figures/faraday_michael.shtml">
Michael Faraday&nbsp;</a> <a
href="http://www.rigb.org/contentControl?action=detail&amp;section=1391&amp;pg=4&amp;filter=pd"><img
alt="faraday" src="faraday.jpg"
style="border: 0px solid ; width: 80px; height: 121px;" align="middle"></a>
- the <span style="font-weight: bold;">electric field</span>.&nbsp;
Every charge creates its own electric field in the space around it
(actually the space around it means all space); other charges then
interact with this field.&nbsp; When a charge moves it creates a
disturbance in its electric field which is propagated away from the
charge at the speed of light.<br>
<br>
<img style="width: 31px; height: 30px;" alt="exclamation"
src="exclamation-icon.gif"> In developing his theory of gravitation
Newton was aware of the same "<span
style="font-style: italic; font-weight: bold;">action-at-a-distance</span>"
problem.&nbsp; To solve the problem, in a similar manner, we introduce
the concept of the gravitational field.<br>
<br>
<img style="width: 31px; height: 30px;" alt="exclamation"
src="exclamation-icon.gif"> Note that the concept of the electric
field is a convenient construct to describe electromagnetic
phenomena,
but its true existence is neither proven nor essential.</div>
<ul>
<br>
&nbsp;
<li> The electric field vector, <span style="font-weight: bold;">E</span>,&nbsp;
is defined in the following way.&nbsp; If a charge, q, feels a force <b><u>F</u></b>,
then
the
electric field, <b><u>E</u></b>, at the location of the charge
is
given by</li>
<center>
<p><br>
<b><u><img alt="" src="elec_field_eqn1.gif"
style="width: 43px; height: 44px;"></u></b><br>
</p>
</center>
<br>
<li> Units of electric field are&nbsp; Newtons/Coulomb (N/C) or (as
we shall see later) Volts/metre (V/m).</li>
<br>
&nbsp;
<li> If the electric field felt by the charge q is due to
a point
charge Q, located a distance R from q, then its magnitude is given by</li>
<br>
<center>
<p><img alt="" src="elec_field_eqn2.gif"
style="width: 55px; height: 41px;"><br>
</p>
</center>
<br>
<li> The electric field due to many point charges is given by the
vector
sum of the fields due to the individual charges</li>
<br>
<center>
<p><b><u>E</u></b>&nbsp; =&nbsp; <b><u>E</u></b><sub>1</sub>&nbsp; +
<b><u>
E</u></b><sub> 2</sub> +&nbsp; <b><u>E</u></b> <sub>3</sub> +&nbsp;
.....</p>
</center>
<br>
<p>In performing this sum the direction of each <b><u>E</u></b>&nbsp;
is
the
same as the force felt by a <b><i>positive</i></b> charge. <br>
&nbsp; </p>
<li> The electric field in a region of space can be represented by
electric field lines otherwise known as "<b><i>lines of force</i></b>".</li>
<br>
<center>
<p><img src="efield_lines1.gif" align="texttop" height="221"
width="370"> </p>
</center>
<br>
<p>The direction of the electric field line is the same as that of
the force
felt by a positive charge.&nbsp; The density of the field lines
provides a
measure of the magnitude of the field.&nbsp; FIeld lines alway begin on
positive
charges and end on negative charges; they cannot be left 'hanging' in
empty
space. <br>
</p>
</ul>
<div style="text-align: center;"><img
style="width: 745px; height: 254px;" alt="efield_lines3.jpg"
src="efield_lines3.jpg"><br>
</div>
<ul>
<p><br>
</p>
<center>
<p>The diagrams above display the electric field lines in the
vicinity of
two equal point charges.</p>
</center>
</ul>
<div style="text-align: left;"><img src="netbar.gif" height="40"
width="100%">
</div>
<center><br>
<span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;"><span
style="color: rgb(255, 0, 0); font-style: italic;">"Two things are
infinite: the universe and human
stupidity; and I'm not sure about the universe."</span><br style="">
<!--[if !supportLineBreakNewLine]-->Albert Einstein</span><br>
<br>
<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>
<p><img src="header-index.gif" height="51" width="92">
</p>
</center>
<p><br>
</p>
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