297 lines
9.6 KiB
HTML
297 lines
9.6 KiB
HTML
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<!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>Magnetism - Force on Charges - Physics 299</title>
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<meta content="C. L. Davis" name="author">
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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);" alink="#ff0000" link="#0000ee" vlink="#551a8b">
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<center>
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<h1> <img src="ULPhys1.gif" align="texttop" height="50"
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width="189"></h1>
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</center>
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<center>
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<h1>Magnetic Forces on Charged Particles <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>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</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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</i></font>
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<div class="copy-paste-block"><font color="#ff0000"><i><span
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class="bqQuoteLink">"A</span></i></font><font
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color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
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statement that everyone believes. It is innocent,
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unless found guilty. A hypothesis is a novel
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suggestion that no one wants to believe. It is
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guilty, until found effective</span></i><span></span>"</font><br>
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</div>
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<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
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</center>
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<img src="netbar.gif" align="middle" height="40" width="100%"> <br>
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<ul>
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<li> Proceeding under the assumption that magnetic fields exist -
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created by an as yet not described mechanism - the magnetic
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force on a <b>positively</b> charged particle is found
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experimentally to be given by
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<div align="center"><img alt="magforcechargeeqn1"
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src="mag_force_charge_eqn1.jpg" align="middle" height="33"
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width="135"></div>
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</li>
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</ul>
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<blockquote>
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<p>where q is the charge (positive) of the particle, <b>v </b>its
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velocity, <b>F<sub>B</sub> </b>the force it experiences and <b>B</b>
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the magnetic field causing the force.<br>
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</p>
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</blockquote>
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<ul>
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<li>
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<div align="center">
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<div align="left"> <img alt="exclamation"
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src="exclamation-icon.gif" height="30" width="31"> Note
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that this equation is the magnetic equivalent of the
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electric expression <b>F<sub>E</sub> = </b>q<b>E</b></div>
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</div>
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</li>
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</ul>
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<ul>
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<div align="left">
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<li>The expression for the magnetic force is written in terms of
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a vector (cross) product, which means, like it or not, you
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have to work in three dimensions. Several important
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facts emerge from this equation. <br>
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<ol>
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<br>
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<li>If <b>v</b> = 0 there is no force. Electric
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charges at rest in a magnetic field do not feel a magnetic
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force. </li>
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<br>
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<li>The magnitude of <b>F<sub>B</sub> </b>is given by
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<div align="center"><img alt="magforcechargeeqn2"
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src="mag_force_charge_eqn2.jpg" height="37"
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width="162"></div>
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<br>
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where φ is the angle between <b>v</b> and <b>B</b>.
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<ul>
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</ul>
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<ul>
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<li> So that, when <b>v</b> is parallel to <b>B</b> (φ
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= 0) or antiparallel to <b>B (</b>φ = 180<sup>o</sup>)
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then sinφ = 0 and <b>F<sub>B</sub> </b>= 0.
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Therefore, charged particles moving along magnetic
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field lines experience no magnetic force. </li>
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</ul>
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<ul>
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<li> When <b>v</b> and <b>B</b> are at 90<sup>o</sup>
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<b>F<sub>B</sub> </b>has its maximum value, F<sub>B</sub>
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= qvB. </li>
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</ul>
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</li>
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<br>
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<li> <b>F<sub>B</sub> </b>is at right angles to <b>v</b>
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and <b>B</b>. The "sense" is given by the usual
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rules for the vector (cross) product, sometimes called
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(the) "<b>Right Hand Rule"</b>.
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<div align="center"><img alt="magforcechargefig1"
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src="mag_force_charge_fig1.jpg" height="243"
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width="479"><br>
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</div>
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<br>
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This leads to circular (or spiral) motion around the <b>B</b>
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field lines.<br>
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<br>
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<div align="center"><img alt="magforcechargefig2"
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src="mag_force_charge_fig2.jpg" height="378"
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width="337"> <img
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alt="magforcechargefig3"
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src="mag_force_charge_fig3.jpg" height="315"
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width="401"><br>
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<br>
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</div>
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<div align="center">
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<div><img alt="hot" src="hot.gif" height="43" width="79">Don't
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forget that the direction of the magnetic force
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obtained above is for a <b>positive</b> charge.
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For a negative charge the direction of <b>F<sub>B</sub> </b>
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is reversed. <br>
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</div>
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</div>
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</li>
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<div align="left"> <br>
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<li>The work done by the magnetic force when a charged
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particle is displaced by <b>ds</b> is given by, </li>
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</div>
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<br>
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<div align="center"><br>
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<img alt="magforcechargeeqn3"
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src="mag_force_charge_eqn3.jpg" height="32" width="244">
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</div>
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<div align="left">where θ is the angle between <b>F<sub>B</sub></b><sub>
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</sub>and <b>ds</b>.<br>
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</div>
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<div align="left"> The displacement <b>ds</b> and the
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velocity of the particle, <b>v</b>, are in the same
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direction, so θ is also the angle between <b>F<sub>B</sub></b><sub>
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</sub>and <b>v</b>. But from the form of the
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magnetic force we know <b>F<sub>B</sub></b><sub> </sub>and
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<b>v </b>are perpendicular (θ = 90<sup>o</sup>) therefore
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dW is always zero. In other words the <i><b>magnetic
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force does no work,</b></i> which means, unlike the
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electric force, it cannot give a charged particle energy
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(increase or decrease its kinteic energy). The effect of a
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magnetic force is to change the direction not the kinetic
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energy.</div>
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</ol>
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</li>
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</div>
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<br>
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</ul>
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<div align="center"><img alt="divider" src="divider_ornbarblu.gif"
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height="64" width="393"><br>
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</div>
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<ul>
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<li> If a charged particle feels both a magnetic and electric
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field the resultant force is given by </li>
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</ul>
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<br>
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<div align="center"><img alt="magforcechargeeqn4"
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src="mag_force_charge_eqn4.jpg" height="35" width="189"><br>
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<blockquote> </blockquote>
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<blockquote>
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<div align="left">this is known as the Lorentz Force Law.<br>
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<br>
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<div align="center"><img alt="divider"
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src="divider_ornbarblu.gif" height="64" width="393"><br>
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<br>
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</div>
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</div>
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</blockquote>
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<div align="left">
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<div align="left">
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<ul>
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<li><big><u><b>UNITS</b></u></big></li>
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</ul>
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<blockquote>
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<p>From the form of the magnetic force we see that the units
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of <b>B</b> are N/(C.m/s) = N/(A.m). This
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combination of basic units is defined as the Tesla.<br>
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</p>
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<div align="center"> <img alt="magforcechargeeqn5"
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src="mag_force_charge_eqn5.jpg" height="56" width="153">
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</div>
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<p>The Tesla is a very large unit of magnetic field.
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For this reason you may occasionally come across the
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smaller unit of magnteic field, the Gauss; where 1
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Tesla = 10<sup>4</sup> Gauss.<br>
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</p>
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</blockquote>
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</div>
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</div>
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<blockquote>
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<div align="left"> </div>
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</blockquote>
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<blockquote> </blockquote>
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</div>
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<img src="netbar.gif" height="40" width="100%">
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<center>
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<p style="color: rgb(255, 0, 0); font-style: italic;"
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class="MsoNormal">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</p>
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<font color="#ff0000"><i>Q: What did one quantum physicist say
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when he wanted to fight another quantum physicist?<br>
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A: Let me <font color="#ff0000">atom</font>. </i></font><br>
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<br>
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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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