Tyler Clarke
81608a95f8
All checks were successful
Build / Build-Docker-Image (push) Successful in 37s
346 lines
45 KiB
HTML
346 lines
45 KiB
HTML
<?xml version="1.0" encoding="UTF-8"?>
|
||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd">
|
||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
|
||
<!--This file was converted to xhtml by LibreOffice - see https://cgit.freedesktop.org/libreoffice/core/tree/filter/source/xslt for the code.-->
|
||
|
||
<head profile="http://dublincore.org/documents/dcmi-terms/">
|
||
<meta http-equiv="Content-Type" content="application/xhtml+xml; charset=utf-8"/>
|
||
<title xml:lang="en-US">- no title specified</title>
|
||
<meta name="DCTERMS.title" content="" xml:lang="en-US"/>
|
||
|
||
<meta name="DCTERMS.language" content="en-US" scheme="DCTERMS.RFC4646"/>
|
||
<meta name="DCTERMS.source" content="http://xml.openoffice.org/odf2xhtml"/>
|
||
|
||
<meta name="DCTERMS.issued" content="2025-03-07T12:36:55.052635005" scheme="DCTERMS.W3CDTF"/>
|
||
|
||
<meta name="DCTERMS.modified" content="2025-03-07T14:44:03.076224426" scheme="DCTERMS.W3CDTF"/>
|
||
|
||
|
||
<meta name="xsl:vendor" content="libxslt"/>
|
||
<link rel="schema.DC" href="http://purl.org/dc/elements/1.1/" hreflang="en"/>
|
||
<link rel="schema.DCTERMS" href="http://purl.org/dc/terms/" hreflang="en"/>
|
||
<link rel="schema.DCTYPE" href="http://purl.org/dc/dcmitype/" hreflang="en"/>
|
||
<link rel="schema.DCAM" href="http://purl.org/dc/dcam/" hreflang="en"/>
|
||
|
||
<style>
|
||
table { border-collapse:collapse; border-spacing:0; empty-cells:show }
|
||
td, th { vertical-align:top; font-size:12pt;}
|
||
h1, h2, h3, h4, h5, h6 { clear:both;}
|
||
ol, ul { margin:0; padding:0;}
|
||
li { list-style: none; margin:0; padding:0;}
|
||
span.footnodeNumber { padding-right:1em; }
|
||
span.annotation_style_by_filter { font-size:95%; font-family:Arial; background-color:#fff000; margin:0; border:0; padding:0; }
|
||
span.heading_numbering { margin-right: 0.8rem; }* { margin:0;}
|
||
.graphic-fr1{ background-color:transparent; font-size:12pt; font-family:'Liberation Serif'; vertical-align:top; writing-mode:horizontal-tb; direction:ltr; }
|
||
.graphic-fr2{ background-color:transparent; font-size:12pt; margin-left:0in; margin-right:0in; font-family:'Liberation Serif'; vertical-align:top; writing-mode:horizontal-tb; direction:ltr; }
|
||
.paragraph-P1{ font-size:12pt; font-family:'Liberation Serif'; writing-mode:horizontal-tb; direction:ltr;font-weight:bold; }
|
||
.paragraph-P2{ font-size:12pt; font-family:'Liberation Serif'; writing-mode:horizontal-tb; direction:ltr;font-weight:normal; }
|
||
.paragraph-P3{ font-size:12pt; font-family:'Liberation Serif'; writing-mode:horizontal-tb; direction:ltr;font-style:normal; font-weight:normal; }
|
||
.paragraph-P4{ font-size:12pt; font-family:'Liberation Serif'; writing-mode:horizontal-tb; direction:ltr;}
|
||
.paragraph-P5{ font-size:12pt; font-family:'Liberation Serif'; writing-mode:horizontal-tb; direction:ltr;}
|
||
.paragraph-P6{ font-size:12pt; font-family:'Liberation Serif'; writing-mode:horizontal-tb; direction:ltr;}
|
||
.text-T1{ font-style:italic; }
|
||
.text-T2{ font-style:normal; }
|
||
.text-T3{ font-style:normal; text-decoration:none ! important; font-weight:normal; }
|
||
.text-T4{ font-style:normal; text-decoration:none ! important; font-weight:normal; }
|
||
.text-T5{ font-style:italic; text-decoration:none ! important; font-weight:normal; }
|
||
.text-T6{ font-style:normal; text-decoration:none ! important; font-weight:normal; }
|
||
/* ODF styles with no properties representable as CSS:
|
||
.dp1 { } */
|
||
</style>
|
||
</head>
|
||
|
||
<body dir="ltr" style="max-width:8.5in;margin-top:0.7874in; margin-bottom:0.7874in; margin-left:0.7874in; margin-right:0.7874in; ">
|
||
|
||
<p class="paragraph-P1">Compass Angle Hell</p>
|
||
|
||
<p class="paragraph-P2">by Tyler Clarke</p>
|
||
<p class="paragraph-P2"> </p>
|
||
<p class="paragraph-P2">Well, <span class="text-T1">je suis retourné</span><span class="text-T2">! The exam went well, and although I’m not sure what I got exactly, I think it was probably good. One thing I noticed was an uncomfortable amount of trigonometry: I had to derive polar coordinate forms for a translated circle, among other things. Fortunately, trig was always a strong suit.</span></p>
|
||
|
||
<p class="paragraph-P3">My other classes seem to be picking up on the trig craze too, which is in fact why I’m here: the very first question on my homework set for this week in Physics (yeah, I know I’m doing it pretty late, shoot me) requires finding the magnetic dipole of a bar magnet… knowing nothing but the local strength of the earth’s magnetic field, and the angle of a compass affected by both.</p>
|
||
|
||
<p class="paragraph-P3">The problem is not too hard from a trigonometry perspective, but there are a few stumbling blocks. Rather than trust my geometric intuition, I drew this handy lil’ diagram:</p>
|
||
|
||
<!--Next 'div' was a 'text:p'.-->
|
||
<div class="paragraph-P2">
|
||
<!--Next 'div' is a draw:frame. -->
|
||
<div style="height:4.3035in;width:4.8366in; padding:0; float:left; position:relative; left:-0.173cm; top:0.1011cm; " class="graphic-fr1" id="Image1"><img style="height:10.9309cm;width:12.285cm;" alt="" src="data:image/png;base64,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"/></div><div style="clear:both; line-height:0; width:0; height:0; margin:0; padding:0;"> </div><span class="text-T2"/></div>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<p class="paragraph-P2"><span class="text-T2"/></p>
|
||
|
||
<!--Next 'div' was a 'text:p'.-->
|
||
<div class="paragraph-P4"><span class="text-T3">We know that the magnetic field of the Earth is 3e-5 Tesla at the observation point (the origin), the bar magnet is at </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object1"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<mo fence="true" form="prefix" stretchy="false">[</mo>
|
||
<mrow>
|
||
<mrow>
|
||
<mrow>
|
||
<mo stretchy="false">−</mo>
|
||
<mn>0.189</mn>
|
||
</mrow>
|
||
<mi>,</mi>
|
||
<mn>0</mn>
|
||
<mi>,</mi>
|
||
<mn>0</mn>
|
||
</mrow>
|
||
</mrow>
|
||
<mo fence="true" form="postfix" stretchy="false">]</mo>
|
||
</mrow>
|
||
</math> </span><span class="text-T3">, and the angle between the total field and the magnet is 13.4deg. To find the magnetic dipole, we’ll work backwards from magnetic field and distance. The equation relating the values is </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object2"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<mi>tan</mi>
|
||
<mrow>
|
||
<mrow>
|
||
<mo fence="true" form="prefix" stretchy="false">(</mo>
|
||
<mrow>
|
||
<mi>θ</mi>
|
||
</mrow>
|
||
<mo fence="true" form="postfix" stretchy="false">)</mo>
|
||
</mrow>
|
||
<mo stretchy="false">=</mo>
|
||
<mfrac>
|
||
<msub>
|
||
<mi>b</mi>
|
||
<mi mathvariant="italic">earth</mi>
|
||
</msub>
|
||
<msub>
|
||
<mi>b</mi>
|
||
<mi mathvariant="italic">mag</mi>
|
||
</msub>
|
||
</mfrac>
|
||
</mrow>
|
||
</mrow>
|
||
</math> </span><span class="text-T3"> (one of the basic trig relationships). Because we know</span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object4"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<msub>
|
||
<mi>b</mi>
|
||
<mi mathvariant="italic">earth</mi>
|
||
</msub>
|
||
</math> </span><span class="text-T3">, and we know </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object3"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mi>θ</mi>
|
||
</math> </span><span class="text-T3">, this can be algebra’d to get </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object5"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<msub>
|
||
<mi>b</mi>
|
||
<mi mathvariant="italic">mag</mi>
|
||
</msub>
|
||
<mo stretchy="false">=</mo>
|
||
<mfrac>
|
||
<msub>
|
||
<mi>b</mi>
|
||
<mi mathvariant="italic">earth</mi>
|
||
</msub>
|
||
<mrow>
|
||
<mi>tan</mi>
|
||
<mrow>
|
||
<mo fence="true" form="prefix" stretchy="false">(</mo>
|
||
<mrow>
|
||
<mi>θ</mi>
|
||
</mrow>
|
||
<mo fence="true" form="postfix" stretchy="false">)</mo>
|
||
</mrow>
|
||
</mrow>
|
||
</mfrac>
|
||
<mo stretchy="false">=</mo>
|
||
<mfrac>
|
||
<mn>3e-5</mn>
|
||
<mrow>
|
||
<mi>tan</mi>
|
||
<mrow>
|
||
<mo fence="true" form="prefix" stretchy="false">(</mo>
|
||
<mrow>
|
||
<mn>13.4</mn>
|
||
</mrow>
|
||
<mo fence="true" form="postfix" stretchy="false">)</mo>
|
||
</mrow>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
</math> </span><span class="text-T3">. This evaluates “nicely” to 1.2592681e-4. Great.</span></div>
|
||
|
||
<!--Next 'div' was a 'text:p'.-->
|
||
<div class="paragraph-P5"><span class="text-T4">Unfortunately, this isn’t the final answer: we need the magnitude of the </span><span class="text-T5">magnetic dipole moment</span><span class="text-T4">, not the </span><span class="text-T5">magnetic field</span><span class="text-T4">. There’s a handy fact about magnets that becomes useful here: for a distance </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object6"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<mi>r</mi>
|
||
<mo stretchy="false">≫</mo>
|
||
<mi>s</mi>
|
||
</mrow>
|
||
</math> </span><span class="text-T4"> (where </span><span class="text-T5">s</span><span class="text-T4"> is the length of the magnet), the magnetic field on the parallel axis is just </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object7"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>m</mi>
|
||
</msub>
|
||
<mfrac>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
<mi>u</mi>
|
||
</mrow>
|
||
<msup>
|
||
<mi>r</mi>
|
||
<mn>3</mn>
|
||
</msup>
|
||
</mfrac>
|
||
</mrow>
|
||
</math> </span><span class="text-T4">, where </span><span class="text-T5">u</span><span class="text-T4"> is the magnitude of the magnetic dipole moment and </span><span class="text-T5">r</span><span class="text-T4"> is the distance (which, handily, we know). This works </span><span class="text-T4">out to an equation </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object8"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<mrow>
|
||
<mn>1.2592681e-4</mn>
|
||
<mo stretchy="false">=</mo>
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>m</mi>
|
||
</msub>
|
||
</mrow>
|
||
<mfrac>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
<mi>u</mi>
|
||
</mrow>
|
||
<msup>
|
||
<mi>r</mi>
|
||
<mn>3</mn>
|
||
</msup>
|
||
</mfrac>
|
||
<mo stretchy="false">→</mo>
|
||
<mrow>
|
||
<mi>u</mi>
|
||
<mo stretchy="false">=</mo>
|
||
<mfrac>
|
||
<mn>1.2592681e-4</mn>
|
||
<mrow>
|
||
<mn>2</mn>
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>m</mi>
|
||
</msub>
|
||
</mrow>
|
||
</mfrac>
|
||
</mrow>
|
||
<msup>
|
||
<mi>r</mi>
|
||
<mn>3</mn>
|
||
</msup>
|
||
</mrow>
|
||
</math> </span><span class="text-T4">. </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object9"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<msub>
|
||
<mi>k</mi>
|
||
<mi>m</mi>
|
||
</msub>
|
||
</math> </span><span class="text-T4"> is just the magnetic constant </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object10"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<mfrac>
|
||
<msub>
|
||
<mi>u</mi>
|
||
<mn>0</mn>
|
||
</msub>
|
||
<mrow>
|
||
<mn>4</mn>
|
||
<mi>π</mi>
|
||
</mrow>
|
||
</mfrac>
|
||
<mo stretchy="false">=</mo>
|
||
<mn>1e-7</mn>
|
||
</mrow>
|
||
</math> </span><span class="text-T4">, and </span><span class="text-T5">r</span><span class="text-T4"> is -</span><span class="text-T6">0.189</span><span class="text-T4"> (see above), so the magnitude of the dipole moment must be </span>
|
||
<!--Next 'span' is a draw:frame. -->
|
||
<span id="Object11"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
|
||
<mrow>
|
||
<mrow>
|
||
<mi>u</mi>
|
||
<mo stretchy="false">=</mo>
|
||
<msup>
|
||
<mrow>
|
||
<mo fence="true" form="prefix" stretchy="false">(</mo>
|
||
<mrow>
|
||
<mrow>
|
||
<mo stretchy="false">−</mo>
|
||
<mn>0.189</mn>
|
||
</mrow>
|
||
</mrow>
|
||
<mo fence="true" form="postfix" stretchy="false">)</mo>
|
||
</mrow>
|
||
<mn>3</mn>
|
||
</msup>
|
||
</mrow>
|
||
<mrow>
|
||
<mfrac>
|
||
<mn>1.2592681e-4</mn>
|
||
<mn>2e-7</mn>
|
||
</mfrac>
|
||
<mo stretchy="false">=</mo>
|
||
<mrow>
|
||
<mo stretchy="false">−</mo>
|
||
<mn>4.25082884311</mn>
|
||
</mrow>
|
||
</mrow>
|
||
</mrow>
|
||
</math> </span><span class="text-T4">. </span><span class="text-T6">Yay for horrible trigonometry!</span></div>
|
||
|
||
<p class="paragraph-P6"><span class="text-T4"/></p>
|
||
</body>
|
||
|
||
</html>
|