{"id":1103,"date":"2022-01-17T17:19:32","date_gmt":"2022-01-17T08:19:32","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=1103"},"modified":"2026-01-30T10:49:20","modified_gmt":"2026-01-30T01:49:20","slug":"%e9%9b%bb%e7%a3%81%e5%a0%b4%e3%81%ae%e5%a4%89%e6%8f%9b%e3%81%ae%e5%bf%85%e8%a6%81%e6%80%a7","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%83%ad%e3%83%bc%e3%83%ac%e3%83%b3%e3%83%84%e5%a4%89%e6%8f%9b%e3%81%ab%e3%82%88%e3%82%89%e3%81%aa%e3%81%84%e7%9b%b8%e5%af%be%e8%ab%96%e3%81%ae%e7%90%86%e8%a7%a3\/%e9%9b%bb%e7%a3%81%e5%a0%b4%e3%81%ae%e5%a4%89%e6%8f%9b%e3%81%ae%e5%bf%85%e8%a6%81%e6%80%a7\/","title":{"rendered":"\u96fb\u78c1\u5834\u306e\u5909\u63db\u306e\u5fc5\u8981\u6027"},"content":{"rendered":"

<\/p>\n

\u306a\u305c\u96fb\u78c1\u5834\u306e\u5909\u63db\u6027\u3092\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3060\u308d\u3046\u304b\uff1f\u4ee5\u4e0b\u306e\u4f8b\u3067\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u89b3\u6e2c\u53ef\u80fd\u306a\u7269\u7406\u7684\u73fe\u8c61\u304c\u89b3\u6e2c\u8005\u306e\u904b\u52d5\u72b6\u614b\uff08\u901f\u5ea6\uff09\u306b\u3088\u3089\u305a\u306b\u77db\u76fe\u306a\u304f\u6c7a\u3081\u3089\u308c\u308b\u305f\u3081\u306b\uff0c\u5fc5\u8981\u306a\u306e\u3067\u3042\u308b\u3002<\/p>\n

\u96fb\u7dda\u3068\u904b\u52d5\u3059\u308b\u8377\u96fb\u7c92\u5b50<\/h3>\n

\"\"<\/p>\n

\u56f3\u306e\u3088\u3046\u306b\uff0c\u5168\u4f53\u3068\u3057\u3066\u5e2f\u96fb\u3057\u3066\u3044\u306a\u3044\uff08\u3064\u307e\u308a \\(\\rho=0\\) \u3060\u304b\u3089\u96fb\u5834\u3092\u3064\u304f\u3089\u306a\u3044\uff09\u96fb\u7dda\u306b\u96fb\u6d41 \\(I\\) \u304c\u6d41\u308c\u3066\u3044\u308b\u3002\u56f3\u306e\u3088\u3046\u306b\u5ea7\u6a19\u8ef8\u3092\u8a2d\u5b9a\u3059\u308b\u3068 \\(\\vec{I} = (I, 0, 0)\\)\u3002<\/p>\n

\u3053\u306e\u3068\u304d\uff0c\u96fb\u7dda\u304b\u3089\u8ddd\u96e2 \\(r\\)\u00a0 \u96e2\u308c\u305f\u3068\u3053\u308d\u3092\u96fb\u7dda\u306b\u5e73\u884c\u306a\u901f\u5ea6 \\(\\vec{v} = (v, 0, 0)\\) \u3067\u904b\u52d5\u3059\u308b\u96fb\u8377 \\(q>0\\) \u3092\u3082\u3064\u8377\u96fb\u7c92\u5b50\u304c\u53d7\u3051\u308b\u30ed\u30fc\u30ec\u30f3\u30c4\u529b\u306f\uff1f<\/p>\n

\u89e3\u7b54\u4f8b\uff1a<\/h3>\n

\u307e\u305a\u96fb\u7dda\u306f\u5e2f\u96fb\u3057\u3066\u3044\u306a\u3044\u306e\u3067\uff0c\u96fb\u5834\u306f\u30bc\u30ed\u3002\\(\\vec{E} = \\vec{0}\\)\u3002<\/p>\n

\u3057\u305f\u304c\u3063\u3066\uff0c\u96fb\u8377\u304c\u3046\u3051\u308b\u30ed\u30fc\u30ec\u30f3\u30c4\u529b\u306f<\/p>\n

$$\\vec{F} = q \\vec{v} \\times \\vec{B}$$<\/p>\n

\u76f4\u7dda\u96fb\u6d41\u306b\u3088\u3063\u3066\u3064\u304f\u3089\u308c\u308b\u78c1\u5834\u306f\u30a2\u30f3\u30da\u30fc\u30eb\u306e\u6cd5\u5247\u304b\u3089\uff0c\u8377\u96fb\u7c92\u5b50\u306e\u4f4d\u7f6e\u3067\u306f<\/p>\n

$$\\vec{B} = (0, B_y, 0), \\quad B_y = \\frac{I}{2\\pi\\varepsilon_0 c^2 r}$$<\/p>\n

\u3057\u305f\u304c\u3063\u3066\uff0c\u8377\u96fb\u7c92\u5b50\u306b\u306f\u305f\u3089\u304f\u30ed\u30fc\u30ec\u30f3\u30c4\u529b\u306e\u5404\u6210\u5206\u306f<\/p>\n

\\begin{eqnarray}
F_x &=& q (v_y B_z -v_z B_y) = 0\\\\
F_y &=& q(v_z B_x -v_x B_z) =\u00a0 0\\\\
F_z &=& q(v_x B_y -v_y B_x) = \\frac{q v I}{2\\pi\\varepsilon_0 c^2 r}
\\end{eqnarray}<\/p>\n

\u3088\u3063\u3066\uff0c\u8377\u96fb\u7c92\u5b50\u306f\u96fb\u7dda\u306b\u5f15\u304d\u4ed8\u3051\u3089\u308c\u308b\u5411\u304d\u306b\u529b\u304c\u306f\u305f\u3089\u304f\u3002<\/p>\n

\u3053\u308c\u3092\u901f\u5ea6 \\(\\vec{v}\\) \u3067\u904b\u52d5\u3059\u308b\u6163\u6027\u7cfb\u3067\u307f\u308b\u3068…<\/h3>\n

\u4e0a\u8a18\u306e\u554f\u984c\u3092\uff0c\u8377\u96fb\u7c92\u5b50\u306e\u901f\u5ea6 \\(\\vec{v}\\) \u3067\u904b\u52d5\u3059\u308b\u6163\u6027\u7cfb\u304b\u3089\u307f\u308b\u3068\uff0c\u901f\u5ea6\u306e\u5408\u6210\u5247\u306b\u3088\u308a\uff0c\u3053\u306e\u6163\u6027\u7cfb\u306e\u89b3\u6e2c\u8005\u304b\u3089\u307f\u308b\u8377\u96fb\u7c92\u5b50\u306e\u901f\u5ea6 \\(\\vec{v}’\\) \u306f<\/p>\n

$$ \\vec{v}’ = \\vec{v}-\\vec{v} = \\vec{0}$$<\/p>\n

\u3068\u306a\u308a\uff0c\u30ed\u30fc\u30ec\u30f3\u30c4\u529b\u306f\u30bc\u30ed\u306b\u306a\u3063\u3066\u3057\u307e\u3046\uff01\uff1f<\/p>\n

$$\\vec{F}’ = q \\vec{v}’ \\times \\vec{B} = \\vec{0}$$<\/p>\n

\u529b\u304c\u306f\u305f\u3089\u304b\u306a\u3051\u308c\u3070\u96fb\u7dda\u306b\u5f15\u304d\u4ed8\u3051\u3089\u308c\u308b\u3053\u3068\u306f\u306a\u3044\u3002\u8377\u96fb\u7c92\u5b50\u306e\u904b\u52d5\u306f\uff0c\u89b3\u6e2c\u3059\u308b\u5ea7\u6a19\u7cfb\u306b\u3088\u3063\u3066\u5909\u308f\u3063\u3066\u3057\u307e\u3046\u306e\u3067\u3042\u308d\u3046\u304b\uff1f<\/p>\n

\u679c\u305f\u3057\u3066… \uff1f<\/p>\n

\u96fb\u78c1\u5834\u306e\u76f8\u5bfe\u6027<\/h3>\n

\u89b3\u6e2c\u3059\u308b\u5ea7\u6a19\u7cfb\u306e\u9055\u3044\u306b\u3088\u3063\u3066\u7269\u7406\u5b66\u7684\u306a\u904b\u52d5\u304c\u7570\u306a\u3063\u3066\u3057\u307e\u3046\u3053\u3068\u306f\uff0c\u3042\u308a\u3048\u306a\u3044\u3002\u4e0a\u306e\u8b70\u8ad6\u306f\u3069\u3053\u304b\u304c\u304a\u304b\u3057\u3044\u3002<\/p>\n

\u3059\u3067\u306b\u300c\u96fb\u78c1\u5834\u306e\u5909\u63db<\/a>\u300d\u3067\u8aac\u660e\u3057\u305f\u3088\u3046\u306b\uff0c\u8377\u96fb\u7c92\u5b50\u306e\u901f\u5ea6 \\(\\boldsymbol{v}\\) \u3067\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306f\uff0c<\/p>\n

\\begin{eqnarray}
\n\\bar{E}_{\\perp} &=& \\frac{E_{\\perp}+ (\\boldsymbol{v}\\times\\boldsymbol{B})_{\\perp}}{\\sqrt{1 -v^2}}\\\\
\n\\end{eqnarray}<\/p>\n

\u3068\u3044\u3046\u96fb\u5834\u3092\u611f\u3058\u308b\u306e\u3067\uff0c\u3053\u306e\u96fb\u5834\u306b\u3088\u3063\u3066\uff0c\u3053\u306e\u554f\u984c\u306e\u3088\u3046\u306b\u305f\u3068\u3048 \\(E_{\\perp} = 0\\) \u3067\u3042\u3063\u3066\u3082\uff01<\/strong><\/span>\u3084\u306f\u308a\u8377\u96fb\u7c92\u5b50\u306f\u96fb\u7dda\u306b\u5f15\u304d\u3064\u3051\u3089\u308c\u308b\u529b\u3092\u53d7\u3051\u3066\u904b\u52d5\u3059\u308b\u3002<\/p>\n

4\u5143\u529b\u3068\u3057\u3066\u306e\u76f8\u5bfe\u8ad6\u7684\u306a\u30ed\u30fc\u30ec\u30f3\u30c4\u529b<\/h3>\n

\u8377\u96fb\u7c92\u5b50\u306e4\u5143\u901f\u5ea6\u3092 \\(\\boldsymbol{v} = v^{\\mu} \\boldsymbol{e}_{\\mu}\\) \u3068\u3059\u308b\u3068\uff0c\u3053\u306e\u8377\u96fb\u7c92\u5b50\u304c\u53d7\u3051\u308b4\u5143\u529b<\/strong><\/span>\u3068\u3057\u3066\u306e\u76f8\u5bfe\u8ad6\u7684\u306a\u30ed\u30fc\u30ec\u30f3\u30c4\u529b<\/strong><\/span>\u306e\u6210\u5206 \\(f_{\\mu}\\) \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n

$$f_{\\mu} \\equiv q F_{\\mu\\nu} v^{\\nu}$$\u3053\u3053\u3067 \\(F_{\\mu\\nu}\\) \u306f\u96fb\u78c1\u5834\u30c6\u30f3\u30bd\u30eb<\/strong><\/span>\u3067\u3042\u308b\u3002<\/p>\n

\u89b3\u6e2c\u8005 \\(A\\) \u304b\u3089\u307f\u308b\u3068\uff0c\u8377\u96fb\u7c92\u5b50\u306f\u901f\u5ea6 \\(v \\boldsymbol{e}\\) \u3067\u904b\u52d5\u3057\u3066\u3044\u308b\u306e\u3067\uff0c4\u5143\u901f\u5ea6\u306e\u5408\u6210\u5247<\/strong><\/span>\u304b\u3089
\n$${v}^{\\mu} = \\frac{{u}^{\\mu} + v {e}^{\\mu}}{\\sqrt{1 -v^2}}$$<\/p>\n

\u3057\u305f\u304c\u3063\u3066\u76f8\u5bfe\u8ad6\u7684\u306a\u30ed\u30fc\u30ec\u30f3\u30c4\u529b<\/strong><\/span>\u306f<\/p>\n

\\begin{eqnarray}
\nf_{\\mu} &=& q F_{\\mu\\nu} v^{\\nu} \\\\
\n&=& q F_{\\mu\\nu} \\frac{{u}^{\\mu} + v {e}^{\\mu}}{\\sqrt{1 -v^2}}\\\\
\n&=& q \\frac{F_{\\mu\\nu}{u}^{\\mu} + F_{\\mu\\nu} v {e}^{\\mu}}{\\sqrt{1 -v^2}} \\\\
\n&=& q \\frac{E_{\\mu} + (\\boldsymbol{v}\\times\\boldsymbol{B})_{\\mu}}{\\sqrt{1 -v^2}}
\n\\end{eqnarray}<\/p>\n

\u4e0a\u8a18\u306e\u7d50\u679c\u304b\u3089\u3082\u308f\u304b\u308b\u3088\u3046\u306b\uff0c4\u5143\u529b<\/strong><\/span>\u3068\u3057\u3066\u306e\u76f8\u5bfe\u8ad6\u7684\u306a\u30ed\u30fc\u30ec\u30f3\u30c4\u529b\u306e\u7a7a\u9593\u6210\u5206\u306f\uff0c\u3044\u308f\u3086\u308b\uff083\u6b21\u5143\u7684\u306a\uff09\u30ed\u30fc\u30ec\u30f3\u30c4\u529b \\(q (\\vec{E} + \\vec{v}\\times\\vec{B})\\) \u3068\u306f\u30ed\u30fc\u30ec\u30f3\u30c4\u56e0\u5b50<\/strong><\/span> \\(\\gamma \\equiv 1\/\\sqrt{1-v^2}\\) \u306e\u5206\u3060\u3051\u7570\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n

\u4e00\u65b9\uff0c\u8377\u96fb\u7c92\u5b50\u3068\u540c\u3058\u901f\u5ea6\u3067\u904b\u52d5\u3057\u3066\u3044\u308b\u89b3\u6e2c\u8005 \\(B\\) \u304b\u3089\u307f\u308b\u3068\uff0c
\n$${v}^{\\mu} = \\bar{u}^{\\mu} $$<\/p>\n

\u3057\u305f\u304c\u3063\u3066\u76f8\u5bfe\u8ad6\u7684\u306a\u30ed\u30fc\u30ec\u30f3\u30c4\u529b\u306f<\/p>\n

\\begin{eqnarray}
\nf_{\\mu} &=& q F_{\\mu\\nu} v^{\\nu} \\\\
\n&=& q F_{\\mu\\nu} \\bar{u}^{\\nu} \\\\
\n&=& q \\bar{E}_{\\mu}
\n\\end{eqnarray}<\/p>\n","protected":false},"excerpt":{"rendered":"

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