{"id":209106,"date":"2024-03-21T14:06:00","date_gmt":"2024-03-21T14:06:00","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/%e3%83%a9%e3%83%97%e3%83%a9%e3%82%b9%e6%96%b9%e7%a8%8b%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%80%81%e8%a7%a3%e6%b3%95%e3%80%81%e5%bf%9c%e7%94%a8%e4%be%8b\/"},"modified":"2024-05-17T15:07:19","modified_gmt":"2024-05-17T15:07:19","slug":"%e3%83%a9%e3%83%97%e3%83%a9%e3%82%b9%e6%96%b9%e7%a8%8b%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%80%81%e8%a7%a3%e6%b3%95%e3%80%81%e5%bf%9c%e7%94%a8%e4%be%8b","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/ja\/%e3%83%a9%e3%83%97%e3%83%a9%e3%82%b9%e6%96%b9%e7%a8%8b%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%80%81%e8%a7%a3%e6%b3%95%e3%80%81%e5%bf%9c%e7%94%a8%e4%be%8b\/","title":{"rendered":"\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f | \u6982\u8981\u3001\u89e3\u6cd5\u3001\u5fdc\u7528\u4f8b"},"content":{"rendered":"

\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u6982\u8981\u3001\u89e3\u6cd5\u3001\u96fb\u78c1\u6c17\u5b66\u3084\u71b1\u4f1d\u5c0e\u306a\u3069\u306e\u5fdc\u7528\u4f8b\u3092\u8a73\u3057\u304f\u89e3\u8aac\u3059\u308b\u8a18\u4e8b\u3067\u3059\u3002<\/p>\n

\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f | \u6982\u8981\u3001\u89e3\u6cd5\u3001\u5fdc\u7528\u4f8b<\/h2>\n

\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306f\u3001\u7269\u7406\u5b66\u3068\u5de5\u5b66\u306b\u304a\u3051\u308b\u591a\u304f\u306e\u73fe\u8c61\u3092\u8a18\u8ff0\u3059\u308b\u91cd\u8981\u306a\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3059\u3002\u7279\u306b\u96fb\u78c1\u6c17\u5b66\u3001\u6d41\u4f53\u529b\u5b66\u3001\u71b1\u4f1d\u5c0e\u306a\u3069\u306e\u5206\u91ce\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u6982\u8981\u3001\u89e3\u6cd5\u3001\u304a\u3088\u3073\u5fdc\u7528\u4f8b\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n

\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u6982\u8981<\/h2>\n

\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306f\u3001\u30b9\u30ab\u30e9\u30fc\u5834 \\( \\phi \\) \u306b\u5bfe\u3059\u308b\u6b21\u306e\u5f62\u306e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3059\uff1a<\/p>\n

\n\\[ \\nabla^2 \\phi = 0 \\]\n<\/p>\n

\u3053\u3053\u3067\u3001\\( \\nabla^2 \\) \u306f\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u3068\u547c\u3070\u308c\u308b\u6f14\u7b97\u5b50\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n

\n\\[ \\nabla^2 = \\frac{\\partial^2}{\\partial x^2} + \\frac{\\partial^2}{\\partial y^2} + \\frac{\\partial^2}{\\partial z^2} \\]\n<\/p>\n

\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u3001\u8abf\u548c\u95a2\u6570\u307e\u305f\u306f\u8abf\u548c\u5834\u3068\u547c\u3070\u308c\u308b\u7279\u6027\u3092\u6301\u3064\u95a2\u6570\u306b\u5bfe\u3057\u3066\u306e\u307f\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n

\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5<\/h2>\n

\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u6700\u3082\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u306e\u4e00\u3064\u306f\u5206\u96e2\u5909\u6570\u6cd5\u3067\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u3001\u89e3\u3092\u7a7a\u9593\u5909\u6570\u306e\u7a4d\u3067\u8868\u73fe\u3057\u3001\u5404\u5909\u6570\u3054\u3068\u306b\u72ec\u7acb\u3057\u305f\u901a\u5e38\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u5206\u96e2\u3059\u308b\u3082\u306e\u3067\u3059\u3002<\/p>\n

\u5206\u96e2\u5909\u6570\u6cd5\u306e\u624b\u9806<\/h3>\n
    \n
  1. \u4eee\u5b9a\uff1a\u89e3 \\(\\phi(x, y, z)\\) \u3092\u6b21\u306e\u3088\u3046\u306b\u5206\u89e3\u3059\u308b \u2192 \\(\\phi(x, y, z) = X(x)Y(y)Z(z)\\)<\/li>\n
  2. \u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306b\u4ee3\u5165\u3057\u3001\u5404\u5909\u6570\u3054\u3068\u306b\u5206\u96e2\u3059\u308b\u3002<\/li>\n
  3. \u7d50\u679c\u3068\u3057\u3066\u5f97\u3089\u308c\u308b\u5404\u901a\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3002<\/li>\n
  4. \u5883\u754c\u6761\u4ef6\u3092\u7528\u3044\u3066\u5177\u4f53\u7684\u306a\u89e3\u3092\u6c42\u3081\u308b\u3002<\/li>\n<\/ol>\n

    \u4f8b\u3048\u3070\u30012\u6b21\u5143\u554f\u984c\u306b\u304a\u3044\u3066\u306f\uff1a<\/p>\n

    \n\\[ \\frac{1}{X(x)} \\frac{d^2 X(x)}{dx^2} + \\frac{1}{Y(y)} \\frac{d^2 Y(y)}{dy^2} = 0 \\]\n<\/p>\n

    \u3053\u306e\u5f0f\u3092\u6b21\u306e\u3088\u3046\u306b\u5206\u96e2\u3067\u304d\u307e\u3059\uff1a<\/p>\n

    \n\\[ \\frac{d^2 X(x)}{dx^2} = -\\lambda X(x) \\]
    \n\\[ \\frac{d^2 Y(y)}{dy^2} = \\lambda Y(y) \\]\n<\/p>\n

    \u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u5fdc\u7528\u4f8b<\/h2>\n

    \u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306f\u3001\u591a\u304f\u306e\u73fe\u5b9f\u4e16\u754c\u306e\u554f\u984c\u306b\u5fdc\u7528\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3044\u304f\u3064\u304b\u306e\u4ee3\u8868\u7684\u306a\u5fdc\u7528\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n

    \u96fb\u78c1\u6c17\u5b66<\/h3>\n

    \u96fb\u78c1\u6c17\u5b66\u3067\u306f\u3001\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306f\u9759\u96fb\u5834\u3084\u9759\u78c1\u5834\u306e\u8a08\u7b97\u306b\u4f7f\u308f\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u96fb\u4f4d \\(\\phi\\) \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u96fb\u5834 \\(\\mathbf{E}\\) \u306f\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\uff1a<\/p>\n

    \n\\[ \\mathbf{E} = -\\nabla \\phi \\]\n<\/p>\n

    \u71b1\u4f1d\u5c0e<\/h3>\n

    \u5b9a\u5e38\u72b6\u614b\u306e\u71b1\u4f1d\u5c0e\u3067\u306f\u3001\u6e29\u5ea6\u5206\u5e03 \\( T \\) \u304c\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6e29\u5ea6\u306f\u6642\u9593\u3068\u3068\u3082\u306b\u5909\u308f\u3089\u305a\u3001\u7a7a\u9593\u7684\u306b\u8abf\u548c\u3059\u308b\u72b6\u614b\u3092\u793a\u3057\u307e\u3059\uff1a<\/p>\n

    \n\\[ \\nabla^2 T = 0 \\]\n<\/p>\n

    \u6d41\u4f53\u529b\u5b66<\/h3>\n

    \u6d41\u4f53\u529b\u5b66\u3067\u306f\u3001\u6f5c\u5728\u6d41\u308c\u306e\u901f\u5ea6\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb \\(\\phi\\) \u304c\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059\uff1a<\/p>\n

    \n\\[ \\nabla^2 \\phi = 0 \\]\n<\/p>\n

    \u3053\u306e\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3092\u7528\u3044\u3066\u3001\u6d41\u4f53\u306e\u901f\u5ea6\u5834\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

    \u307e\u3068\u3081<\/h2>\n

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