{"id":2765,"date":"2022-03-29T17:53:37","date_gmt":"2022-03-29T08:53:37","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2765"},"modified":"2025-02-03T12:14:39","modified_gmt":"2025-02-03T03:14:39","slug":"%e7%9c%9f%e7%a9%ba%e4%b8%ad%e3%81%ae%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%a8%e9%9b%bb%e7%a3%81%e6%b3%a2","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\/%e7%9c%9f%e7%a9%ba%e4%b8%ad%e3%81%ae%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%a8%e9%9b%bb%e7%a3%81%e6%b3%a2\/","title":{"rendered":"\u771f\u7a7a\u4e2d\u306e\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u3068\u96fb\u78c1\u6ce2"},"content":{"rendered":"<p><!--more--><\/p>\n<h3 id=\"yui_3_17_2_1_1648543930760_1523\" dir=\"ltr\">\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n<p><span id=\"selectionBoundary_1643507611808_7776307476778866\" class=\"rangySelectionBoundary\"><\/span>\\begin{eqnarray}<br id=\"yui_3_17_2_1_1648543930760_1525\" \/>\\nabla\\cdot \\boldsymbol{D} &amp;=&amp; \\rho\\\\<br id=\"yui_3_17_2_1_1648543930760_1526\" \/>\\nabla\\cdot\\boldsymbol{B} &amp;=&amp; 0\\\\<br id=\"yui_3_17_2_1_1648543930760_1527\" \/>\\nabla\\times\\boldsymbol{E} + \\frac{\\partial \\boldsymbol{B}}{\\partial t} &amp;=&amp; \\boldsymbol{0} \\\\<br id=\"yui_3_17_2_1_1648543930760_1528\" \/>\\nabla\\times\\boldsymbol{H} -\\frac{\\partial \\boldsymbol{D}}{\\partial t} &amp;=&amp; \\boldsymbol{J} <br id=\"yui_3_17_2_1_1648543930760_1529\" \/>\\end{eqnarray}<br id=\"yui_3_17_2_1_1648543930760_1530\" \/><br id=\"yui_3_17_2_1_1648543930760_1531\" \/><\/p>\n<h3 id=\"yui_3_17_2_1_1648543930760_1532\">\u771f\u7a7a\u4e2d\u306e\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u300c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u771f\u7a7a<\/strong><\/span>\u300d\u3068\u3044\u3046\u3068\u4f55\u304b\u606f\u3082\u3067\u304d\u306a\u3044\u3088\u3046\u306a\u5b87\u5b99\u7a7a\u9593\u3092\u30a4\u30e1\u30fc\u30b8\u3059\u308b\u304b\u3082\u77e5\u308c\u306a\u3044\u304c\uff0c\u3053\u3053\u3067\u306f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u96fb\u8377\u3082\u96fb\u6d41\u3082\u306a\u3044\u3068\u3044\u3046\u3053\u3068<\/strong><\/span>\uff0c\u3059\u306a\u308f\u3061 \\(\\rho = 0, \\ \\boldsymbol{J} = \\boldsymbol{0}\\)\u3002<br id=\"yui_3_17_2_1_1648543930760_1533\" \/><br id=\"yui_3_17_2_1_1648543930760_1534\" \/><\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1535\">$$ \\boldsymbol{E} \\equiv \\frac{1}{\\varepsilon_0} \\boldsymbol{D}, \\quad\\boldsymbol{H} \\equiv \\frac{1}{\\mu_0} \\boldsymbol{B}$$<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1537\">\u3092\u4f7f\u3063\u3066\uff0c\\(\\boldsymbol{E}\\) \u304a\u3088\u3073 \\(\\boldsymbol{B}\\) \u3067\u8868\u3059\u3068<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1538\"><span id=\"selectionBoundary_1643508373303_7254765342682294\" class=\"rangySelectionBoundary\"><\/span>\\begin{eqnarray}<br id=\"yui_3_17_2_1_1648543930760_1539\" \/>\\nabla\\cdot \\boldsymbol{E} &amp;=&amp; 0 \\tag{1}\\\\<br id=\"yui_3_17_2_1_1648543930760_1540\" \/>\\nabla\\cdot\\boldsymbol{B} &amp;=&amp; 0 \\tag{2}\\\\<br id=\"yui_3_17_2_1_1648543930760_1541\" \/>\\nabla\\times\\boldsymbol{E} + \\frac{\\partial \\boldsymbol{B}}{\\partial t} &amp;=&amp; \\boldsymbol{0}\u00a0 \\tag{3}\\\\<br id=\"yui_3_17_2_1_1648543930760_1542\" \/>\\frac{1}{\\mu_0}\\nabla\\times\\boldsymbol{B}<br \/>\n-\\varepsilon_0\\frac{\\partial \\boldsymbol{E}}{\\partial t} &amp;=&amp; \\boldsymbol{0} \\tag{4}<br id=\"yui_3_17_2_1_1648543930760_1544\" \/>\\end{eqnarray}<\/p>\n<h3 id=\"yui_3_17_2_1_1648543930760_1545\">\u6ce2\u52d5\u65b9\u7a0b\u5f0f<\/h3>\n<p id=\"yui_3_17_2_1_1648543930760_1547\">\\((4)\\) \u5f0f\u306b \\(\\mu_0\\) \u3092\u304b\u3051\u3066\u6642\u9593 \\(t\\) \u3067\u504f\u5fae\u5206\u3057\uff0c\\((3)\\) \u5f0f\u3084 \\((1)\\) \u5f0f\u3092\u4f7f\u3046\u3068<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1548\"><span id=\"selectionBoundary_1643509729141_18041266133215395\" class=\"rangySelectionBoundary\"><\/span>\\begin{eqnarray}<br id=\"yui_3_17_2_1_1648543930760_1549\" \/>\\frac{\\partial }{\\partial t} \\left\\{\\nabla\\times\\boldsymbol{B}<br \/>\n-\\varepsilon_0\\mu_0 \\frac{\\partial \\boldsymbol{E}}{\\partial t}\u00a0 \\right\\} <br id=\"yui_3_17_2_1_1648543930760_1551\" \/>&amp;=&amp; <br id=\"yui_3_17_2_1_1648543930760_1552\" \/>\\nabla\\times \\frac{\\partial \\boldsymbol{B}}{\\partial t} <br id=\"yui_3_17_2_1_1648543930760_1553\" \/>\u00a0 -\\varepsilon_0\\mu_0 \\frac{\\partial^2 \\boldsymbol{E}}{\\partial t^2}\\\\<br id=\"yui_3_17_2_1_1648543930760_1554\" \/>&amp;=&amp; -\\nabla\\times\\left(\\nabla\\times\\boldsymbol{E} \\right)<br id=\"yui_3_17_2_1_1648543930760_1555\" \/>\u00a0 -\\varepsilon_0\\mu_0 \\frac{\\partial^2 \\boldsymbol{E}}{\\partial t^2}\\\\<br id=\"yui_3_17_2_1_1648543930760_1556\" \/>&amp;=&amp; -\\left\\{\\nabla (\\nabla\\cdot\\boldsymbol{E}) -\\nabla^2 \\boldsymbol{E} \\right\\}<br id=\"yui_3_17_2_1_1648543930760_1557\" \/>\u00a0 -\\varepsilon_0\\mu_0 \\frac{\\partial^2 \\boldsymbol{E}}{\\partial t^2}\\\\<br id=\"yui_3_17_2_1_1648543930760_1558\" \/>&amp;=&amp; \\nabla^2 \\boldsymbol{E}<br id=\"yui_3_17_2_1_1648543930760_1559\" \/>\u00a0 -\\varepsilon_0\\mu_0 \\frac{\\partial^2 \\boldsymbol{E}}{\\partial t^2} = \\boldsymbol{0}<br id=\"yui_3_17_2_1_1648543930760_1560\" \/>\\end{eqnarray}<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1561\">\u4e00\u822c\u306b\uff0c\\(\\displaystyle \\nabla^2 f -\\frac{1}{v^2} \\frac{\\partial^2 f}{\\partial t^2} = 0\\) \u306e\u5f62\u306e\u5f0f\u306f\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong id=\"yui_3_17_2_1_1648543930760_1562\">\u6ce2\u52d5\u65b9\u7a0b\u5f0f<\/strong><\/span>\u3068\u547c\u3070\u308c\uff0c\u901f\u3055 \\(v\\) \u3067\u4f1d\u308f\u308b\u6ce2\u3092\u8868\u3057\u3066\u3044\u308b\u3002<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1563\">\u5f93\u3063\u3066\uff0c\u6ce2\u52d5\u65b9\u7a0b\u5f0f<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1564\">$$\\nabla^2 \\boldsymbol{E}<br id=\"yui_3_17_2_1_1648543930760_1565\" \/>\u00a0 -\\varepsilon_0\\mu_0 \\frac{\\partial^2 \\boldsymbol{E}}{\\partial t^2} = \\boldsymbol{0} $$<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1566\">\u306f\uff0c\u96fb\u5834 \\(\\boldsymbol{E}\\) \u304c\u901f\u3055 \\(\\displaystyle \\frac{1}{\\sqrt{\\varepsilon_0\\mu_0}}\\) \u3067\u4f1d\u308f\u308b\u6ce2\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1567\">\u540c\u69d8\u306b\u3057\u3066\uff0c<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1568\">$$\\nabla^2 \\boldsymbol{B}<br id=\"yui_3_17_2_1_1648543930760_1569\" \/>\u00a0 -\\varepsilon_0\\mu_0 \\frac{\\partial^2 \\boldsymbol{B}}{\\partial t^2} = \\boldsymbol{0} $$<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1570\">\u3082\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1571\">\u5f93\u3063\u3066\uff0c\u96fb\u78c1\u5834 \\(\\boldsymbol{E}, \\boldsymbol{B}\\) \u306f\u771f\u7a7a\u4e2d\u3092\u901f\u3055 \\(\\displaystyle \\frac{1}{\\sqrt{\\varepsilon_0\\mu_0}}\\) \u3067\u4f1d\u308f\u308b\u6ce2\uff0c\u3059\u306a\u308f\u3061<span style=\"font-family: helvetica, arial, sans-serif;\"><strong id=\"yui_3_17_2_1_1648543930760_1572\">\u96fb\u78c1\u6ce2<\/strong><\/span>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1573\">\u771f\u7a7a\u306e\u8a98\u96fb\u7387 \\(\\varepsilon_0\\) \u3084\u771f\u7a7a\u306e\u900f\u78c1\u7387 \\(\\mu_0 \\) \u306e\u5024\u306f\u5b9f\u9a13\u3067\u6c42\u3081\u3089\u308c\u308b\u3060\u308d\u3046\u304b\u3089\u305d\u306e\u5024\u3092\u5165\u308c\u3066\u8a08\u7b97\u3059\u308b\u3068\uff0c\u96fb\u78c1\u6ce2\u306e\u4f1d\u308f\u308b\u901f\u3055 \\(\\displaystyle \\frac{1}{\\sqrt{\\varepsilon_0\\mu_0}}\\) \u306f\u79d2\u901f 30\u4e07 km \u307b\u3069\u3067\u3042\u308b\u3053\u3068\u3082\u308f\u304b\u3063\u305f\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n<h3 id=\"yui_3_17_2_1_1648543930760_1574\">\u521d\u3081\u306b\u5149\u3042\u308a\u304d\uff0c\u305d\u306e\u6b63\u4f53\u306f\uff1f<\/h3>\n<p id=\"yui_3_17_2_1_1648543930760_1575\">\u3055\u3066\uff0c\u53e4\u6765\u3088\u308a\u5149\u3068\u306f\u4f55\u304b\uff0c\u305d\u306e\u6b63\u4f53\u3092\u63a2\u308b\u3079\u304f\u591a\u304f\u306e\u79d1\u5b66\u8005\u304c\u7814\u7a76\u3092\u7d9a\u3051\u3066\u304d\u305f\u3002<\/p>\n<h4 id=\"yui_3_17_2_1_1648543930760_1576\">\u5149\u306e\u7c92\u5b50\u8aac<\/h4>\n<p id=\"yui_3_17_2_1_1648543930760_1578\">\u30cb\u30e5\u30fc\u30c8\u30f3\u306f\uff0c\u5149\u304c\u76f4\u9032\u3059\u308b\u3053\u3068\u3084\u53cd\u5c04\u306e\u6cd5\u5247\uff0c\u307e\u305f\u5149\u7dda\u304c\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u4f1d\u9054\u3059\u308b\u3053\u3068\u304b\u3089\uff0c\u5149\u306e\u7c92\u5b50\u8aac\u3092\u5531\u3048\u305f\u3002<\/p>\n<h4 id=\"yui_3_17_2_1_1648543930760_1579\">\u5149\u306e\u6ce2\u52d5\u8aac<\/h4>\n<p id=\"yui_3_17_2_1_1648543930760_1580\">\u30db\u30a4\u30d8\u30f3\u30b9\u3089\u306f\uff0c\u56de\u6298\u3084\u5e72\u6e09\u3068\u3044\u3063\u305f\u6ce2\u7279\u6709\u306e\u73fe\u8c61\u304c\u5149\u3067\u3082\u89b3\u6e2c\u3055\u308c\u308b\u3053\u3068\u304b\u3089\u5149\u306e\u6ce2\u52d5\u8aac\u3092\u5531\u3048\u305f\u3002\u5149\u306e\u4f1d\u308f\u308b\u901f\u3055\u304c\u79d2\u901f 30\u4e07 km \u307b\u3069\u3067\u3042\u308b\u3053\u3068\u3084\uff0c\u504f\u5149\u73fe\u8c61\u304b\u3089\u5149\u306f\u6a2a\u6ce2\u3067\u3042\u308b\u3053\u3068\u3082\u308f\u304b\u3063\u3066\u304d\u305f\u3002<\/p>\n<h4 id=\"yui_3_17_2_1_1648543930760_1581\">\u5149\u306e\u96fb\u78c1\u6ce2\u8aac<\/h4>\n<p id=\"yui_3_17_2_1_1648543930760_1582\">\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u304b\u3089\u5c0e\u304b\u308c\u305f\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306e\u89e3\u3068\u3057\u3066\u306e\u96fb\u78c1\u6ce2\u306e\u6027\u8cea\u3092\u3064\u3089\u3064\u3089\u3068\u773a\u3081\u3066\u307f\u308b\u3068\uff0c\u3053\u308c\u306f\u5149\u306e\u6027\u8cea\u305d\u306e\u3082\u306e\u3060\uff01\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u3063\u3066\uff0c\u6700\u7d42\u7684\u306b\u306f<\/p>\n<h4 id=\"yui_3_17_2_1_1648543930760_1583\" style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong id=\"yui_3_17_2_1_1648543930760_1584\">\u5149\u306f\u96fb\u78c1\u6ce2\u3067\u3042\u308b\uff01<\/strong><\/span><\/h4>\n<p id=\"yui_3_17_2_1_1648543930760_1585\">\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u3063\u305f\u3002<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1587\">\u3068\u3044\u3046\u3053\u3068\u3067\u5149\u306e\u901f\u3055\uff0c\u5149\u901f\u3092 \\(c\\) \u3068\u66f8\u304f\u3068<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1588\">$$ c = \\frac{1}{\\sqrt{\\varepsilon_0\\mu_0}}, \\quad \\therefore \\varepsilon_0\\mu_0 = \\frac{1}{c^2}$$<\/p>\n<p id=\"yui_3_17_2_1_1648543930760_1589\">\u771f\u7a7a\u306e\u8a98\u96fb\u7387 \\(\\varepsilon_0\\) \u3068\u771f\u7a7a\u306e\u900f\u78c1\u7387 \\(\\mu_0 \\) \u304c\u5149\u901f \\(c\\) \u3092\u901a\u3058\u3066\u95a2\u4fc2\u3057\u3066\u3044\u308b\u3053\u3068\u306f\uff0c\u6388\u696d\u306e\u306a\u304b\u3067\u65e2\u306b\u4f7f\u3063\u3066\u3044\u3066\uff0c\u300c\u3042\u3068\u3067\u6642\u9593\u304c\u3042\u308c\u3070\u8aac\u660e\u3059\u308b\u304b\u3089\u306d\u300d\u306a\u3069\u3068\u8a00\u3063\u3066\u305f\u304b\u3082\u77e5\u308c\u306a\u3044\u3002\u4eca\uff0c\u3068\u3046\u3068\u3046\u305d\u306e\u8b0e\u304c\u89e3\u3051\u305f\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5149\u306f\u901f\u3055 $c$ \u3067\u4f1d\u64ad\u3059\u308b\u96fb\u78c1\u6ce2\u3067\u3042\u308b<\/strong><\/span>\u3053\u3068\u304b\u3089\\(\\displaystyle \\mu_0 = \\frac{1}{\\varepsilon_0 c^2}\\) \u306a\u306e\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u3053\u307e\u3067\u306f 19\u4e16\u7d00\u672b\u307e\u3067\u306e\u8a71\u3002<\/p>\n<h4>\u3075\u305f\u305f\u3073\u5149\u306e\u7c92\u5b50\u8aac\uff1f<\/h4>\n<p>\u3068\u3053\u308d\u304c\uff0c20\u4e16\u7d00\u306b\u5165\u308b\u3068\uff0c\u9ed2\u4f53\u653e\u5c04\u30fb\u30d7\u30e9\u30f3\u30af\u5206\u5e03\uff0c\u5149\u96fb\u52b9\u679c\uff0c\u30b3\u30f3\u30d7\u30c8\u30f3\u52b9\u679c\uff0c\u306a\u3069\u306e\u73fe\u8c61\u304c\u660e\u3089\u304b\u306b\u306a\u3063\u3066\u304d\u305f\u3002\u3053\u308c\u3089\u306f\u5149\u304c\uff0c1\u500b1\u500b\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u904b\u52d5\u91cf\u3092\u6301\u3064\u7c92\u3005\uff08\u3064\u3076\u3064\u3076\uff09\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u8aac\u660e\u3067\u304d\u308b\u73fe\u8c61\u3067\u3042\u308b\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\uff0c\u3075\u305f\u305f\u3073\uff0c\u5149\u306e\u7c92\u5b50\u8aac\u304c&#8230; \u3068\u306a\u308b\u306e\u3060\u304c\uff0c\u3053\u308c\u306f\u300c\u91cf\u5b50\u529b\u5b66\u300d\u306e\u5206\u91ce\u3067\u3042\u308a\u5f53\u5b66\u79d1\u3067\u306f\u958b\u8b1b\u3057\u3066\u306a\u3044\u6388\u696d\u306a\u306e\u3067\uff0c\u3044\u305a\u308c\u6a5f\u4f1a\u304c\u3042\u308c\u3070&#8230;<\/p>\n<h4>\u5149\u901f $c$ \u3068\u306f\u4f55\u306b\u5bfe\u3059\u308b\u901f\u3055\u306a\u306e\u304b\uff1f<\/h4>\n<p>\u3055\u3066\uff0c20\u4e16\u7d00\u306b\u5165\u3063\u3066\u554f\u984c\u3068\u306a\u3063\u3066\u304d\u305f\u306e\u306f\u3082\u3046\u4e00\u3064\u3002\u5149\u304c\u5149\u901f $c$ \u3067\u4f1d\u308f\u308b\u6ce2\u306a\u306e\u3067\u3042\u308c\u3070\uff0c\u5149\u901f $c$\u00a0 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