{"id":2623,"date":"2022-03-26T14:44:06","date_gmt":"2022-03-26T05:44:06","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2623"},"modified":"2024-06-14T16:00:11","modified_gmt":"2024-06-14T07:00:11","slug":"%e5%8f%82%e8%80%83%ef%bc%9a%e3%82%b9%e3%83%88%e3%83%bc%e3%82%af%e3%82%b9%e3%81%ae%e5%ae%9a%e7%90%86%e3%81%ae%e8%a8%bc%e6%98%8e","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%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%e3%81%ae%e7%a9%8d%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9a%e3%82%b9%e3%83%88%e3%83%bc%e3%82%af%e3%82%b9%e3%81%ae%e5%ae%9a%e7%90%86%e3%81%ae%e8%a8%bc%e6%98%8e\/","title":{"rendered":"\u53c2\u8003\uff1a\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406\u306e\u8a3c\u660e"},"content":{"rendered":"

<\/p>\n

\u30b9\u30c8\u30fc\u30af\u30b9\u306e\u5b9a\u7406<\/h4>\n

$$ \\iint_S (\\nabla\\times\\boldsymbol{a})\\cdot\\boldsymbol{n}\\,dS = \\oint_C \\boldsymbol{a}\\cdot d\\boldsymbol{r}$$<\/p>\n

\u3053\u3053\u3067 \\(S\\) \u306f\u9589\u66f2\u7dda \\(C\\) \u3067\u56f2\u307e\u308c\u305f\u66f2\u9762\u3067\u3042\u308a\uff0c\\(\\boldsymbol{n}\\) \u306f\u305d\u306e\u66f2\u9762\u306e\u5fae\u5c0f\u9762\u7a4d \\(dS\\) \u306b\u5782\u76f4\u306a\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3002<\/p>\n

\"\"<\/p>\n

\u56f3\u306e\u3088\u3046\u306b\uff0c$z$ \u8ef8\u306b\u5782\u76f4\u306a $xy$ \u5e73\u9762\u4e0a\u306b\uff0c\u305d\u308c\u305e\u308c\u306e\u8fba\u306e\u9577\u3055\u304c \\(\\varDelta x, \\varDelta y\\) \u3067\u3042\u308b\u5fae\u5c0f\u30eb\u30fc\u30d7 \\(\\varDelta C_z\\) \u3067\u56f2\u307e\u308c\u305f\u5fae\u5c0f\u9762\u7a4d $\\varDelta S_z$ \u3092\u8003\u3048\uff0c\u3053\u306e\u5fae\u5c0f\u30eb\u30fc\u30d7\u306b\u6cbf\u3063\u305f\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{a}\\) \u306e\u63a5\u7dda\u6210\u5206\u3092\u53cd\u6642\u8a08\u56de\u308a\u306b1\u5468\uff0c\u7dda\u7a4d\u5206\u3059\u308b\u3002<\/p>\n

\\begin{eqnarray}
\n\\oint_{\\varDelta C_z} \\boldsymbol{a}\\cdot d\\boldsymbol{r} &=& a_x(1) \\varDelta x + a_y(2) \\varDelta y -a_x(3) \\varDelta x -a_y(4) \\varDelta y \\\\
\n&=& -\\left( a_x(3) -a_x(1)\\right) \\varDelta x + \\left(a_y(2) -a_y(4)\\right) \\varDelta y\\\\
\n&=& -\\frac{\\partial a_x}{\\partial y} \\varDelta y\\, \\varDelta x+ \\frac{\\partial a_y}{\\partial x} \\varDelta x\\, \\varDelta y \\\\
\n&=& \\left(\\frac{\\partial a_y}{\\partial x} -\\frac{\\partial a_x}{\\partial y}\\right)\\, \\varDelta x \\varDelta y \\\\
\n&=& \\left(\\nabla\\times \\boldsymbol{a}\\right)_z\\,\u00a0 \\varDelta x \\varDelta y \\\\
\n&=& \\left(\\nabla\\times \\boldsymbol{a}\\right)\\cdot\\boldsymbol{n}_z \\,\\varDelta S_z
\n\\end{eqnarray}<\/p>\n

\u3053\u306e\u5fae\u5c0f\u30eb\u30fc\u30d7\u3092\u7a4d\u5206\u3057\u3066\uff0c<\/p>\n

\u6709\u9650\u306e\u9762\u7a4d \\(S\\) \u306e\u66f2\u9762\u3068\u305d\u308c\u3092\u56f2\u3080\u9589\u66f2\u7dda \\(C\\) \u306b\u3064\u3044\u3066\u306f\uff0c\u305d\u308c\u3089\u3092\u69cb\u6210\u3057\u3066\u3044\u308b\u5fae\u5c0f\u8981\u7d20\u306e\u7dcf\u548c\u3092\u53d6\u308b\u3053\u3068\u306b\u306a\u308b\u304c\uff0c\u7121\u9650\u5c0f\u9023\u7d9a\u6975\u9650\u3067\u306f $\\displaystyle \\sum_i \\oint_{\\varDelta C_i} \\Rightarrow \\oint_{C}, \\ \\sum_i\\, \\varDelta S_i \\Rightarrow \\iint_S \\, dS$ \u3068\u306a\u308b\u3053\u3068\u304b\u3089\uff0c<\/p>\n

\\begin{eqnarray}
\n\\sum_i \\, \\oint_{\\varDelta C_i} \\boldsymbol{a}\\cdot d\\boldsymbol{r} &=&
\n\\sum_i \\, \\left(\\nabla\\times \\boldsymbol{a}\\right)\\cdot\\boldsymbol{n}_i \\,\\varDelta S_i \\\\
\n&\\Downarrow & \\\\
\n\\oint_{C} \\boldsymbol{a}\\cdot d\\boldsymbol{r} &=& \\iint_S \\left(\\nabla\\times \\boldsymbol{a}\\right)\\cdot\\boldsymbol{n} \\,dS
\n\\end{eqnarray}<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":2615,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2623","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\/2623","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=2623"}],"version-history":[{"count":4,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2623\/revisions"}],"predecessor-version":[{"id":8915,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2623\/revisions\/8915"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2615"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}