{"id":209084,"date":"2024-03-21T14:05:53","date_gmt":"2024-03-21T14:05:53","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/%e7%90%83%e5%bd%a2%e3%82%b3%e3%83%b3%e3%83%87%e3%83%b3%e3%82%b5%e3%81%ae%e5%85%ac%e5%bc%8f-%e8%a7%a3%e8%aa%ac%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95\/"},"modified":"2024-05-17T15:07:03","modified_gmt":"2024-05-17T15:07:03","slug":"%e7%90%83%e5%bd%a2%e3%82%b3%e3%83%b3%e3%83%87%e3%83%b3%e3%82%b5%e3%81%ae%e5%85%ac%e5%bc%8f-%e8%a7%a3%e8%aa%ac%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/ja\/%e7%90%83%e5%bd%a2%e3%82%b3%e3%83%b3%e3%83%87%e3%83%b3%e3%82%b5%e3%81%ae%e5%85%ac%e5%bc%8f-%e8%a7%a3%e8%aa%ac%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u516c\u5f0f | \u89e3\u8aac\u3068\u8a08\u7b97\u65b9\u6cd5"},"content":{"rendered":"<p class=\"sidekick\">\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u516c\u5f0f\u3068\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3002\u57fa\u672c\u69cb\u9020\u304b\u3089\u516c\u5f0f\u306e\u5c0e\u51fa\u3001\u5177\u4f53\u7684\u306a\u9759\u96fb\u5bb9\u91cf\u306e\u8a08\u7b97\u4f8b\u307e\u3067\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<h2>\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u516c\u5f0f | \u89e3\u8aac\u3068\u8a08\u7b97\u65b9\u6cd5<\/h2>\n<p>\u96fb\u6c17\u5b66\u3084\u78c1\u6c17\u5b66\u306e\u5206\u91ce\u3067\u3088\u304f\u767b\u5834\u3059\u308b\u30b3\u30f3\u30c7\u30f3\u30b5\u306f\u3001\u96fb\u6c17\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u84c4\u3048\u308b\u91cd\u8981\u306a\u7d20\u5b50\u3067\u3059\u3002\u305d\u306e\u4e2d\u3067\u3082\u3001\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306f\u7279\u6b8a\u306a\u5f62\u72b6\u3092\u6301\u3064\u305f\u3081\u3001\u305d\u306e\u7279\u6027\u3084\u8a08\u7b97\u65b9\u6cd5\u304c\u72ec\u81ea\u3067\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u57fa\u672c\u7684\u306a\u516c\u5f0f\u3068\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<h2>\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u57fa\u672c\u69cb\u9020<\/h2>\n<p>\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306f\u3001\u4e8c\u3064\u306e\u540c\u5fc3\u7403\uff08\u4e2d\u5fc3\u304c\u540c\u3058\u4e8c\u3064\u306e\u7403\uff09\u304b\u3089\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u5185\u5074\u306e\u7403\u306e\u534a\u5f84\u3092 \\( a \\)\u3001\u5916\u5074\u306e\u7403\u306e\u534a\u5f84\u3092 \\( b \\) \u3068\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u4e8c\u3064\u306e\u7403\u306e\u9593\u306b\u306f\u96fb\u6c17\u7d76\u7e01\u4f53\u304c\u8a70\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u5185\u5074\u306e\u7403\u3068\u5916\u5074\u306e\u7403\u306e\u9593\u306b\u96fb\u4f4d\u5dee\u3092\u6301\u305f\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u516c\u5f0f<\/h2>\n<p>\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u9759\u96fb\u5bb9\u91cf \\( C \\) \u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u6c42\u3081\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p>\\[ C = 4 \\pi \\epsilon_0 \\frac{ab}{b &#8211; a} \\]<\/p>\n<p>\u3053\u3053\u3067\u3001<br \/>\n&#8211; \\( \\epsilon_0 \\) \u306f\u771f\u7a7a\u306e\u8a98\u96fb\u7387\uff08\u7d04 \\( 8.85 \\times 10^{-12} \\, \\text{F\/m} \\)\uff09\u3067\u3059\u3002<br \/>\n&#8211; \\( a \\) \u306f\u5185\u5074\u306e\u7403\u306e\u534a\u5f84\u3067\u3059\u3002<br \/>\n&#8211; \\( b \\) \u306f\u5916\u5074\u306e\u7403\u306e\u534a\u5f84\u3067\u3059\u3002<\/p>\n<h2>\u516c\u5f0f\u306e\u5c0e\u51fa\u65b9\u6cd5<\/h2>\n<p>\u3053\u306e\u516c\u5f0f\u306f\u30ac\u30a6\u30b9\u306e\u6cd5\u5247\u3092\u4f7f\u3063\u3066\u5c0e\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3001\u305d\u306e\u5c0e\u51fa\u904e\u7a0b\u3092\u7c21\u5358\u306b\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<p>1. **\u30ac\u30a6\u30b9\u306e\u6cd5\u5247\u306e\u9069\u7528**\uff1a\u5185\u5074\u306e\u534a\u5f84 \\( r \\) \u3068\u3057\u3066\u3001\u7403\u5bfe\u79f0\u7cfb\u3067\u306e\u96fb\u5834 \\( E \\) \u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<p>\\[ \\oint \\mathbf{E} \\cdot d\\mathbf{A} = \\frac{Q_{\\text{\u5185}}}{\\epsilon_0} \\]<\/p>\n<p>\u3053\u3053\u3067\u3001\u7a4d\u5206\u7bc4\u56f2\u306f\u534a\u5f84 \\( r \\) \u306e\u7403\u9762\u3067\u3059\u3002<\/p>\n<p>2. **\u96fb\u5834\u306e\u8a08\u7b97**\uff1a\u96fb\u5834 \\( E \\) \u306f\u5185\u5074\u306e\u7403\u306e\u5916\u5074\u3067\u4e00\u69d8\u3067\u3059\u306e\u3067\u3001<\/p>\n<p>\\[ E \\cdot 4 \\pi r^2 = \\frac{Q}{\\epsilon_0} \\]<\/p>\n<p>\\[ E = \\frac{Q}{4 \\pi \\epsilon_0 r^2} \\]<\/p>\n<p>3. **\u96fb\u4f4d\u5dee\u306e\u8a08\u7b97**\uff1a\u5185\u5074\u306e\u7403\u3068\u5916\u5074\u306e\u7403\u306e\u9593\u306e\u96fb\u4f4d\u5dee \\( V \\) \u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\[ V = \\int_a^b E \\, dr = \\int_a^b \\frac{Q}{4 \\pi \\epsilon_0 r^2} \\, dr \\]<\/p>\n<p>\u3053\u308c\u3092\u7a4d\u5206\u3059\u308b\u3068\u3001<\/p>\n<p>\\[ V = \\left[ -\\frac{Q}{4 \\pi \\epsilon_0 r} \\right]_a^b = \\frac{Q}{4 \\pi \\epsilon_0} \\left( \\frac{1}{a} &#8211; \\frac{1}{b} \\right) \\]<\/p>\n<p>4. **\u9759\u96fb\u5bb9\u91cf\u306e\u7b97\u51fa**\uff1a<\/p>\n<p>\\[ C = \\frac{Q}{V} = 4 \\pi \\epsilon_0 \\frac{ab}{b &#8211; a} \\]<\/p>\n<h2>\u8a08\u7b97\u4f8b<\/h2>\n<p>\u5b9f\u969b\u306e\u4f8b\u3092\u4f7f\u3063\u3066\u3001\u9759\u96fb\u5bb9\u91cf\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4f8b\u3048\u3070\u3001\u5185\u5074\u306e\u7403\u306e\u534a\u5f84 \\( a = 1 \\, \\text{cm} \\)\u3001\u5916\u5074\u306e\u7403\u306e\u534a\u5f84 \\( b = 2 \\, \\text{cm} \\) \u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u306e\u9759\u96fb\u5bb9\u91cf \\( C \\) \u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a\u3001\u5358\u4f4d\u3092\u30e1\u30fc\u30c8\u30eb\u306b\u5909\u63db\u3057\u307e\u3059\u3002<\/p>\n<p>\\[ a = 0.01 \\, \\text{m}, \\, b = 0.02 \\, \\text{m} \\]<\/p>\n<p>\u6b21\u306b\u3001\u516c\u5f0f\u306b\u4ee3\u5165\u3057\u307e\u3059\u3002<\/p>\n<p>\\[ C = 4 \\pi \\epsilon_0 \\frac{(0.01 \\, \\text{m})(0.02 \\, \\text{m})}{0.02 \\, \\text{m} &#8211; 0.01 \\, \\text{m}} \\]<\/p>\n<p>\\[ C = 4 \\pi \\epsilon_0 \\frac{0.0002 \\, \\text{m}^2}{0.01 \\, \\text{m}} \\]<\/p>\n<p>\\[ C = 4 \\pi \\epsilon_0 \\times 0.02 \\, \\text{F} \\]<\/p>\n<p>\\[ C \\approx 4 \\times 3.14 \\times 8.85 \\times 10^{-12} \\times 0.02 \\, \\text{F} \\]<\/p>\n<p>\\[ C \\approx 2.22 \\times 10^{-12} \\, \\text{F} \\]<\/p>\n<p>\u3064\u307e\u308a\u3001\u9759\u96fb\u5bb9\u91cf\u306f\u7d04 \\( 2.22 \\, \\text{pF} \\)\uff08\u30d4\u30b3\u30d5\u30a1\u30e9\u30c9\uff09\u3067\u3059\u3002<\/p>\n<h2>\u307e\u3068\u3081<\/h2>\n<p>\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u9759\u96fb\u5bb9\u91cf\u306f\u3001\u7279\u5b9a\u306e\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u7c21\u5358\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u516c\u5f0f\u306e\u7406\u89e3\u3092\u901a\u3058\u3066\u3001\u96fb\u6c17\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u84c4\u7a4d\u65b9\u6cd5\u306b\u3064\u3044\u3066\u306e\u7406\u89e3\u3092\u6df1\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u7269\u7406\u3084\u5de5\u5b66\u306e\u4ed6\u306e\u5206\u91ce\u3067\u3082\u5fdc\u7528\u3067\u304d\u308b\u77e5\u8b58\u3067\u3059\u306e\u3067\u3001\u305c\u3072\u899a\u3048\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7403\u5f62\u30b3\u30f3\u30c7\u30f3\u30b5\u306e\u516c\u5f0f\u3068\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3002\u57fa\u672c\u69cb\u9020\u304b\u3089\u516c\u5f0f\u306e\u5c0e\u51fa\u3001\u5177\u4f53\u7684\u306a\u9759\u96fb\u5bb9\u91cf\u306e\u8a08\u7b97\u4f8b\u307e\u3067\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_generate-full-width-content":"","footnotes":""},"categories":[96],"tags":[97],"class_list":["post-209084","post","type-post","status-publish","format-standard","hentry","category-96","tag-97","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- 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