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</style></head><body><article id="295f378f-c262-45cc-a6de-6acf732f706e" class="page sans"><header><h1 class="page-title">Unit 21: Coulomb’s Law</h1></header><div class="page-body"><h1 id="134d1a28-4600-435c-9206-e23772fa314d" class="">21.1 - Coulomb’s Law</h1><p id="bed27861-f580-4d17-9ad7-ffc134ac518b" class="">The strength of a particle’s electrical interaction with objects around it depends on its electric charge (usually represented as <style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><span data-token-index="0" contenteditable="false" class="notion-text-equation-token" style="user-select:all;-webkit-user-select:all;-moz-user-select:all"><span></span><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span></span><span></span></span>), which can be either positive or negative. Particles with the same sign of charge repel each other, and particles with opposite signs of charge attract each other.</p><p id="e85a469e-e03a-4ad8-b02c-dc09516b1315" class="">An object with equal amounts of the two kinds of charge is electrically <em>neutral</em>, whereas one with an imbalance is electrically charged and has an excess charge.</p><p id="b12d4a72-b93a-4b27-bb16-3a99f87ed4cd" class=""><strong>Conductors </strong>are materials in which a significant number of electrons are free to move. The charged particles in <strong>nonconductors </strong>(insulators) are not free to move.</p><p id="dadc267d-fad5-47fb-b10b-04f5b45ebd08" class=""><strong>Electric current</strong> (<style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><span data-token-index="0" contenteditable="false" class="notion-text-equation-token" style="user-select:all;-webkit-user-select:all;-moz-user-select:all"><span></span><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span></span><span></span></span>) is the rate <style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><span data-token-index="0" contenteditable="false" class="notion-text-equation-token" style="user-select:all;-webkit-user-select:all;-moz-user-select:all"><span></span><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>q</mi><mi mathvariant="normal">/</mi><mi>d</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">dq/dt</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mord">/</span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span></span></span><span></span></span> at which charge passes a point:</p><figure id="0038c33e-0bdf-4bbd-95df-142de0715908" class="equation"><style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><div class="equation-container"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>i</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>q</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation enc
</strong>The net electric charge of any isolated system is <em>always </em>conserved.</div></figure><h2 id="bf984fce-a0bb-4b89-90d8-39801dd779cb" class="">Annihilation Process</h2><p id="6575b69b-4bbb-452c-903f-d68fa8ba456b" class="">An annihilation process occurs when an electron <style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><span data-token-index="0" contenteditable="false" class="notion-text-equation-token" style="user-select:all;-webkit-user-select:all;-moz-user-select:all"><span></span><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>e</mi><mo>−</mo></msup></mrow><annotation encoding="application/x-tex">e^-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.771331em;vertical-align:0em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">−</span></span></span></span></span></span></span></span></span></span></span></span><span></span></span> (charge <style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><span data-token-index="0" contenteditable="false" class="notion-text-equation-token" style="user-select:all;-webkit-user-select:all;-moz-user-select:all"><span></span><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mi>e</mi></mrow><annotation encoding="application/x-tex">-e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">−</span><span class="mord mathnormal">e</span></span></span></span></span><span></span></span>) and its antiparticle, the positron <style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><span data-token-index="0" contenteditable="false" class="notion-text-equation-token" style="user-select:all;-webkit-user-select:all;-moz-user-select:all"><span></span><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>e</mi><mo>+</mo></msup></mrow><annotation encoding="application/x-tex">e^+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.771331em;vertical-align:0em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span></span></span></span></span><span></span></span> (charge <style>@import url('https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.2/katex.min.css')</style><span data-token-index="0" contenteditable="false" class="notion-text-equation-token" style="user-select:all;-webkit-user-select:all;-moz-user-select:all"><span></span><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>e</mi></mrow><annotation encoding="application/x-tex">e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">e</span></span></span></span></span><span></span></span>), undergo , transforming into two gamma rays (high-energy light):</p><p id="ed3dac3f-3919-4a82-a25d-46452b22f35e" clas
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