toshiki-notebook/assets/academic_physics_ipho-formulas-jpn_9.md.51af935a.lean.js

2 lines
104 KiB
JavaScript
Raw Blame History

This file contains invisible Unicode characters

This file contains invisible Unicode characters that are indistinguishable to humans but may be processed differently by a computer. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

import{_ as t,c as n,o as m,d as l,a as s,b as a}from"./app.c5602d86.js";const Y=JSON.parse('{"title":"Formulas for IPhO 日本語版: Section 9","description":"","frontmatter":{},"headers":[{"level":2,"title":"9: 電磁気学","slug":"_9-電磁気学","link":"#_9-電磁気学","children":[{"level":3,"title":"9.1: Coulomb の法則","slug":"_9-1-coulomb-の法則","link":"#_9-1-coulomb-の法則","children":[]},{"level":3,"title":"9.2: Gauss の法則","slug":"_9-2-gauss-の法則","link":"#_9-2-gauss-の法則","children":[]},{"level":3,"title":"9.3: 循環定理","slug":"_9-3-循環定理","link":"#_9-3-循環定理","children":[]},{"level":3,"title":"9.4: 電流素片により生じる磁束密度","slug":"_9-4-電流素片により生じる磁束密度","link":"#_9-4-電流素片により生じる磁束密度","children":[]},{"level":3,"title":"9.5: ローレンツ力","slug":"_9-5-ローレンツ力","link":"#_9-5-ローレンツ力","children":[]},{"level":3,"title":"9.6: Gauss の定理と循環定理より","slug":"_9-6-gauss-の定理と循環定理より","link":"#_9-6-gauss-の定理と循環定理より","children":[]},{"level":3,"title":"9.7: 長いソレノイド","slug":"_9-7-長いソレノイド","link":"#_9-7-長いソレノイド","children":[]},{"level":3,"title":"9.8: 磁場を小型コイルや衝撃検流計で測定する","slug":"_9-8-磁場を小型コイルや衝撃検流計で測定する","link":"#_9-8-磁場を小型コイルや衝撃検流計で測定する","children":[]},{"level":3,"title":"9.9: 静電場のエネルギー","slug":"_9-9-静電場のエネルギー","link":"#_9-9-静電場のエネルギー","children":[]},{"level":3,"title":"9.10: 一様に帯電した球面や円筒面の各部分の間に働く力","slug":"_9-10-一様に帯電した球面や円筒面の各部分の間に働く力","link":"#_9-10-一様に帯電した球面や円筒面の各部分の間に働く力","children":[]},{"level":3,"title":"9.11: 全ての電荷","slug":"_9-11-全ての電荷","link":"#_9-11-全ての電荷","children":[]},{"level":3,"title":"9.12: 外部電荷","slug":"_9-12-外部電荷","link":"#_9-12-外部電荷","children":[]},{"level":3,"title":"9.14: 導体","slug":"_9-14-導体","link":"#_9-14-導体","children":[]},{"level":3,"title":"9.15: 静電容量","slug":"_9-15-静電容量","link":"#_9-15-静電容量","children":[]},{"level":3,"title":"9.16: 双極子モーメント","slug":"_9-16-双極子モーメント","link":"#_9-16-双極子モーメント","children":[]},{"level":3,"title":"9.17: 双極子場","slug":"_9-17-双極子場","link":"#_9-17-双極子場","children":[]},{"level":3,"title":"9.18: 双極子に働く力","slug":"_9-18-双極子に働く力","link":"#_9-18-双極子に働く力","children":[]},{"level":3,"title":"9.19: 磁気双極子としての点電荷","slug":"_9-19-磁気双極子としての点電荷","link":"#_9-19-磁気双極子としての点電荷","children":[]},{"level":3,"title":"9.20: 鏡像法","slug":"_9-20-鏡像法","link":"#_9-20-鏡像法","children":[]},{"level":3,"title":"9.21: 一様(電)場中の球 (円柱) の分極","slug":"_9-21-一様-電-場中の球-円柱-の分極","link":"#_9-21-一様-電-場中の球-円柱-の分極","children":[]},{"level":3,"title":"9.22: 渦電流","slug":"_9-22-渦電流","link":"#_9-22-渦電流","children":[]}]}],"relativePath":"academic/physics/ipho-formulas-jpn/9.md","lastUpdated":1679479428000}'),e={name:"academic/physics/ipho-formulas-jpn/9.md"},i=l("",3),r=s("ol",null,[s("li",null,[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"F"),s("mo",null,"="),s("mi",null,"k"),s("msub",null,[s("mi",null,"q"),s("mn",null,"1")]),s("msub",null,[s("mi",null,"q"),s("mn",null,"2")]),s("mi",{mathvariant:"normal"},"/"),s("msup",null,[s("mi",null,"r"),s("mn",null,"2")]),s("mo",{separator:"true"},","),s("mi",null,"U"),s("mo",null,"="),s("mi",null,"k"),s("msub",null,[s("mi",null,"q"),s("mn",null,"1")]),s("msub",null,[s("mi",null,"q"),s("mn",null,"2")]),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"F=k q_1 q_2 / r^2, U=k q_1 q_2 / r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.13889em"}},"F"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3011em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"1")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3011em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mord"},"/"),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.10903em"}},"U"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3011em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"1")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3011em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])]),a(" で, Kepler の法則が 使える ("),s("a",{href:"./12"},"Section 12 参照"),a(").")])],-1),p=s("h3",{id:"_9-2-gauss-の法則",tabindex:"-1"},[a("9.2: Gauss の法則 "),s("a",{class:"header-anchor",href:"#_9-2-gauss-の法則","aria-hidden":"true"},"#")],-1),c=s("ol",{start:"2"},[s("li",null,[s("p",null,[a("Gauss の法則 : "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",null,"∮"),s("mi",{mathvariant:"bold-italic"},"B"),s("mo",null,"⋅"),s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"S"),s("mo",null,"="),s("mn",null,"0")]),s("annotation",{encoding:"application/x-tex"},"\\oint \\boldsymbol{B} \\cdot \\mathrm{d} \\boldsymbol{S}=0")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.1111em","vertical-align":"-0.3061em"}}),s("span",{class:"mop op-symbol small-op",style:{"margin-right":"0.19445em",position:"relative",top:"-0.0006em"}},"∮"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.04835em"}},"B")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05382em"}},"S")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6444em"}}),s("span",{class:"mord"},"0")])])]),a(",")]),s("p",{class:"katex-block"},[s("span",{class:"katex-display"},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("semantics",null,[s("mrow",null,[s("mo",null,"∮"),s("mi",null,"ε"),s("mi",{mathvariant:"bold-italic"},"E"),s("mo",null,"⋅"),s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"S"),s("mo",null,"="),s("mi",null,"Q"),s("mo",{separator:"true"},","),s("mo",null,"∮"),s("mi",{mathvariant:"bold-italic"},"g"),s("mo",null,"⋅"),s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"S"),s("mo",null,"="),s("mo",null,""),s("mn",null,"4"),s("mi",null,"π"),s("mi",null,"G"),s("mi",null,"M")]),s("annotation",{encoding:"application/x-tex"},"\\oint \\varepsilon \\boldsymbol{E} \\cdot \\mathrm{d} \\boldsymbol{S}=Q, \\oint \\boldsymbol{g} \\cdot \\mathrm{d} \\boldsymbol{S}=-4 \\pi G M ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.2222em","vertical-align":"-0.8622em"}}),s("span",{class:"mop op-symbol large-op",style:{"margin-right":"0.44445em",position:"relative",top:"-0.0011em"}},"∮"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal"},"ε"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05451em"}},"E")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05382em"}},"S")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.2222em","vertical-align":"-0.8622em"}}),s("span",{class:"mord mathnormal"},"Q"),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mop op-symbol large-op",style:{"margin-right":"0.44445em",position:"relative",top:"-0.0011em"}},"∮"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03704em"}},"g")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05382em"}},"S")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.7667em","vertical-align":"-0.0833em"}}),s("span",{class:"mord"},""),s("span",{class:"mord"},"4"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"π"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.10903em"}},"GM")])])])])])])],-1),h=s("h3",{id:"_9-3-循環定理",tabindex:"-1"},[a("9.3: 循環定理 "),s("a",{class:"header-anchor",href:"#_9-3-循環定理","aria-hidden":"true"},"#")],-1),o=s("ol",{start:"3"},[s("li",null,[s("p",null,"循環定理 :"),s("p",{class:"katex-block"},[s("span",{class:"katex-display"},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("semantics",null,[s("mrow",null,[s("mo",null,"∮"),s("mi",{mathvariant:"bold-italic"},"E"),s("mo",null,"⋅"),s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"l"),s("mo",null,"="),s("mn",null,"0"),s("mo",{stretchy:"false"},"("),s("mo",null,"="),s("mover",{accent:"true"},[s("mi",{mathvariant:"normal"},"Φ"),s("mo",null,"˙")]),s("mo",{stretchy:"false"},")"),s("mo",{separator:"true"},","),s("mo",null,"∮"),s("mfrac",null,[s("mrow",null,[s("mi",{mathvariant:"bold-italic"},"B"),s("mo",null,"⋅"),s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"l")]),s("mi",null,"μ")]),s("mo",null,"="),s("mi",null,"I"),s("mo",{separator:"true"},","),s("mo",null,"∮"),s("mi",{mathvariant:"bold-italic"},"g"),s("mo",null,"⋅"),s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"l"),s("mo",null,"="),s("mn",null,"0")]),s("annotation",{encoding:"application/x-tex"},"\\oint \\boldsymbol{E} \\cdot \\mathrm{d} \\boldsymbol{l}=0(=\\dot{\\Phi}), \\oint \\frac{\\boldsymbol{B} \\cdot \\mathrm{d} \\boldsymbol{l}}{\\mu}=I, \\oint \\boldsymbol{g} \\cdot \\mathrm{d} \\boldsymbol{l}=0 ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.2222em","vertical-align":"-0.8622em"}}),s("span",{class:"mop op-symbol large-op",style:{"margin-right":"0.44445em",position:"relative",top:"-0.0011em"}},"∮"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05451em"}},"E")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.0088em"}},"l")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"0"),s("span",{class:"mopen"},"("),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.2519em","vertical-align":"-0.8804em"}}),s("span",{class:"mord accent"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.9202em"}},[s("span",{style:{top:"-3em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},"Φ")]),s("span",{style:{top:"-3.2523em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"accent-body",style:{left:"-0.1389em"}},[s("span",{class:"mord"},"˙")])])])])])]),s("span",{class:"mclose"},")"),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mop op-symbol large-op",style:{"margin-right":"0.44445em",position:"relative",top:"-0.0011em"}},"∮"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.3714em"}},[s("span",{style:{top:"-2.314em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"μ")])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.677em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.04835em"}},"B")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.0088em"}},"l")])])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8804em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.2222em","vertical-align":"-0.8622em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07847em"}},"I"),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mop op-symbol large-op",style:{"margin-right":"0.44445em",position:"relative",top:"-0.0011em"}},"∮"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03704em"}},"g")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.0088em"}},"l")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6444em"}}),s("span",{class:"mord"},"0")])])])])])])],-1),g=s("h3",{id:"_9-4-電流素片により生じる磁束密度",tabindex:"-1"},[a("9.4: 電流素片により生じる磁束密度 "),s("a",{class:"header-anchor",href:"#_9-4-電流素片により生じる磁束密度","aria-hidden":"true"},"#")],-1),d=s("ol",{start:"4"},[s("li",null,[a("電流素片により生じる磁束密度 :"),s("p",{class:"katex-block"},[s("span",{class:"katex-display"},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"B"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"μ"),s("mi",null,"I")]),s("mrow",null,[s("mn",null,"4"),s("mi",null,"π")])]),s("mfrac",null,[s("mrow",null,[s("mi",{mathvariant:"normal"},"d"),s("mi",{mathvariant:"bold-italic"},"l"),s("mo",null,"×"),s("msub",null,[s("mi",{mathvariant:"bold-italic"},"e"),s("mi",null,"r")])]),s("msup",null,[s("mi",null,"r"),s("mn",null,"2")])]),s("mi",{mathvariant:"normal"},".")]),s("annotation",{encoding:"application/x-tex"},"\\mathrm{d} \\boldsymbol{B}=\\frac{\\mu I}{4 \\pi} \\frac{\\mathrm{d} \\boldsymbol{l} \\times \\boldsymbol{e}_r}{r^2} . ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.04835em"}},"B")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.0574em","vertical-align":"-0.686em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.3603em"}},[s("span",{style:{top:"-2.314em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"4"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"π")])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.677em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"μ"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07847em"}},"I")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.686em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.3714em"}},[s("span",{style:{top:"-2.314em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.7401em"}},[s("span",{style:{top:"-2.989em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.677em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.0088em"}},"l")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"×"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"e")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.1514em"}},[s("span",{style:{top:"-2.55em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.02778em"}},"r")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.686em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mord"},".")])])])])]),a(" したがって電流 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"I")]),s("annotation",{encoding:"application/x-tex"},"I")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07847em"}},"I")])])]),a(" が流れる円形回路の中心では "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"B"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("msub",null,[s("mi",null,"μ"),s("mn",null,"0")]),s("mi",null,"I")]),s("mrow",null,[s("mn",null,"2"),s("mi",null,"r")])])]),s("annotation",{encoding:"application/x-tex"},"B=\\frac{\\mu_0 I}{2 r}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.2694em","vertical-align":"-0.345em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.9244em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"2"),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.02778em"}},"r")])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.4461em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight"},"μ"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3173em"}},[s("span",{style:{top:"-2.357em","margin-left":"0em","margin-right":"0.0714em"}},[s("span",{class:"pstrut",style:{height:"2.5em"}}),s("span",{class:"sizing reset-size3 size1 mtight"},[s("span",{class:"mord mtight"},"0")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.143em"}},[s("span")])])])])]),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.07847em"}},"I")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.345em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})])])])]),a(".")])],-1),u=s("h3",{id:"_9-5-ローレンツ力",tabindex:"-1"},[a("9.5: ローレンツ力 "),s("a",{class:"header-anchor",href:"#_9-5-ローレンツ力","aria-hidden":"true"},"#")],-1),y=s("ol",{start:"5"},[s("li",null,[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"bold-italic"},"F"),s("mo",null,"="),s("mi",null,"e"),s("mo",{stretchy:"false"},"("),s("mi",{mathvariant:"bold-italic"},"E"),s("mo",null,"+"),s("mi",{mathvariant:"bold-italic"},"v"),s("mo",null,"×"),s("mi",{mathvariant:"bold-italic"},"B"),s("mo",{stretchy:"false"},")"),s("mo",{separator:"true"},","),s("mi",{mathvariant:"bold-italic"},"F"),s("mo",null,"="),s("mi",{mathvariant:"bold-italic"},"I"),s("mo",null,"×"),s("mi",{mathvariant:"bold-italic"},"B"),s("mi",null,"l")]),s("annotation",{encoding:"application/x-tex"},"\\boldsymbol{F}=e(\\boldsymbol{E}+\\boldsymbol{v} \\times \\boldsymbol{B}), \\boldsymbol{F}=\\boldsymbol{I} \\times \\boldsymbol{B} l")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6861em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.15972em"}},"F")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal"},"e"),s("span",{class:"mopen"},"("),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05451em"}},"E")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"+"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6667em","vertical-align":"-0.0833em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03704em"}},"v")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"×"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.04835em"}},"B")])]),s("span",{class:"mclose"},")"),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.15972em"}},"F")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.7694em","vertical-align":"-0.0833em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.07778em"}},"I")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"×"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.04835em"}},"B")])]),s("span",{class:"mord mathnormal",style:{"margin-right":"0.01968em"}},"l")])])]),a(".")])],-1),v=s("h3",{id:"_9-6-gauss-の定理と循環定理より",tabindex:"-1"},[a("9.6: Gauss の定理と循環定理より "),s("a",{class:"header-anchor",href:"#_9-6-gauss-の定理と循環定理より","aria-hidden":"true"},"#")],-1),b=s("ol",{start:"6"},[s("li",null,[a("Gauss の定理と循環定理より:帯電した導線について "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"E"),s("mo",null,"="),s("mfrac",null,[s("mi",null,"σ"),s("mrow",null,[s("mn",null,"2"),s("mi",null,"π"),s("msub",null,[s("mi",null,"ε"),s("mn",null,"0")]),s("mi",null,"r")])])]),s("annotation",{encoding:"application/x-tex"},"E=\\frac{\\sigma}{2 \\pi \\varepsilon_0 r}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"E"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.1405em","vertical-align":"-0.4451em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.6954em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"2"),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.03588em"}},"π"),s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight"},"ε"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3173em"}},[s("span",{style:{top:"-2.357em","margin-left":"0em","margin-right":"0.0714em"}},[s("span",{class:"pstrut",style:{height:"2.5em"}}),s("span",{class:"sizing reset-size3 size1 mtight"},[s("span",{class:"mord mtight"},"0")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.143em"}},[s("span")])])])])]),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.02778em"}},"r")])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.394em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.03588em"}},"σ")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.4451em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})])])])]),a(", 電流が流れる導線について "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"B"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("msub",null,[s("mi",null,"μ"),s("mn",null,"0")]),s("mi",null,"I")]),s("mrow",null,[s("mn",null,"2"),s("mi",null,"π"),s("mi",null,"r")])])]),s("annotation",{encoding:"application/x-tex"},"B=\\frac{\\mu_0 I}{2 \\pi r}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.2694em","vertical-align":"-0.345em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.9244em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"2"),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.03588em"}},"π"),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.02778em"}},"r")])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.4461em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight"},"μ"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3173em"}},[s("span",{style:{top:"-2.357em","margin-left":"0em","margin-right":"0.0714em"}},[s("span",{class:"pstrut",style:{height:"2.5em"}}),s("span",{class:"sizing reset-size3 size1 mtight"},[s("span",{class:"mord mtight"},"0")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.143em"}},[s("span")])])])])]),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.07847em"}},"I")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.345em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})])])])]),a(". 帯電した面について "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"E"),s("mo",null,"="),s("mfrac",null,[s("mi",null,"σ"),s("mrow",null,[s("mn",null,"2"),s("msub",null,[s("mi",null,"ε"),s("mn",null,"0")])])])]),s("annotation",{encoding:"application/x-tex"},"E=\\frac{\\sigma}{2 \\varepsilon_0}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"E"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.1405em","vertical-align":"-0.4451em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.6954em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"2"),s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight"},"ε"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3173em"}},[s("span",{style:{top:"-2.357em","margin-left":"0em","margin-right":"0.0714em"}},[s("span",{class:"pstrut",style:{height:"2.5em"}}),s("span",{class:"sizing reset-size3 size1 mtight"},[s("span",{class:"mord mtight"},"0")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.143em"}},[s("span")])])])])])])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.394em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.03588em"}},"σ")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.4451em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})])])])]),a(", 電流が流れる面につい て "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"B"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("msub",null,[s("mi",null,"μ"),s("mn",null,"0")]),s("mi",null,"i")]),s("mn",null,"2")])]),s("annotation",{encoding:"application/x-tex"},"B=\\frac{\\mu_0 i}{2}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.2528em","vertical-align":"-0.345em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.9078em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"2")])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.4461em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight"},"μ"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3173em"}},[s("span",{style:{top:"-2.357em","margin-left":"0em","margin-right":"0.0714em"}},[s("span",{class:"pstrut",style:{height:"2.5em"}}),s("span",{class:"sizing reset-size3 size1 mtight"},[s("span",{class:"mord mtight"},"0")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.143em"}},[s("span")])])])])]),s("span",{class:"mord mathnormal mtight"},"i")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.345em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})])])])]),a(". 一様に帯電した球殼(又は無限に長い円 筒)の内部で "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"E"),s("mo",null,"="),s("mn",null,"0")]),s("annotation",{encoding:"application/x-tex"},"E=0")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"E"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6444em"}}),s("span",{class:"mord"},"0")])])]),a(", 軸に沿って表面に電流が流れる 円筒の内部で "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"B"),s("mo",null,"="),s("mn",null,"0")]),s("annotation",{encoding:"application/x-tex"},"B=0")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6444em"}}),s("span",{class:"mord"},"0")])])]),a(". 密度 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"ρ")]),s("annotation",{encoding:"application/x-tex"},"\\rho")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.625em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"ρ")])])]),a(" で一様に帯電, 又は一様 な電流 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"bold-italic"},"i")]),s("annotation",{encoding:"application/x-tex"},"\\boldsymbol{i}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6933em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"i")])])])])]),a(" が流れる, 球 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",{stretchy:"false"},"("),s("mi",null,"d"),s("mo",null,"="),s("mn",null,"3"),s("mo",{stretchy:"false"},")"),s("mi",{mathvariant:"normal"},"/")]),s("annotation",{encoding:"application/x-tex"},"(d=3) /")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mopen"},"("),s("span",{class:"mord mathnormal"},"d"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"3"),s("span",{class:"mclose"},")"),s("span",{class:"mord"},"/")])])]),a(" 円柱 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",{stretchy:"false"},"("),s("mi",null,"d"),s("mo",null,""),s("mn",null,"2"),s("mo",{stretchy:"false"},")"),s("mi",{mathvariant:"normal"},"/")]),s("annotation",{encoding:"application/x-tex"},"(d-2) /")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mopen"},"("),s("span",{class:"mord mathnormal"},"d"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},""),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"2"),s("span",{class:"mclose"},")"),s("span",{class:"mord"},"/")])])]),a(" 平面 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",{stretchy:"false"},"("),s("mi",null,"d"),s("mo",null,"="),s("mn",null,"1"),s("mo",{stretchy:"false"},")")]),s("annotation",{encoding:"application/x-tex"},"(d=1)")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mopen"},"("),s("span",{class:"mord mathnormal"},"d"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"1"),s("span",{class:"mclose"},")")])])]),a(" の内部で,"),s("p",{class:"katex-block"},[s("span",{class:"katex-display"},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"bold-italic"},"E"),s("mo",null,"="),s("mfrac",null,[s("mi",null,"ρ"),s("mrow",null,[s("mi",null,"ε"),s("mi",null,"d")])]),s("mi",{mathvariant:"bold-italic"},"r"),s("mo",{separator:"true"},","),s("mi",{mathvariant:"bold-italic"},"B"),s("mo",null,"="),s("mfrac",null,[s("mn",null,"1"),s("mrow",null,[s("mi",null,"μ"),s("mi",null,"d")])]),s("mi",{mathvariant:"bold-italic"},"i"),s("mo",null,"×"),s("mi",{mathvariant:"bold-italic"},"r")]),s("annotation",{encoding:"application/x-tex"},"\\boldsymbol{E}=\\frac{\\rho}{\\varepsilon d} \\boldsymbol{r}, \\boldsymbol{B}=\\frac{1}{\\mu d} \\boldsymbol{i} \\times \\boldsymbol{r} ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6861em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05451em"}},"E")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.7936em","vertical-align":"-0.686em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.1076em"}},[s("span",{style:{top:"-2.314em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"ε"),s("span",{class:"mord mathnormal"},"d")])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.677em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"ρ")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.686em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03194em"}},"r")])]),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.04835em"}},"B")])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.2019em","vertical-align":"-0.8804em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.3214em"}},[s("span",{style:{top:"-2.314em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"μ"),s("span",{class:"mord mathnormal"},"d")])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.677em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"1")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8804em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"i")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"×"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4444em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03194em"}},"r")])])])])])])])])],-1),x=s("h3",{id:"_9-7-長いソレノイド",tabindex:"-1"},[a("9.7: 長いソレノイド "),s("a",{class:"header-anchor",href:"#_9-7-長いソレノイド","aria-hidden":"true"},"#")],-1),w=s("ol",{start:"7"},[s("li",null,[a("長いソレノイド: 内部で "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"B"),s("mo",null,"="),s("mi",null,"μ"),s("mi",null,"n"),s("mi",null,"I")]),s("annotation",{encoding:"application/x-tex"},"B=\\mu n I")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8778em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"μ"),s("span",{class:"mord mathnormal"},"n"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07847em"}},"I")])])]),a(", 外部で "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"B"),s("mo",null,"="),s("mn",null,"0")]),s("annotation",{encoding:"application/x-tex"},"B=0")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6444em"}}),s("span",{class:"mord"},"0")])])]),a(". 磁束 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"normal"},"Φ"),s("mo",null,"="),s("mi",null,"N"),s("mi",null,"B"),s("mi",null,"S"),s("mrow",null,[s("mo",{fence:"true"},"("),s("mi",null,"n"),s("mo",null,"="),s("mfrac",null,[s("mi",null,"N"),s("mi",null,"l")]),s("mo",{fence:"true"},")")])]),s("annotation",{encoding:"application/x-tex"},"\\Phi=N B S\\left(n=\\frac{N}{l}\\right)")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord"},"Φ"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.2223em","vertical-align":"-0.35em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"NBS"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"minner"},[s("span",{class:"mopen delimcenter",style:{top:"0em"}},[s("span",{class:"delimsizing size1"},"(")]),s("span",{class:"mord mathnormal"},"n"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8723em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.01968em"}},"l")])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.394em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.10903em"}},"N")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.345em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mclose delimcenter",style:{top:"0em"}},[s("span",{class:"delimsizing size1"},")")])])])])]),a(". インダクタンス "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"L"),s("mo",null,"=")]),s("annotation",{encoding:"application/x-tex"},"L=")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal"},"L"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"=")])])]),a(),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"normal"},"Φ"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"I"),s("mo",null,"="),s("mi",null,"μ"),s("msup",null,[s("mi",null,"n"),s("mn",null,"2")]),s("mi",null,"V")]),s("annotation",{encoding:"application/x-tex"},"\\Phi / I=\\mu n^2 V")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"Φ/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07847em"}},"I"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0085em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"μ"),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"n"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),s("span",{class:"mord mathnormal",style:{"margin-right":"0.22222em"}},"V")])])]),a(". 短いソレノイド "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",null,":"),s("msub",null,[s("mi",null,"B"),s("mi",{mathvariant:"normal"},"∥")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"μ"),s("mi",null,"n"),s("mi",null,"I"),s("mi",{mathvariant:"normal"},"Ω")]),s("mrow",null,[s("mn",null,"4"),s("mi",null,"π")])]),s("mo",{stretchy:"false"},"("),s("mi",{mathvariant:"normal"},"Ω")]),s("annotation",{encoding:"application/x-tex"},": B_{\\|}=\\frac{\\mu n I \\Omega}{4 \\pi}(\\Omega")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4306em"}}),s("span",{class:"mrel"},":"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0385em","vertical-align":"-0.3552em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3448em"}},[s("span",{style:{top:"-2.5198em","margin-left":"-0.0502em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"∥")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3552em"}},[s("span")])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.2694em","vertical-align":"-0.345em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.9244em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"4"),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.03588em"}},"π")])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.4461em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight"},"μ"),s("span",{class:"mord mathnormal mtight"},"n"),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.07847em"}},"I"),s("span",{class:"mord mtight"},"Ω")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.345em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mopen"},"("),s("span",{class:"mord"},"Ω")])])]),a(" は 立体角).")])],-1),_=s("h3",{id:"_9-8-磁場を小型コイルや衝撃検流計で測定する",tabindex:"-1"},[a("9.8: 磁場を小型コイルや衝撃検流計で測定する "),s("a",{class:"header-anchor",href:"#_9-8-磁場を小型コイルや衝撃検流計で測定する","aria-hidden":"true"},"#")],-1),k=s("ol",{start:"9"},[s("li",null,[a("磁場を小型コイルや衝撃検流計で測定する: "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"q"),s("mo",null,"=")]),s("annotation",{encoding:"application/x-tex"},"q=")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.625em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"=")])])]),a(),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",null,"∫"),s("mfrac",null,[s("mi",null,"V"),s("mi",null,"R")]),s("mrow",null,[s("mtext",null," "),s("mi",{mathvariant:"normal"},"d")]),s("mi",null,"t"),s("mo",null,"="),s("mi",null,"N"),s("mi",null,"S"),s("mi",{mathvariant:"normal"},"Δ"),s("mi",null,"B"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"R")]),s("annotation",{encoding:"application/x-tex"},"\\int \\frac{V}{R} \\mathrm{~d} t=N S \\Delta B / R")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.2173em","vertical-align":"-0.345em"}}),s("span",{class:"mop op-symbol small-op",style:{"margin-right":"0.19445em",position:"relative",top:"-0.0006em"}},"∫"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8723em"}},[s("span",{style:{top:"-2.655em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.00773em"}},"R")])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.394em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.22222em"}},"V")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.345em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mord"},[s("span",{class:"mspace nobreak"}," "),s("span",{class:"mord mathrm"},"d")]),s("span",{class:"mord mathnormal"},"t"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"NS"),s("span",{class:"mord"},"Δ"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.00773em"}},"R")])])]),a(".")])],-1),z=s("h3",{id:"_9-9-静電場のエネルギー",tabindex:"-1"},[a("9.9: 静電場のエネルギー "),s("a",{class:"header-anchor",href:"#_9-9-静電場のエネルギー","aria-hidden":"true"},"#")],-1),M=s("ol",{start:"9"},[s("li",null,[a("静電場のエネルギー:"),s("p",{class:"katex-block"},[s("span",{class:"katex-display"},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("semantics",null,[s("mrow",null,[s("mi",null,"U"),s("mo",null,"="),s("mi",null,"k"),s("munder",null,[s("mo",null,"∑"),s("mrow",null,[s("mi",null,"i"),s("mo",null,"<"),s("mi",null,"j")])]),s("mfrac",null,[s("mrow",null,[s("msub",null,[s("mi",null,"q"),s("mi",null,"i")]),s("msub",null,[s("mi",null,"q"),s("mi",null,"j")])]),s("msub",null,[s("mi",null,"r"),s("mrow",null,[s("mi",null,"i"),s("mi",null,"j")])])]),s("mo",null,"="),s("mfrac",null,[s("mn",null,"1"),s("mn",null,"2")]),s("mo",null,"∫"),s("mi",null,"ϕ"),s("mo",{stretchy:"false"},"("),s("mi",{mathvariant:"bold-italic"},"r"),s("mo",{stretchy:"false"},")"),s("mi",{mathvariant:"normal"},"d"),s("mi",null,"q"),s("mo",{separator:"true"},","),s("mrow",null,[s("mtext",null," "),s("mi",{mathvariant:"normal"},"d")]),s("mi",null,"q"),s("mo",null,"="),s("mi",null,"ρ"),s("mo",{stretchy:"false"},"("),s("mi",{mathvariant:"bold-italic"},"r"),s("mo",{stretchy:"false"},")"),s("mi",{mathvariant:"normal"},"d"),s("mi",null,"V")]),s("annotation",{encoding:"application/x-tex"},"U=k \\sum_{i<j} \\frac{q_i q_j}{r_{i j}}=\\frac{1}{2} \\int \\phi(\\boldsymbol{r}) \\mathrm{d} q, \\mathrm{~d} q=\\rho(\\boldsymbol{r}) \\mathrm{d} V ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.10903em"}},"U"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.5213em","vertical-align":"-1.4138em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mop op-limits"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.05em"}},[s("span",{style:{top:"-1.8723em","margin-left":"0em"}},[s("span",{class:"pstrut",style:{height:"3.05em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight"},"i"),s("span",{class:"mrel mtight"},"<"),s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.05724em"}},"j")])])]),s("span",{style:{top:"-3.05em"}},[s("span",{class:"pstrut",style:{height:"3.05em"}}),s("span",null,[s("span",{class:"mop op-symbol large-op"},"∑")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.4138em"}},[s("span")])])])]),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.1076em"}},[s("span",{style:{top:"-2.314em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3117em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0278em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.05724em"}},"ij")])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2861em"}},[s("span")])])])])])])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.677em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3117em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"i")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3117em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.05724em"}},"j")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2861em"}},[s("span")])])])])])])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.9721em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"2.2222em","vertical-align":"-0.8622em"}}),s("span",{class:"mord"},[s("span",{class:"mopen nulldelimiter"}),s("span",{class:"mfrac"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"1.3214em"}},[s("span",{style:{top:"-2.314em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"2")])]),s("span",{style:{top:"-3.23em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"frac-line",style:{"border-bottom-width":"0.04em"}})]),s("span",{style:{top:"-3.677em"}},[s("span",{class:"pstrut",style:{height:"3em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},"1")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.686em"}},[s("span")])])])]),s("span",{class:"mclose nulldelimiter"})]),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mop op-symbol large-op",style:{"margin-right":"0.44445em",position:"relative",top:"-0.0011em"}},"∫"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal"},"ϕ"),s("span",{class:"mopen"},"("),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03194em"}},"r")])]),s("span",{class:"mclose"},")"),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mspace nobreak"}," "),s("span",{class:"mord mathrm"},"d")]),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal"},"ρ"),s("span",{class:"mopen"},"("),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03194em"}},"r")])]),s("span",{class:"mclose"},")"),s("span",{class:"mord mathrm"},"d"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.22222em"}},"V")])])])])])])],-1),f=l("",3),B=s("ol",{start:"12"},[s("li",null,[a("全ての電荷が距離 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4306em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])]),a(" にある場合(例えば,不均一に帯 電した球やリングの中心) "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"ϕ"),s("mi",null,"ϕ"),s("mo",null,"="),s("mi",null,"k"),s("mi",null,"Q"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"\\phi \\phi=k Q / r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8889em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"ϕϕ"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),s("span",{class:"mord mathnormal"},"Q"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])])])],-1),L=l("",3),I=s("ol",{start:"14"},[s("li",null,[a("導体は電荷や電場を遮蔽する.例えば,中空の球体の 内部の電荷分布は外から見えない(あたかも "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"Q")]),s("annotation",{encoding:"application/x-tex"},"Q")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8778em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"Q")])])]),a(" という 電荷を持った導電性の球があるように見える).")])],-1),S=s("h3",{id:"_9-15-静電容量",tabindex:"-1"},[a("9.15: 静電容量 "),s("a",{class:"header-anchor",href:"#_9-15-静電容量","aria-hidden":"true"},"#")],-1),E=s("ol",{start:"15"},[s("li",null,[a("静電容量: "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"C"),s("mo",null,"="),s("mi",null,"ε"),s("mi",null,"S"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"d")]),s("annotation",{encoding:"application/x-tex"},"C=\\varepsilon S / d")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07153em"}},"C"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"εS"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal"},"d")])])]),a(" (平板), "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mn",null,"4"),s("mi",null,"π"),s("mi",null,"ε"),s("mi",null,"r")]),s("annotation",{encoding:"application/x-tex"},"4 \\pi \\varepsilon r")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6444em"}}),s("span",{class:"mord"},"4"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"π"),s("span",{class:"mord mathnormal"},"ε"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r")])])]),a(" (球), "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mn",null,"2"),s("mi",null,"π"),s("mi",null,"ε"),s("mi",null,"l"),s("mo",{stretchy:"false"},"("),s("mi",null,"ln"),s("mo",null,""),s("mi",null,"R"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"r"),s("msup",null,[s("mo",{stretchy:"false"},")"),s("mrow",null,[s("mo",null,""),s("mn",null,"1")])])]),s("annotation",{encoding:"application/x-tex"},"2 \\pi \\varepsilon l(\\ln R / r)^{-1}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},"2"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"π"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.01968em"}},"εl"),s("span",{class:"mopen"},"("),s("span",{class:"mop"},"ln"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.00773em"}},"R"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"mclose"},[s("span",{class:"mclose"},")"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},""),s("span",{class:"mord mtight"},"1")])])])])])])])])])])]),a(" (同軸円筒).")])],-1),q=s("h3",{id:"_9-16-双極子モーメント",tabindex:"-1"},[a("9.16: 双極子モーメント "),s("a",{class:"header-anchor",href:"#_9-16-双極子モーメント","aria-hidden":"true"},"#")],-1),T=s("ol",{start:"16"},[s("li",null,[s("p",null,"双極子モーメント:"),s("p",{class:"katex-block"},[s("span",{class:"katex-display"},[s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("semantics",null,[s("mrow",null,[s("msub",null,[s("mi",{mathvariant:"bold-italic"},"p"),s("mi",null,"e")]),s("mo",null,"="),s("mo",null,"∑"),s("msub",null,[s("mi",null,"q"),s("mi",null,"i")]),s("msub",null,[s("mi",{mathvariant:"bold-italic"},"r"),s("mi",null,"i")]),s("mo",null,"="),s("mi",null,"q"),s("mi",{mathvariant:"bold-italic"},"d"),s("mo",{separator:"true"},","),s("msub",null,[s("mi",{mathvariant:"bold-italic"},"p"),s("mi",null,"μ")]),s("mo",null,"="),s("mi",null,"I"),s("mi",{mathvariant:"bold-italic"},"S")]),s("annotation",{encoding:"application/x-tex"},"\\boldsymbol{p}_e=\\sum q_i \\boldsymbol{r}_i=q \\boldsymbol{d}, \\boldsymbol{p}_\\mu=I \\boldsymbol{S} ")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6886em","vertical-align":"-0.2441em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"p")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.0573em"}},[s("span",{style:{top:"-2.4559em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"e")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2441em"}},[s("span")])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.6em","vertical-align":"-0.55em"}}),s("span",{class:"mop op-symbol large-op",style:{position:"relative",top:"0em"}},"∑"),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3117em"}},[s("span",{style:{top:"-2.55em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"i")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.03194em"}},"r")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3117em"}},[s("span",{style:{top:"-2.55em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"i")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0747em","vertical-align":"-0.3802em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"q"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"d")])]),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"p")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.0573em"}},[s("span",{style:{top:"-2.4559em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"μ")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3802em"}},[s("span")])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6861em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.07847em"}},"I"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05382em"}},"S")])])])])])])])])],-1),F=s("h3",{id:"_9-17-双極子場",tabindex:"-1"},[a("9.17: 双極子場 "),s("a",{class:"header-anchor",href:"#_9-17-双極子場","aria-hidden":"true"},"#")],-1),V=s("ol",{start:"17"},[s("li",null,[a("双極子場 : "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"ϕ"),s("mo",null,"="),s("mi",null,"k"),s("mi",{mathvariant:"bold-italic"},"p"),s("mo",null,"⋅"),s("msub",null,[s("mi",{mathvariant:"bold-italic"},"e"),s("mi",null,"r")]),s("mi",{mathvariant:"normal"},"/"),s("msup",null,[s("mi",null,"r"),s("mn",null,"2")]),s("mo",{separator:"true"},","),s("mi",null,"E"),s("mo",{separator:"true"},","),s("mi",null,"B"),s("mo",null,"∝"),s("msup",null,[s("mi",null,"r"),s("mrow",null,[s("mo",null,""),s("mn",null,"3")])])]),s("annotation",{encoding:"application/x-tex"},"\\phi=k \\boldsymbol{p} \\cdot \\boldsymbol{e}_r / r^2, E, B \\propto r^{-3}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8889em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal"},"ϕ"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8889em","vertical-align":"-0.1944em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.03148em"}},"k"),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"p")])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"e")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.1514em"}},[s("span",{style:{top:"-2.55em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight",style:{"margin-right":"0.02778em"}},"r")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.15em"}},[s("span")])])])])]),s("span",{class:"mord"},"/"),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"E"),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"∝"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},""),s("span",{class:"mord mtight"},"3")])])])])])])])])])])])])],-1),N=s("h3",{id:"_9-18-双極子に働く力",tabindex:"-1"},[a("9.18: 双極子に働く力 "),s("a",{class:"header-anchor",href:"#_9-18-双極子に働く力","aria-hidden":"true"},"#")],-1),P=s("ol",{start:"19"},[s("li",null,[a("双極子に働く力 : "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"F"),s("mo",null,"="),s("msup",null,[s("mrow",null,[s("mo",{fence:"true"},"("),s("msub",null,[s("mi",{mathvariant:"bold-italic"},"p"),s("mi",null,"e")]),s("mo",null,"⋅"),s("mi",{mathvariant:"bold-italic"},"E"),s("mo",{fence:"true"},")")]),s("mo",{mathvariant:"normal",lspace:"0em",rspace:"0em"},"")]),s("mo",{separator:"true"},","),s("mi",null,"F"),s("mo",null,"="),s("msup",null,[s("mrow",null,[s("mo",{fence:"true"},"("),s("msub",null,[s("mi",{mathvariant:"bold-italic"},"p"),s("mi",null,"μ")]),s("mo",null,"⋅"),s("mi",{mathvariant:"bold-italic"},"B"),s("mo",{fence:"true"},")")]),s("mo",{mathvariant:"normal",lspace:"0em",rspace:"0em"},"")])]),s("annotation",{encoding:"application/x-tex"},"F=\\left(\\boldsymbol{p}_e \\cdot \\boldsymbol{E}\\right)^{\\prime}, F=\\left(\\boldsymbol{p}_\\mu \\cdot \\boldsymbol{B}\\right)^{\\prime}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.13889em"}},"F"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.1418em","vertical-align":"-0.25em"}}),s("span",{class:"minner"},[s("span",{class:"minner"},[s("span",{class:"mopen delimcenter",style:{top:"0em"}},"("),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"p")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.0573em"}},[s("span",{style:{top:"-2.4559em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"e")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2441em"}},[s("span")])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.05451em"}},"E")])]),s("span",{class:"mclose delimcenter",style:{top:"0em"}},")")]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8918em"}},[s("span",{style:{top:"-3.2029em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"")])])])])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mpunct"},","),s("span",{class:"mspace",style:{"margin-right":"0.1667em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.13889em"}},"F"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"="),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.372em","vertical-align":"-0.3802em"}}),s("span",{class:"minner"},[s("span",{class:"minner"},[s("span",{class:"mopen delimcenter",style:{top:"0em"}},[s("span",{class:"delimsizing size1"},"(")]),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol"},"p")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.0573em"}},[s("span",{style:{top:"-2.4559em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"μ")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.3802em"}},[s("span")])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mbin"},"⋅"),s("span",{class:"mspace",style:{"margin-right":"0.2222em"}}),s("span",{class:"mord"},[s("span",{class:"mord"},[s("span",{class:"mord boldsymbol",style:{"margin-right":"0.04835em"}},"B")])]),s("span",{class:"mclose delimcenter",style:{top:"0em"}},[s("span",{class:"delimsizing size1"},")")])]),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.9918em"}},[s("span",{style:{top:"-3.3029em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},"")])])])])])])])])])])]),a(" [訳 者注 : ここの微分はむしろ "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",{mathvariant:"normal"},"grad"),s("mo",null,"")]),s("annotation",{encoding:"application/x-tex"},"\\operatorname{grad}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8889em","vertical-align":"-0.1944em"}}),s("span",{class:"mop"},[s("span",{class:"mord mathrm"},"grad")])])])]),a(" である]. 2 つの双極 子間の相互作用 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",null,":"),s("mi",null,"F"),s("mo",null,"∝"),s("msup",null,[s("mi",null,"r"),s("mrow",null,[s("mo",null,""),s("mn",null,"4")])])]),s("annotation",{encoding:"application/x-tex"},": F \\propto r^{-4}")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4306em"}}),s("span",{class:"mrel"},":"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.13889em"}},"F"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"∝"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.8141em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.02778em"}},"r"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mord mtight"},""),s("span",{class:"mord mtight"},"4")])])])])])])])])])])]),a(".")])],-1),C=s("h3",{id:"_9-19-磁気双極子としての点電荷",tabindex:"-1"},[a("9.19: 磁気双極子としての点電荷 "),s("a",{class:"header-anchor",href:"#_9-19-磁気双極子としての点電荷","aria-hidden":"true"},"#")],-1),R=s("ol",{start:"19"},[s("li",null,[a("磁気双極子としての点電荷 : "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("msub",null,[s("mi",null,"p"),s("mi",null,"μ")]),s("mo",null,"∝"),s("mi",{mathvariant:"normal"},"Φ"),s("mo",null,"∝"),s("msubsup",null,[s("mi",null,"v"),s("mo",{lspace:"0em",rspace:"0em"},"⊥"),s("mn",null,"2")]),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"B")]),s("annotation",{encoding:"application/x-tex"},"p_\\mu \\propto \\Phi \\propto v_{\\perp}^2 / B")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.7167em","vertical-align":"-0.2861em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"p"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.1514em"}},[s("span",{style:{top:"-2.55em","margin-left":"0em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mathnormal mtight"},"μ")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2861em"}},[s("span")])])])])]),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"∝"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord"},"Φ"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"∝"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0972em","vertical-align":"-0.2831em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"v"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t vlist-t2"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-2.4169em","margin-left":"-0.0359em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},[s("span",{class:"mrel mtight"},"⊥")])])]),s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])]),s("span",{class:"vlist-s"},"")]),s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.2831em"}},[s("span")])])])])]),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B")])])]),a(" は断熱 不変量 ("),s("a",{href:"./4#_4-22-断熱不変量"},"Section 4: #22"),a(" 参照).")])],-1),A=l("",3),j=s("ol",{start:"21"},[s("li",null,[a("一様(電)場中の球 (円柱) の分極 : "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",{stretchy:"false"},"("),s("mo",null,"+"),s("mi",null,"ρ")]),s("annotation",{encoding:"application/x-tex"},"(+\\rho")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1em","vertical-align":"-0.25em"}}),s("span",{class:"mopen"},"("),s("span",{class:"mord"},"+"),s("span",{class:"mord mathnormal"},"ρ")])])]),a(" と "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",null,""),s("mi",null,"ρ")]),s("annotation",{encoding:"application/x-tex"},"-\\rho")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.7778em","vertical-align":"-0.1944em"}}),s("span",{class:"mord"},""),s("span",{class:"mord mathnormal"},"ρ")])])]),a(" に一 様に帯電した球 (円柱) の重ね合わせで, "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"d"),s("mo",null,"∝"),s("mi",null,"E")]),s("annotation",{encoding:"application/x-tex"},"d \\propto E")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathnormal"},"d"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"∝"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.05764em"}},"E")])])]),a(".")])],-1),G=s("h3",{id:"_9-22-渦電流",tabindex:"-1"},[a("9.22: 渦電流 "),s("a",{class:"header-anchor",href:"#_9-22-渦電流","aria-hidden":"true"},"#")],-1),Q=s("ol",{start:"22"},[s("li",null,[a("渦電流: 電流損失密度 "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mo",null,"≈"),s("msup",null,[s("mi",null,"B"),s("mn",null,"2")]),s("msup",null,[s("mi",null,"v"),s("mn",null,"2")]),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"ρ"),s("mi",{mathvariant:"normal"},"."),s("mn",null,"1")]),s("annotation",{encoding:"application/x-tex"},"\\approx B^2 v^2 / \\rho .1")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4831em"}}),s("span",{class:"mrel"},"≈"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.03588em"}},"v"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal"},"ρ"),s("span",{class:"mord"},".1")])])]),a(" 回の通過で与え られる運動量 : "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"F"),s("mi",null,"τ"),s("mo",null,"≈"),s("msup",null,[s("mi",null,"B"),s("mn",null,"2")]),s("msup",null,[s("mi",null,"a"),s("mn",null,"3")]),s("mi",null,"d"),s("mi",{mathvariant:"normal"},"/"),s("mi",null,"ρ")]),s("annotation",{encoding:"application/x-tex"},"F \\tau \\approx B^2 a^3 d / \\rho")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6833em"}}),s("span",{class:"mord mathnormal",style:{"margin-right":"0.13889em"}},"F"),s("span",{class:"mord mathnormal",style:{"margin-right":"0.1132em"}},"τ"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}}),s("span",{class:"mrel"},"≈"),s("span",{class:"mspace",style:{"margin-right":"0.2778em"}})]),s("span",{class:"base"},[s("span",{class:"strut",style:{height:"1.0641em","vertical-align":"-0.25em"}}),s("span",{class:"mord"},[s("span",{class:"mord mathnormal",style:{"margin-right":"0.05017em"}},"B"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"2")])])])])])])]),s("span",{class:"mord"},[s("span",{class:"mord mathnormal"},"a"),s("span",{class:"msupsub"},[s("span",{class:"vlist-t"},[s("span",{class:"vlist-r"},[s("span",{class:"vlist",style:{height:"0.8141em"}},[s("span",{style:{top:"-3.063em","margin-right":"0.05em"}},[s("span",{class:"pstrut",style:{height:"2.7em"}}),s("span",{class:"sizing reset-size6 size3 mtight"},[s("span",{class:"mord mtight"},"3")])])])])])])]),s("span",{class:"mord mathnormal"},"d"),s("span",{class:"mord"},"/"),s("span",{class:"mord mathnormal"},"ρ")])])]),a(" (ここで "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"d")]),s("annotation",{encoding:"application/x-tex"},"d")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.6944em"}}),s("span",{class:"mord mathnormal"},"d")])])]),a(" は厚さ, "),s("span",{class:"katex"},[s("span",{class:"katex-mathml"},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("semantics",null,[s("mrow",null,[s("mi",null,"a")]),s("annotation",{encoding:"application/x-tex"},"a")])])]),s("span",{class:"katex-html","aria-hidden":"true"},[s("span",{class:"base"},[s("span",{class:"strut",style:{height:"0.4306em"}}),s("span",{class:"mord mathnormal"},"a")])])]),a(" は大きさ).")])],-1),U=[i,r,p,c,h,o,g,d,u,y,v,b,x,w,_,k,z,M,f,B,L,I,S,E,q,T,F,V,N,P,C,R,A,j,G,Q];function D(O,$,J,K,H,W){return m(),n("div",null,U)}const Z=t(e,[["render",D]]);export{Y as __pageData,Z as default};