{"id":2639,"date":"2022-03-26T15:55:22","date_gmt":"2022-03-26T06:55:22","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2639"},"modified":"2024-11-11T10:53:51","modified_gmt":"2024-11-11T01:53:51","slug":"%e5%8f%82%e8%80%83%ef%bc%9a%e9%9b%bb%e8%8d%b7%e3%81%ae%e4%bf%9d%e5%ad%98%e5%89%87","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e3%83%9e%e3%82%af%e3%82%b9%e3%82%a6%e3%82%a7%e3%83%ab%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ab%e7%8f%be%e3%82%8c%e3%82%8b%e8%ab%b8%e9%87%8f%e3%81%ae%e8%a7%a3%e8%aa%ac\/%e5%8f%82%e8%80%83%ef%bc%9a%e9%9b%bb%e8%8d%b7%e3%81%ae%e4%bf%9d%e5%ad%98%e5%89%87\/","title":{"rendered":"\u53c2\u8003\uff1a\u96fb\u8377\u306e\u4fdd\u5b58\u5247"},"content":{"rendered":"<p><!--more--><\/p>\n<h3 id=\"yui_3_17_2_1_1648277665480_1358\">\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n<p dir=\"ltr\">\\begin{eqnarray}\\nabla\\cdot \\boldsymbol{D} &amp;=&amp; \\rho\u00a0 \\tag{1}\\\\<br \/>\n\\nabla\\cdot\\boldsymbol{B} &amp;=&amp; 0\u00a0 \\tag{2}\\\\<br \/>\n\\nabla\\times\\boldsymbol{E} + \\frac{\\partial \\boldsymbol{B}}{\\partial t} &amp;=&amp; \\boldsymbol{0}\u00a0 \\tag{3}\\\\<br \/>\n\\nabla\\times\\boldsymbol{H} &#8211; \\frac{\\partial \\boldsymbol{D}}{\\partial t} &amp;=&amp; \\boldsymbol{J} \\tag{4}<br \/>\n\\end{eqnarray}<\/p>\n<h3 dir=\"ltr\">\u96fb\u8377\u306e\u4fdd\u5b58\u5247\uff08\u5fae\u5206\u5f62\uff09<\/h3>\n<p dir=\"ltr\">\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u306e (1) \u5f0f\u306e\u4e21\u8fba\u3092\u6642\u9593 \\(t\\) \u3067\u504f\u5fae\u5206\u3059\u308b\u3068\uff08\u504f\u5fae\u5206\u3067\u3042\u308b \\(\\displaystyle \\frac{\\partial}{\\partial t}\\) \u3068 \\(\\nabla\\) \u306f\u4ea4\u63db\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3092\u4f7f\u3063\u3066\uff09<\/p>\n<p dir=\"ltr\">$$\\nabla\\cdot \\frac{\\partial \\boldsymbol{D}}{\\partial t} = \\frac{\\partial \\rho}{\\partial t}$$<\/p>\n<p dir=\"ltr\">\u307e\u305f\uff0c(4) \u5f0f\u306e\u4e21\u8fba\u306e\u767a\u6563\u3092\u3068\u308b\u3068\uff08\u56de\u8ee2\u306e\u767a\u6563\u306f\u6052\u7b49\u7684\u306b\u30bc\u30ed\uff0c\u3064\u307e\u308a \\(\\nabla\\cdot(\\nabla\\times\\boldsymbol{H}) = 0 \\) \u3067\u3042\u308b\u3053\u3068\u304b\u3089\uff09<\/p>\n<p dir=\"ltr\">$$-\\nabla\\cdot \\frac{\\partial \\boldsymbol{D}}{\\partial t} = \\nabla\\cdot\\boldsymbol{J}$$<\/p>\n<p dir=\"ltr\">\u3053\u308c\u30892\u3064\u306e\u5f0f\u306e\u4e21\u8fba\u3092\u8db3\u3059\u3068\u4ee5\u4e0b\u306e\u5f0f\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n<p dir=\"ltr\">$$\\frac{\\partial \\rho}{\\partial t} + \\nabla\\cdot\\boldsymbol{J} = 0$$<\/p>\n<p dir=\"ltr\">\u3053\u306e\u5f62\u306e\u5f0f\u306f\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u9023\u7d9a\u306e\u5f0f<\/strong><\/span>\u300d\u3068\u547c\u3070\u308c\u308b\u304c\uff0c\u4ee5\u4e0b\u306b\u8ff0\u3079\u308b\u8aac\u660e\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u96fb\u8377\u306e\u4fdd\u5b58\u5247<\/strong><\/span>\u300d\u3092\u8868\u3057\u3066\u3044\u308b\u3002<\/p>\n<ul>\n<li dir=\"ltr\">\u53c2\u8003\uff1a<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E9%80%A3%E7%B6%9A%E3%81%AE%E6%96%B9%E7%A8%8B%E5%BC%8F\">\u9023\u7d9a\u306e\u65b9\u7a0b\u5f0f &#8211; Wikipedia<\/a><\/li>\n<\/ul>\n<h3 dir=\"ltr\">\u96fb\u8377\u306e\u4fdd\u5b58\u5247\uff08\u7a4d\u5206\u5f62\uff09<\/h3>\n<p dir=\"ltr\">\u4e0a\u8a18\u306e\u300c<strong>\u9023\u7d9a\u306e\u5f0f<\/strong>\u300d\u3092\u4e00\u5b9a\u306e\u4f53\u7a4d \\(V\\) \u3067\u4f53\u7a4d\u5206\u3057\u3066\u4e00\u90e8\u3092\u79fb\u884c\u3057\u3066\u3084\u308b\u3068<\/p>\n<p dir=\"ltr\">$$\\iiint_V \\frac{\\partial \\rho}{\\partial t}\\, dV = &#8211; \\iiint_V \\nabla\\cdot\\boldsymbol{J}\\, dV $$<\/p>\n<p dir=\"ltr\">\u53f3\u8fba\u306e\u7a4d\u5206\u30d1\u30fc\u30c8\u306f\u30ac\u30a6\u30b9\u306e\u5b9a\u7406\u3092\u4f7f\u3063\u3066\uff0c<\/p>\n<p dir=\"ltr\">$$\\iiint_V \\nabla\\cdot\\boldsymbol{J}\\, dV = \\iint_S \\boldsymbol{J}\\cdot\\boldsymbol{n}\\, dS$$ \u3068\u306a\u308a\uff0c\u3053\u308c\u306f\u4f53\u7a4d \\(V\\) \u3092\u56f2\u3080\u9589\u66f2\u9762 \\(S\\) \u3092\u8cab\u3044\u3066\u5916\u5074\u306b\u51fa\u3066\u3044\u304f\u96fb\u6d41\uff0c\u3064\u307e\u308a\u5358\u4f4d\u6642\u9593\u3042\u305f\u308a\u306e\u96fb\u8377\u306e\u6d41\u308c\u3068\u306a\u308b\u3002<\/p>\n<p dir=\"ltr\">\u4e00\u65b9\uff0c\u5de6\u8fba\u306f<\/p>\n<p dir=\"ltr\">$$\u00a0 \\iiint_V \\frac{\\partial \\rho}{\\partial t}\\, dV =\u00a0 \\frac{d}{dt} \\iiint_V \\rho \\, dV = \\frac{d Q}{dt} $$ \u3068\u306a\u308b\u3002\u3053\u3053\u3067 \\(Q\\) \u306f\u4f53\u7a4d \\(V\\) \u5185\u306e\u5168\u96fb\u8377\u3067\u3042\u308b\u3002<\/p>\n<p dir=\"ltr\">\u307e\u3068\u3081\u308b\u3068\uff0c<\/p>\n<p dir=\"ltr\">$$ \\frac{d Q}{dt} = -\\iint_S \\boldsymbol{J}\\cdot\\boldsymbol{n}\\, dS $$<\/p>\n<p dir=\"ltr\">\u3068\u306a\u308a\uff0c\u4f53\u7a4d \\(V\\) \u3092\u56f2\u3080\u9589\u66f2\u9762 \\(S\\) \u3092\u8cab\u3044\u3066\u96fb\u8377\u304c\u5916\u5074\u306b\u51fa\u3066\u3044\u304f\u3068\uff0c\u305d\u308c\u3060\u3051\u4f53\u7a4d \\(V\\)\u00a0 \u5185\u306e\u96fb\u8377\u304c\u6e1b\u5c11\u3059\u308b\u3053\u3068\u3092\u3042\u3089\u308f\u3057\uff0c\u51fa\u3066\u884c\u3063\u305f\u5206\u306e\u96fb\u8377\u3060\u3051\u4e2d\u306b\u3042\u3063\u305f\u96fb\u8377\u304c\u6e1b\u308b\u3068\u3044\u3046\u5f62\u306b\u306a\u3063\u3066\u3044\u308b\u3002\u3053\u308c\u304c\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u96fb\u8377\u306e\u4fdd\u5b58\u5247<\/strong><\/span>\u300d\u3067\u3042\u308b\u3002\u96fb\u8377\u306f\u4f55\u3082\u306a\u3044\u3068\u3053\u308d\u304b\u3089\u6025\u306b\u51fa\u73fe\u3057\u305f\u308a\uff0c\u4eca\u307e\u3067\u3042\u3063\u305f\u306e\u304c\u6025\u306b\u8de1\u5f62\u3082\u306a\u304f\u6d88\u6ec5\u3057\u305f\u308a\u306f\u3057\u306a\u3044\u3002\u3061\u3083\u3093\u3068\u7406\u7531\u304c\u3042\u3063\u3066\uff08\u5916\u304b\u3089\u5165\u3063\u3066\u304d\u305f\u308a\uff0c\u5916\u3078\u51fa\u3066\u884c\u3063\u305f\u308a\u3057\u3066\uff09\\(Q\\) \u304c\u5909\u5316\u3059\u308b\u306e\u3060\u3068\u3044\u3046\u610f\u5473\u3002<\/p>\n<p dir=\"ltr\">\u7279\u306b\uff0c\u9589\u66f2\u9762 \\(S\\) \u3092\u8cab\u3044\u3066\u51fa\u3066\u3044\u304f\u96fb\u6d41\u304c\u6b63\u5473\uff08\u30d7\u30e9\u30b9\u30de\u30a4\u30ca\u30b9\u3067\uff09\u30bc\u30ed\u3068\u3044\u3046\u5834\u5408\u306b\u306f\uff0c<\/p>\n<p dir=\"ltr\">$$\\frac{d Q}{dt} = 0 $$<\/p>\n<p dir=\"ltr\">\u3068\u306a\u308a\uff0c\\(Q\\) \u306f\u4e00\u5b9a\u3068\u306a\u308a\uff0c\u307e\u3055\u306b\u300c\u4fdd\u5b58\u300d\u3055\u308c\u308b\u3002<\/p>\n<p dir=\"ltr\">\u96fb\u8377\u306e\u4fdd\u5b58\u5247\u306f\uff0c\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u3068\u306f\u5225\u306b\u4eee\u5b9a\u3055\u308c\u308b\u3082\u306e\u3067\u306f\u306a\u304f\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><u><strong>\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u304c\u96fb\u8377\u306e\u4fdd\u5b58\u5247\u3092\u542b\u3093\u3067\u3044\u308b\u306e\u3060<\/strong><\/u><\/span>\uff01\u3068\u3044\u3046\u306e\u304c\u5927\u4e8b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":2626,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2639","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=2639"}],"version-history":[{"count":8,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2639\/revisions"}],"predecessor-version":[{"id":7553,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2639\/revisions\/7553"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2626"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}