{"id":34388,"date":"2024-04-29T22:43:14","date_gmt":"2024-04-29T22:43:14","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%A9%E3%83%97%E3%83%A9%E3%82%B9%E6%96%B9%E7%A8%8B%E5%BC%8F-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-04-29T22:43:14","modified_gmt":"2024-04-29T22:43:14","slug":"%E3%83%A9%E3%83%97%E3%83%A9%E3%82%B9%E6%96%B9%E7%A8%8B%E5%BC%8F-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=34388","title":{"rendered":"\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f &#8211; \u5b9a\u7fa9"},"content":{"rendered":"<div><div><table cellspacing=\"0\"><tr><td colspan=\"2\"><strong><big>\u30d9\u30af\u30c8\u30eb\u89e3\u6790<\/big>\u8a18\u4e8b<\/strong><\/td><\/tr><tr><td colspan=\"2\"><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/0YUjJYMG9us\/0.jpg\" style=\"width:100%;\"\/><\/figure><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/e4meWbwA_5c\/0.jpg\" style=\"width:100%;\"\/><\/figure><\/td><\/tr><tr><td colspan=\"2\"><i>\u7814\u7a76\u5bfe\u8c61<\/i><\/td><\/tr><tr><td>\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9<\/td><td>\u30b9\u30ab\u30e9\u30fc\u30d5\u30a3\u30fc\u30eb\u30c9<\/td><\/tr><tr><td colspan=\"2\">\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f<\/td><\/tr><tr><td colspan=\"2\"><strong>\u30e9\u30d7\u30e9\u30b9<\/strong>\u2013<span><a href=\"https:\/\/science-hub.click\/?p=33270\">\u30dd\u30ef\u30bd\u30f3<\/a><\/span><\/td><\/tr><tr><td colspan=\"2\"><i>\u30aa\u30da\u30ec\u30fc\u30bf\u30fc<\/i><\/td><\/tr><tr><td><span><a href=\"https:\/\/science-hub.click\/?p=68357\">\u30ca\u30d6\u30e9<\/a><\/span><\/td><td>\u52fe\u914d<\/td><\/tr><tr><td><span><a href=\"https:\/\/science-hub.click\/?p=67139\">\u56de\u8ee2<\/a><\/span><\/td><td>\u767a\u6563<\/td><\/tr><tr><td>\u30b9\u30ab\u30e9\u30fc\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3<\/td><td>\u30d3\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3<\/td><\/tr><tr><td>\u30d9\u30af\u30c8\u30eb\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3<\/td><td>\u30c0\u30e9\u30f3\u30d9\u30eb\u30c6\u30a3\u30a2\u30f3<\/td><\/tr><tr><td colspan=\"2\"><i>\u5b9a\u7406<\/i><\/td><\/tr><tr><td>by \u30b0\u30ea\u30fc\u30f3<\/td><td>\u30b9\u30c8\u30fc\u30af\u30b9\u8457<\/td><\/tr><tr><td>\u30d8\u30eb\u30e0\u30db\u30eb\u30c4\u8457<\/td><td>\u6d41\u308c\u306e\u5206\u5c90\u306e<\/td><\/tr><tr><td>\u30b0\u30e9\u30c7\u30fc\u30b7\u30e7\u30f3\u306e<\/td><td>\u56de\u8ee2\u5f0f<\/td><\/tr><\/table><p><span><a href=\"https:\/\/science-hub.click\/?p=58791\">\u30d9\u30af\u30c8\u30eb\u89e3\u6790<\/a><\/span>\u306b\u304a\u3051\u308b<strong>\u30e9\u30d7\u30e9\u30b9<span><a href=\"https:\/\/science-hub.click\/?p=66517\">\u65b9\u7a0b\u5f0f\u306f<\/a><\/span><\/strong>2 \u6b21\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\u3001\u305d\u306e\u540d\u524d\u306f<span><a href=\"https:\/\/science-hub.click\/?p=17102\">\u6570\u7406<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=84429\">\u7269\u7406\u5b66\u8005<\/a><\/span><span>\u30d4\u30a8\u30fc\u30eb\uff1d\u30b7\u30e2\u30f3\u30fb\u30e9\u30d7\u30e9\u30b9<\/span>\u306b\u3061\u306a\u3093\u3067\u4ed8\u3051\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p><p><span><a href=\"https:\/\/science-hub.click\/?p=29624\">\u30cb\u30e5\u30fc\u30c8\u30f3\u529b\u5b66<\/a><\/span>\u306e\u5fc5\u8981\u6027\u306e\u305f\u3081\u306b\u5c0e\u5165\u3055\u308c\u305f\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=99759\">\u5929\u6587\u5b66<\/a><\/span>\u3001<span><a href=\"https:\/\/science-hub.click\/?p=10448\">\u9759\u96fb\u6c17\u5b66<\/a><\/span>\u3001<span><a href=\"https:\/\/science-hub.click\/?p=29868\">\u6d41\u4f53\u529b\u5b66<\/a><\/span>\u3001<span><a href=\"https:\/\/science-hub.click\/?p=53385\">\u71b1<\/a><\/span>\u4f1d\u64ad\u3001<span><a href=\"https:\/\/science-hub.click\/?p=74347\">\u62e1\u6563<\/a><\/span>\u3001<span><a href=\"https:\/\/science-hub.click\/?p=102643\">\u30d6\u30e9\u30a6\u30f3\u904b\u52d5<\/a><\/span>\u3001<span><a href=\"https:\/\/science-hub.click\/?p=9894\">\u91cf\u5b50\u529b\u5b66<\/a><\/span>\u306a\u3069\u3001\u7406\u8ad6<span><a href=\"https:\/\/science-hub.click\/?p=54039\">\u7269\u7406\u5b66<\/a><\/span>\u306e\u4ed6\u306e\u591a\u304f\u306e\u5206\u91ce\u306b\u767b\u5834\u3057\u307e\u3059\u3002<\/p><p>\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u89e3\u95a2\u6570\u306f<span><a href=\"https:\/\/science-hub.click\/?p=39212\">\u8abf\u548c\u95a2\u6570<\/a><\/span>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p><h2><span>\u4e09\u6b21\u5143\u306e\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f<\/span><\/h2><p>3<span><a href=\"https:\/\/science-hub.click\/?p=84871\">\u6b21\u5143<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=3842\">\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593<\/a><\/span>\u306e <span><a href=\"https:\/\/science-hub.click\/?p=34348\">\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19<\/a><\/span>\u3067\u306f\u3001\u554f\u984c\u306f 3 \u3064\u306e\u5b9f\u6570\u5909\u6570\u3092\u6301\u3064\u3059\u3079\u3066\u306e\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\varphi(x,y,z)} $$<\/div>\u3053\u308c\u306f 2 \u6b21\u306e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f<sup class=\"reference\" id=\"_ref-0\"><span>[<\/span> 1 <span>]<\/span><\/sup>\u3092\u691c\u8a3c\u3057\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial^2 \\varphi}{\\partial x^2} \\ + \\ \\frac{\\partial^2 \\varphi}{\\partial y^2} \\ + \\ \\frac{\\partial^2 \\varphi}{\\partial z^2} \\ =   \\ 0} $$<\/div><\/td><\/tr><\/table><p>\u8a18\u8ff0\u3092\u7c21\u7d20\u5316\u3059\u308b\u305f\u3081\u306b\u3001\u524d\u306e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u30b3\u30f3\u30d1\u30af\u30c8\u306b\u8a18\u8ff0\u3055\u308c\u308b\u3088\u3046\u306b\u3001 <span>\u0394<\/span>\u3067\u793a\u3055\u308c\u3001<i>\u30e9\u30d7\u30e9\u30b9\u6f14\u7b97\u5b50<\/i>\u307e\u305f\u306f\u5358\u306b<strong>\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3<\/strong>\u3068\u547c\u3070\u308c\u308b<span>\u5fae\u5206<\/span>\u6f14\u7b97\u5b50\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\Delta \\varphi \\ = \\ 0} $$<\/div><\/td><\/tr><\/table><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/s9B9Ix0XWiE\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2> <span>2\u6b21\u5143\u306e\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f<\/span><\/h2><p>2<span><a href=\"https:\/\/science-hub.click\/?p=20918\">\u6b21\u5143<\/a><\/span>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u306e\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u3067\u306f\u3001\u554f\u984c\u306f\u3001\u6b21\u3092\u6e80\u305f\u3059 2 \u3064\u306e\u5b9f\u6570\u5909\u6570<span><i>V<\/i> ( <i>x<\/i> , <i>y<\/i> )<\/span>\u3092\u6301\u3064\u3059\u3079\u3066\u306e\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial^2 V}{\\partial x^2} \\ + \\ \\frac{\\partial^2 V}{\\partial y^2} \\ = \\ 0} $$<\/div><\/td><\/tr><\/table><p>\u4efb\u610f\u306e\u6b63\u5247\u95a2\u6570\u304c\u5b9f\u6570\u90e8\u3068\u865a\u6570\u90e8\u306b\u3088\u3063\u3066 2 \u6b21\u5143\u306e\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u4e0e\u3048\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u3053\u308c\u3089\u306e\u89e3\u306f<span><a href=\"https:\/\/science-hub.click\/?p=95765\">\u3059\u3079\u3066\u306e<\/a><\/span><span><a href=\"https:\/\/science-hub.click\/?p=43578\">\u70b9<\/a><\/span>\u3067\u76f4\u4ea4\u3057\u3066\u3044\u307e\u3059\u3002<\/p><h3><span>\u6b63\u5247\u95a2\u6570\u306b\u95a2\u3059\u308b\u6ce8\u610f\u4e8b\u9805<\/span><\/h3><p>\u8907\u7d20\u4fc2\u6570\u3092\u6301\u3064\u591a\u9805\u5f0f\u95a2\u6570\u306f\u3059\u3079\u3066\u6b63\u5247\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathbb C} $$<\/div> ;\u4e09\u89d2\u95a2\u6570\u3084\u6307\u6570\u95a2\u6570\u3082\u540c\u69d8\u3067\u3059\u3002 (\u4e09\u89d2\u95a2\u6570\u306f\u3001\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6307\u6570\u95a2\u6570\u304b\u3089\u5b9a\u7fa9\u3067\u304d\u308b\u305f\u3081\u3001\u5b9f\u969b\u306b\u306f\u6bd4\u8f03\u7684\u6307\u6570\u95a2\u6570\u306b\u8fd1\u3044\u3082\u306e\u3067\u3059)\u3002<br\/><\/p><ul><li><span>\u5bfe\u6570<\/span>\u95a2\u6570\u306f\u3001\u8ca0\u306e\u5b9f\u6570\u306e<span><a href=\"https:\/\/science-hub.click\/?p=79633\">\u534a\u76f4\u7dda<\/a><\/span>\u3092\u53d6\u308a\u9664\u3044\u305f\u8907\u7d20\u6570\u306e<span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u30bb\u30c3\u30c8<\/a><\/span>\u4e0a\u3067\u6b63\u5247\u3067\u3059 (0 \u304b\u3089\u6765\u308b\u4efb\u610f\u306e\u534a\u76f4\u7dda\u3092\u9078\u629e\u3067\u304d\u307e\u3059)\u3002<\/li><\/ul><ul><li><span><a href=\"https:\/\/science-hub.click\/?p=93175\">\u5e73\u65b9\u6839<\/a><\/span>\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 <\/li><\/ul><dl><dd><div class=\"math-formual notranslate\">$$ {\\sqrt{z} = e^{{1 \\over 2} \\ln{z}}} $$<\/div><\/dd><dd>\u3057\u305f\u304c\u3063\u3066\u3001\u5bfe\u6570\u95a2\u6570\u304c\u3069\u3053\u306b\u3042\u3063\u3066\u3082\u6b63\u5247\u3067\u3059\u3002<br\/><\/dd><\/dl><ul><li><span><a href=\"https:\/\/science-hub.click\/?p=35670\">\u9006<\/a><\/span>\u95a2\u6570<div class=\"math-formual notranslate\">$$ {z\\mapsto 1\/z} $$<\/div>\u306f\u6b63\u5247\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\mathbb C^*} $$<\/div> \u3002<\/li><\/ul><ul><li>\u9006\u4e09\u89d2\u95a2\u6570\u306b\u3082\u540c\u69d8\u306b\u7d99\u304e\u76ee\u304c\u3042\u308a\u3001\u7d99\u304e\u76ee\u4ee5\u5916\u306f\u3069\u3053\u3067\u3082\u6b63\u5247\u3067\u3059\u3002<\/li><\/ul><h3><span><span><a href=\"https:\/\/science-hub.click\/?p=34388\">\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f<\/a><\/span>\u3068\u6b63\u5247\u95a2\u6570<\/span><\/h3><h4><span><span>\u5b9a\u7406<\/span>1<\/span><\/h4><center><table cellpadding=\"10\"><tr><td><strong>\u3042\u3089\u3086\u308b\u89e3\u6790\u95a2\u6570\u306f\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u89e3\u3067\u3059\u3002<\/strong><\/td><\/tr><\/table><\/center><h4><span><span><a href=\"https:\/\/science-hub.click\/?p=52981\">\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/a><\/span><\/span><\/h4><p>\u8907\u7d20<span><a href=\"https:\/\/science-hub.click\/?p=72623\">\u5909\u6570<\/a><\/span><span><i>z<\/i> = <i>x<\/i> + <i>i<\/i> <i>y<\/i><\/span>\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001 <div class=\"math-formual notranslate\">$$ {i^2 = &#8211; \\ 1} $$<\/div>\u305d\u3057\u3066\u3001\u6b63\u5247\u95a2\u6570<span><i>F<\/i> ( <i>z<\/i> )<\/span>\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u5c0e\u51fa\u306b\u3088\u308a\u3001\u6b21\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial F}{\\partial x} \\ = \\ \\frac{d F}{dz} \\ \\frac{\\partial z}{\\partial x} \\ = \\ F'(z)} $$<\/div><\/td><\/tr><\/table><p>\u305d\u306e\u9593 \uff1a <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial F}{\\partial y} \\ = \\ \\frac{dF}{dz} \\ \\frac{\\partial z}{\\partial y} \\ = \\ i \\ F'(z)} $$<\/div> \u3002<\/td><\/tr><\/table><p> 2 \u56de\u5fae\u5206\u3059\u308b\u3068\u3001\u540c\u69d8\u306e\u65b9\u6cd5\u3067<span><a href=\"https:\/\/science-hub.click\/?p=68283\">\u6b21\u306e<\/a><\/span>\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial^2 F}{\\partial x^2} \\ = \\ F&#8221;(z)} $$<\/div><\/td><\/tr><\/table><p>\u305d\u306e\u9593 \uff1a <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial^2 F}{\\partial y^2} \\ = \\ &#8211; \\ F&#8221;(z)} $$<\/div><\/td><\/tr><\/table><p>\u548c\u306f\u30bc\u30ed\u306a\u306e\u3067\u3001\u6b63\u5247\u95a2\u6570<i>F \u306f<\/i>\u5b9f\u969b\u306b\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial^2 F}{\\partial x^2} \\ + \\ \\frac{\\partial^2 F}{\\partial y^2} \\ = \\ 0} $$<\/div><\/td><\/tr><\/table><p>\u6ce8: \u6b63\u5247\u95a2\u6570\u306f\u5e38\u306b\u5b9f\u6570\u90e8\u3068\u865a\u6570\u90e8\u3078\u306e<span><a href=\"https:\/\/science-hub.click\/?p=4434\">\u5206\u89e3<\/a><\/span>\u3092\u8a31\u53ef\u3057\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {F(z) \\ = \\ V(x,y) \\ + \\ i \\ \\phi(x,y)} $$<\/div><\/td><\/tr><\/table><p>\u5b9f\u6570\u90e8\u3068\u865a\u6570\u90e8\u3092\u5225\u3005\u306b\u30ad\u30e3\u30f3\u30bb\u30eb\u3059\u308b\u3068\u3001 <i>2 \u3064<\/i>\u306e\u72ec\u7acb\u3057\u305f\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial^2 V}{\\partial x^2}+ \\frac{\\partial^2 V}{\\partial y^2}=0 \\qquad \\mathrm{et\u00a0:} \\qquad \\frac{\\partial^2 \\phi}{\\partial x^2}+ \\frac{\\partial^2 \\phi}{\\partial y^2}=0} $$<\/div><\/td><\/tr><\/table><h4><span>\u5b9a\u74062<\/span><\/h4><center><table cellpadding=\"10\"><tr><td><strong>\u7b49\u96fb\u4f4d\u306f<span><a href=\"https:\/\/science-hub.click\/?p=93469\">\u529b<\/a><\/span>\u7dda\u306b\u5782\u76f4\u3067\u3059<\/strong><\/td><\/tr><\/table><\/center><h4><span>\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/span><\/h4><p>\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059: <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial F}{\\partial x}\\ = \\ F'(x+iy) \\ = \\ \\frac{\\partial V(x,y)}{\\partial x} \\ + \\ i \\ \\frac{\\partial \\Phi(x,y)}{\\partial x}} $$<\/div><\/td><\/tr><\/table><p>\u305d\u3057\u3066 \uff1a <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial F}{\\partial y} \\ = \\ i F'(x+iy) \\ = \\ \\frac{\\partial V(x,y)}{\\partial y} \\  + \\ i \\ \\frac{\\partial \\Phi(x,y)}{\\partial y}} $$<\/div><\/td><\/tr><\/table><p>\u79c1\u305f\u3061\u306f\u6b21\u306e\u3088\u3046\u306b\u63a8\u6e2c\u3057\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial V(x,y)}{\\partial x} \\ = \\ \\frac{\\partial \\Phi(x,y)}{\\partial y} \\qquad \\mathrm{et\u00a0:} \\qquad \\frac{\\partial \\Phi(x,y)}{\\partial x} \\ = \\ &#8211; \\ \\frac{\\partial V(x,y)}{\\partial y}} $$<\/div><\/td><\/tr><\/table><p>\u307e\u305f\u306f\u6700\u5f8c\u306b: <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\frac{\\partial V(x,y)}{\\partial x} \\cdot \\frac{\\partial \\Phi(x,y)}{\\partial x} \\ + \\ \\frac{\\partial V(x,y)}{\\partial y} \\cdot \\frac{\\partial \\Phi(x,y)}{\\partial y} \\ = \\ 0} $$<\/div><\/td><\/tr><\/table><p>\u3053\u3053\u3067 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e<span><a href=\"https:\/\/science-hub.click\/?p=69519\">\u30b9\u30ab\u30e9\u30fc\u7a4d<\/a><\/span>\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\vec \\mathrm{grad} \\ (V) \\cdot\\vec \\mathrm{grad} \\ (\\Phi) \\ = \\ 0} $$<\/div><\/td><\/tr><\/table><p>\u3053\u308c\u304b\u3089\u3001{ <i>V(x,y)<\/i> = \u5b9a\u6570} \u3068 { <i>\u03c6(x,y)<\/i> = \u5b9a\u6570} \u306b\u304a\u3051\u308b\u66f2\u7dda\u306f<i>\u5782\u76f4\u3067<\/i>\u3042\u308b\u3053\u3068\u304c\u63a8\u6e2c\u3055\u308c\u307e\u3059 (\u5171\u5f62\u5909\u63db)\u3002\u3064\u307e\u308a\u3001{ <i>V(x,y)<\/i> = \u5b9a\u6570} \u304c\u540c\u3058\u96fb\u4f4d\u306e\u66f2\u7dda\u3092\u8868\u3059\u5834\u5408\u3001{ <i>\u03c6(x,y)<\/i> = \u5b9a\u6570} \u306f\u9759\u96fb\u6c17\u529b\u5b66\u306b\u304a\u3051\u308b\u96fb\u529b\u7dda\u3092\u8868\u3059\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p><h2><span>\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f<\/span><\/h2><p>\u53f3\u8fba<span>\u304c\u4e0e\u3048\u3089\u308c\u305f<\/span>\u95a2\u6570<span><i>f<\/i> ( <i>x<\/i> , <i>y<\/i> , <i>z<\/i> )<\/span>\u306e\u5834\u5408\u3001\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p><table align=\"center\"><tr><td><div class=\"math-formual notranslate\">$$ {\\Delta \\varphi = f} $$<\/div><\/td><\/tr><\/table><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9_%D9%84%D8%A7%D8%A8%D9%84%D8%A7%D8%B3\">\u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0627\u0628\u0644\u0627\u0633 \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ast.wikipedia.org\/wiki\/Ecuaci%C3%B3n_de_Laplace\">Ecuaci\u00f3n de Laplace \u2013 asturien<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/az.wikipedia.org\/wiki\/Laplas_t%C9%99nliyi\">Laplas t\u0259nliyi \u2013 azerba\u00efdjanais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/be.wikipedia.org\/wiki\/%D0%A3%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5_%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81%D0%B0\">\u0423\u0440\u0430\u045e\u043d\u0435\u043d\u043d\u0435 \u041b\u0430\u043f\u043b\u0430\u0441\u0430 \u2013 bi\u00e9lorusse<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/bg.wikipedia.org\/wiki\/%D0%A3%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BD%D0%B0_%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81\">\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u041b\u0430\u043f\u043b\u0430\u0441 \u2013 bulgare<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Equaci%C3%B3_de_Laplace\">Equaci\u00f3 de Laplace \u2013 catalan<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f &#8211; \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u30e9\u30d7\u30e9\u30b9\u5909\u63db\u306e\u6c17\u6301\u3061\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/c7g4rfmaTd4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u30d9\u30af\u30c8\u30eb\u89e3\u6790\u8a18\u4e8b \u7814\u7a76\u5bfe\u8c61 \u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9 \u30b9\u30ab\u30e9\u30fc\u30d5\u30a3\u30fc\u30eb\u30c9 \u504f\u5fae\u5206\u65b9\u7a0b\u5f0f \u30e9\u30d7\u30e9\u30b9\u2013\u30dd\u30ef\u30bd\u30f3 \u30aa\u30da\u30ec\u30fc\u30bf\u30fc \u30ca\u30d6\u30e9 \u52fe\u914d \u56de\u8ee2 \u767a\u6563 \u30b9\u30ab\u30e9\u30fc\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3 \u30d3\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3 \u30d9\u30af\u30c8\u30eb\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3 \u30c0\u30e9\u30f3\u30d9\u30eb\u30c6\u30a3\u30a2\u30f3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":34389,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/c7g4rfmaTd4\/0.jpg","fifu_image_alt":"\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f - \u5b9a\u7fa9","footnotes":""},"categories":[5],"tags":[11,13,14,10,35073,35072,12,3944,16,15],"class_list":["post-34388","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-laplace","tag-equation-de-laplace","tag-dossier","tag-equation","tag-sciences","tag-article"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/34388"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=34388"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/34388\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/34389"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=34388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=34388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=34388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}