{"id":30988,"date":"2021-09-21T13:00:45","date_gmt":"2021-09-21T13:00:45","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30988"},"modified":"2025-01-02T22:07:03","modified_gmt":"2025-01-02T22:07:03","slug":"%e7%94%b5%e5%9c%ba%e7%9a%84%e6%a6%82%e5%bf%b5","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e7%94%b5%e5%9c%ba%e7%9a%84%e6%a6%82%e5%bf%b5\/","title":{"rendered":"\u7535\u573a\u7684\u6982\u5ff5"},"content":{"rendered":"<style>\n    p, ul, ol {\n        text-align: justify;\n    }\n    h1, h2 {\n        text-align: center;\n    }\n<\/style>\n<h1>\u7535\u573a\u7684\u6982\u5ff5<\/h1>\n<p style=\"text-align: center;\"><em>\u572819\u4e16\u7eaa\uff0c\u8fc8\u514b\u5c14\u00b7\u6cd5\u62c9\u7b2c\uff08Michael Faraday\uff09\uff0c\u7535\u5b66\u9886\u57df\u6700\u4f1f\u5927\u7684\u5b9e\u9a8c\u5bb6\u4e4b\u4e00\uff0c\u6709\u4e00\u79cd\u72ec\u7279\u7684\u5de5\u4f5c\u65b9\u5f0f\uff1a\u4ed6\u5c06\u5b9e\u9a8c\u5ba4\u5e03\u6ee1\u4e86\u5bfc\u7ebf\u3001\u5e26\u7535\u7403\u4f53\u548c\u88c5\u6709\u5bfc\u7535\u6db2\u4f53\u7684\u5c0f\u5bb9\u5668\u3002\u4e00\u5219\u8457\u540d\u7684\u8f76\u4e8b\u63d0\u5230\uff0c\u4ed6\u5bf9\u53ef\u89c6\u5316\u56f4\u7ed5\u7535\u8377\u7684\u201c\u529b\u7ebf\u201d\u6709\u7740\u8fd1\u4e4e\u6267\u7740\u7684\u8ffd\u6c42\uff0c\u4ee5\u81f3\u4e8e\u5c06\u94c1\u5c51\u6d12\u6ee1\u4e86\u6574\u4e2a\u5b9e\u9a8c\u5ba4\uff0c\u5730\u677f\u4e0a\u7559\u4e0b\u7684\u56fe\u6848\u770b\u8d77\u6765\u50cf\u662f\u73b0\u4ee3\u827a\u672f\u3002\u4ed6\u7684\u540c\u4e8b\u4eec\u56f0\u60d1\u4e0d\u89e3\uff0c\u4ee5\u4e3a\u4ed6\u5931\u53bb\u4e86\u7406\u667a\uff0c\u4f46\u5b9e\u9645\u4e0a\uff0c\u6cd5\u62c9\u7b2c\u6b63\u5728\u63cf\u7ed8\u4e00\u4e2a\u6700\u5177\u9769\u547d\u6027\u7684\u6982\u5ff5\uff1a\u7535\u573a\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u8fd9\u4e9b\u8bde\u751f\u4e8e\u5929\u624d\u4e0e\u5b9e\u9a8c\u7684\u60f3\u6cd5\u5982\u4f55\u5e2e\u52a9\u6211\u4eec\u7ed8\u5236\u548c\u7406\u89e3\u652f\u914d\u7535\u5b66\u7684\u65e0\u5f62\u76f8\u4e92\u4f5c\u7528\u3002\u5982\u679c\u4f60\u66fe\u597d\u5947\u5982\u4f55\u201c\u770b\u89c1\u201d\u65e0\u5f62\u4e4b\u7269\uff0c\u8fd9\u5c06\u662f\u4e00\u6b21\u63a2\u7d22\u4e4b\u65c5\u3002<\/em><\/p>\n<p style=\"text-align: center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u672c\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u7535\u573a\u7684\u6982\u5ff5\u4ee5\u53ca\u5b83\u901a\u8fc7\u5e93\u4ed1\u5b9a\u5f8b\u4e0e\u7535\u529b\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u7535\u573a\u7684\u5b9a\u4e49\u89e3\u51b3\u4e0e\u70b9\u7535\u8377\u76f8\u5173\u7684\u95ee\u9898\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong>\u79bb\u6563\u548c\u8fde\u7eed\u7535\u8377\u5206\u5e03\u4e2d\u7684\u53e0\u52a0\u539f\u7406\u4ee5\u8ba1\u7b97\u7535\u573a\u3002<\/li>\n<li><strong>\u8bc4\u4f30<\/strong>\u7ebf\u6027\u3001\u8868\u9762\u548c\u4f53\u79ef\u5206\u5e03\u7684\u79ef\u5206\u4ee5\u786e\u5b9a\u590d\u6742\u914d\u7f6e\u4e2d\u7684\u7535\u573a\u3002<\/li>\n<li><strong>\u89e3\u51b3<\/strong>\u5305\u62ec\u5e26\u7535\u6746\u3001\u5e26\u7535\u73af\u548c\u65e0\u9650\u5e73\u9762\u914d\u7f6e\u7684\u5b9e\u8df5\u7ec3\u4e60\u3002<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><strong><u>\u5185\u5bb9\u7d22\u5f15<\/u>\uff1a<\/strong><br \/>\n<a href=\"#1\">\u4ec0\u4e48\u662f\u7535\u573a\uff1f<\/a><br \/>\n<a href=\"#2\">\u7535\u573a\u4e0e\u7535\u8377\u5206\u5e03<\/a><br \/>\n<a href=\"#3\">\u7ec3\u4e60<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KWwRfJ9ZRrA\" title=\"YouTube\u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u4ec0\u4e48\u662f\u7535\u573a\uff1f<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=191s\" target=\"_blank\" rel=\"noopener\"><strong>\u5f53\u6211\u4eec\u5728\u67d0\u4e2a\u5730\u65b9\u653e\u7f6e\u4e00\u4e2a\u6e90\u7535\u8377\u65f6<\/strong><\/a>\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u6d4b\u8bd5\u7535\u8377\u611f\u53d7\u5230\u5b83\u7684\u5b58\u5728\uff0c\u56e0\u4e3a\u6d4b\u8bd5\u7535\u8377\u4f1a\u7531\u4e8e\u6e90\u7535\u8377\u7684\u5b58\u5728\u800c\u611f\u53d7\u5230<strong>\u7535\u529b<\/strong>\u3002\u8fd9\u79cd\u529b\u901a\u8fc7\u5e93\u4ed1\u5b9a\u5f8b\u6765\u7814\u7a76\u3002\u57fa\u4e8e\u6b64\uff0c\u6211\u4eec\u8bf4\u6e90\u7535\u8377\u201c\u5145\u6ee1\u7a7a\u95f4\u201d\u4e00\u79cd\u5c5e\u6027\uff0c\u5373\u7535\u573a\uff0c\u5b83\u662f\u4ea7\u751f\u7535\u529b\u7684\u539f\u56e0\u3002<\/p>\n<p>\u4e3a\u4e86\u6d4b\u91cf\u67d0\u70b9\u7a7a\u95f4\u4e2d\u7535\u8377 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u7684\u7535\u573a <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span>\uff0c\u6211\u4eec\u9700\u8981\u5c06\u4e00\u4e2a\u6d4b\u8bd5\u7535\u8377 <span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span> \u653e\u7f6e\u5728\u90a3\u91cc\u3002\u7535\u573a\u53ef\u4ee5\u88ab\u63cf\u8ff0\u4e3a\u6d4b\u8bd5\u7535\u8377 <span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span> \u5355\u4f4d\u7535\u8377\u6240\u611f\u53d7\u5230\u7684\u7535\u529b\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{E}_q(\\vec{r}) = \\displaystyle \\frac{\\vec{F}_{q\\to q_0}(\\vec{r})}{q_0}<\/span>\n<p>\u4f46\u5f53\u6211\u4eec\u8fd9\u6837\u64cd\u4f5c\u65f6\uff0c\u6211\u4eec\u5ffd\u7565\u4e86\u6d4b\u8bd5\u7535\u8377\u4e5f\u4f1a\u6709\u81ea\u5df1\u7684\u7535\u573a\uff0c\u5e76\u4e14\u8fd9\u4e2a\u7535\u573a\u4f1a\u4e0e\u6e90\u7535\u8377\u7684\u7535\u573a\u91cd\u53e0\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u901a\u8fc7\u6781\u9650\u8ba8\u8bba\u7535\u573a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\vec{E}_q(\\vec{r}) = \\lim_{q_0 \\to 0} \\frac{\\vec{F}_{q\\to q_0}(\\vec{r})}{q_0}<\/span>\n<p>\u901a\u8fc7\u6781\u9650\u5b9a\u4e49\uff0c\u6211\u4eec\u786e\u4fdd\u6d4b\u8bd5\u7535\u8377 <span class=\"katex-eq\" data-katex-display=\"false\">q_0<\/span> \u7684\u7535\u573a\u4e0d\u4f1a\u5e72\u6270\u7535\u8377 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u7684\u7535\u573a\u6d4b\u91cf\u3002\u73b0\u5728\uff0c\u56de\u60f3\u5e93\u4ed1\u5b9a\u5f8b\uff0c\u4e00\u4e2a\u5e26\u7535\u7c92\u5b50 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u7684\u7535\u573a\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\vec{E}_q(\\vec{r}) = \\lim_{q_0 \\to 0} \\frac{1}{q_0} \\frac{1}{4\\pi \\epsilon_0} \\frac{qq_0}{\\|\\vec{r} -\\vec{r}^\\prime\\|^2} \\frac{\\vec{r} -\\vec{r}^\\prime}{\\|\\vec{r} -\\vec{r}^\\prime\\|} = \\frac{q}{4\\pi\\epsilon_0} \\frac{\\vec{r} -\\vec{r}^\\prime}{\\|\\vec{r} -\\vec{r}^\\prime\\|^3} <\/span>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{F}_{q\\to q_0}(\\vec{r}) = q_0 \\vec{E}_q(\\vec{r}) <\/span>\n<p><a name=\"2\"><\/a> <\/p>\n<h2>\u7535\u573a\u4e0e\u7535\u8377\u5206\u5e03<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=565s\" target=\"_blank\" rel=\"noopener\"><strong>\u7531\u4e8e\u7535\u573a<\/strong><\/a>\u662f\u6839\u636e\u529b\u8fdb\u884c\u7814\u7a76\u7684\uff0c\u5e76\u4e14\u5b83\u6ee1\u8db3\u53e0\u52a0\u539f\u7406\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u7814\u7a76\u4e0d\u540c\u7535\u8377\u5206\u5e03\u7684\u7535\u573a\u3002<\/p>\n<h3>\u79bb\u6563\u5206\u5e03<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=587s\" target=\"_blank\" rel=\"noopener\"><strong>\u8003\u8651\u4e00\u4e2a\u7531 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u4e2a\u79bb\u6563\u7535\u8377\u7ec4\u6210\u7684\u5206\u5e03<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">q_1, q_2, \\cdots, q_n<\/span>\uff0c\u5b83\u4eec\u7684\u4f4d\u7f6e\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}^\\prime_1, \\vec{r}^\\prime_2, \\cdots, \\vec{r}^\\prime_n.<\/span> \u5982\u679c\u6211\u4eec\u60f3\u8ba1\u7b97\u67d0\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> \u7684\u7535\u573a\uff0c\u5219\u6709\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\vec{E}_q(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\sum_{i=1}^n q_i \\frac{\\vec{r} -\\vec{r}_i^\\prime}{\\|\\vec{r} -\\vec{r}_i^\\prime\\|^3} <\/span>\n<p>\u5373\u6240\u6709\u5355\u4e2a\u7535\u573a\u7684\u603b\u548c\u3002<\/p>\n<h3>\u8fde\u7eed\u5206\u5e03<\/h3>\n<p>\u8fde\u7eed\u7535\u8377\u5206\u5e03\u6709\u4e09\u79cd\u7c7b\u578b\uff0c\u6bcf\u79cd\u7c7b\u578b\u4e0e\u63cf\u8ff0\u5176\u7a7a\u95f4\u6392\u5217\u6240\u9700\u7684\u53c2\u6570\u6570\u91cf\u76f8\u5173\u3002\u8fd9\u4e9b\u7c7b\u578b\u662f\u7ebf\u6027\u5206\u5e03\u3001\u8868\u9762\u5206\u5e03\u548c\u4f53\u79ef\u5206\u5e03\u3002<\/p>\n<h4>\u7ebf\u6027\u5206\u5e03<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=688s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u7ebf\u6027\u7535\u8377\u5206\u5e03\u4e2d\uff0c<\/strong><\/a>\u5e26\u7535\u4f53\u7684\u6bcf\u4e2a\u7ebf\u5143\u7d20\u5177\u6709\u7ebf\u6027\u7535\u8377\u5bc6\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\lambda(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dl<\/span>\uff0c\u56e0\u6b64\u7535\u573a\u7684\u5fae\u5143\u8868\u793a\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">d\\vec{E}(\\vec{r}) =\\displaystyle \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\lambda(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dl<\/span>\n<p>\u5c06\u8be5\u8868\u8fbe\u5f0f\u79ef\u5206\u540e\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\int_{\\mathcal{C}} \\lambda(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dl<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}<\/span> \u662f\u63cf\u8ff0\u5e26\u7535\u4f53\u5f62\u72b6\u7684\u66f2\u7ebf\u7684\u53c2\u6570\u5316\u8868\u793a\u3002<\/p>\n<h4>\u8868\u9762\u5206\u5e03<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=899s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u8868\u9762\u7535\u8377\u5206\u5e03\u4e2d\uff0c<\/strong><\/a>\u5e26\u7535\u4f53\u7684\u6bcf\u4e2a\u8868\u9762\u5143\u7d20\u5177\u6709\u8868\u9762\u7535\u8377\u5bc6\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\sigma(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dS<\/span>\uff0c\u56e0\u6b64\u7535\u573a\u7684\u5fae\u5143\u8868\u793a\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle d\\vec{E}(\\vec{r}) = \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\sigma(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dS<\/span>\n<p>\u5c06\u8be5\u8868\u8fbe\u5f0f\u79ef\u5206\u540e\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\iint_{\\mathcal{A}} \\sigma(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dS<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span> \u662f\u63cf\u8ff0\u5e26\u7535\u4f53\u5f62\u72b6\u7684\u8868\u9762\u7684\u53c2\u6570\u5316\u8868\u793a\u3002<\/p>\n<h4>\u4f53\u79ef\u5206\u5e03<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=1054s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u4f53\u79ef\u7535\u8377\u5206\u5e03\u4e2d\uff0c<\/strong><\/a>\u5e26\u7535\u4f53\u7684\u6bcf\u4e2a\u4f53\u79ef\u5143\u7d20\u5177\u6709\u4f53\u79ef\u7535\u8377\u5bc6\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\rho(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dV<\/span>\uff0c\u56e0\u6b64\u7535\u573a\u7684\u5fae\u5143\u8868\u793a\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle d\\vec{E}(\\vec{r}^\\prime) = \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\rho(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dV<\/span>\n<p>\u5c06\u8be5\u8868\u8fbe\u5f0f\u79ef\u5206\u540e\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\iiint_{\\mathcal{V}} \\rho(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dV<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{V}<\/span> \u662f\u63cf\u8ff0\u5e26\u7535\u4f53\u5f62\u72b6\u7684\u4f53\u79ef\u7684\u53c2\u6570\u5316\u8868\u793a\u3002<\/p>\n<p><a name=\"2\"><\/a> <\/p>\n<h2>\u7535\u573a\u4e0e\u7535\u8377\u5206\u5e03<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=565s\" target=\"_blank\" rel=\"noopener\"><strong>\u7531\u4e8e\u7535\u573a<\/strong><\/a>\u662f\u6839\u636e\u529b\u8fdb\u884c\u7814\u7a76\u7684\uff0c\u5e76\u4e14\u5b83\u6ee1\u8db3\u53e0\u52a0\u539f\u7406\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u7814\u7a76\u4e0d\u540c\u7535\u8377\u5206\u5e03\u7684\u7535\u573a\u3002<\/p>\n<h3>\u79bb\u6563\u5206\u5e03<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=587s\" target=\"_blank\" rel=\"noopener\"><strong>\u8003\u8651\u4e00\u4e2a\u7531 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u4e2a\u79bb\u6563\u7535\u8377\u7ec4\u6210\u7684\u5206\u5e03<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">q_1, q_2, \\cdots, q_n<\/span>\uff0c\u5b83\u4eec\u7684\u4f4d\u7f6e\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}^\\prime_1, \\vec{r}^\\prime_2, \\cdots, \\vec{r}^\\prime_n.<\/span> \u5982\u679c\u6211\u4eec\u60f3\u8ba1\u7b97\u67d0\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{r}<\/span> \u7684\u7535\u573a\uff0c\u5219\u6709\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\vec{E}_q(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\sum_{i=1}^n q_i \\frac{\\vec{r} -\\vec{r}_i^\\prime}{\\|\\vec{r} -\\vec{r}_i^\\prime\\|^3} <\/span>\n<p>\u5373\u6240\u6709\u5355\u4e2a\u7535\u573a\u7684\u603b\u548c\u3002<\/p>\n<h3>\u8fde\u7eed\u5206\u5e03<\/h3>\n<p>\u8fde\u7eed\u7535\u8377\u5206\u5e03\u6709\u4e09\u79cd\u7c7b\u578b\uff0c\u6bcf\u79cd\u7c7b\u578b\u4e0e\u63cf\u8ff0\u5176\u7a7a\u95f4\u6392\u5217\u6240\u9700\u7684\u53c2\u6570\u6570\u91cf\u76f8\u5173\u3002\u8fd9\u4e9b\u7c7b\u578b\u662f\u7ebf\u6027\u5206\u5e03\u3001\u8868\u9762\u5206\u5e03\u548c\u4f53\u79ef\u5206\u5e03\u3002<\/p>\n<h4>\u7ebf\u6027\u5206\u5e03<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=688s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u7ebf\u6027\u7535\u8377\u5206\u5e03\u4e2d\uff0c<\/strong><\/a>\u5e26\u7535\u4f53\u7684\u6bcf\u4e2a\u7ebf\u5143\u7d20\u5177\u6709\u7ebf\u6027\u7535\u8377\u5bc6\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\lambda(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dl<\/span>\uff0c\u56e0\u6b64\u7535\u573a\u7684\u5fae\u5143\u8868\u793a\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">d\\vec{E}(\\vec{r}) =\\displaystyle \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\lambda(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dl<\/span>\n<p>\u5c06\u8be5\u8868\u8fbe\u5f0f\u79ef\u5206\u540e\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\int_{\\mathcal{C}} \\lambda(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dl<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{C}<\/span> \u662f\u63cf\u8ff0\u5e26\u7535\u4f53\u5f62\u72b6\u7684\u66f2\u7ebf\u7684\u53c2\u6570\u5316\u8868\u793a\u3002<\/p>\n<h4>\u8868\u9762\u5206\u5e03<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=899s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u8868\u9762\u7535\u8377\u5206\u5e03\u4e2d\uff0c<\/strong><\/a>\u5e26\u7535\u4f53\u7684\u6bcf\u4e2a\u8868\u9762\u5143\u7d20\u5177\u6709\u8868\u9762\u7535\u8377\u5bc6\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\sigma(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dS<\/span>\uff0c\u56e0\u6b64\u7535\u573a\u7684\u5fae\u5143\u8868\u793a\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle d\\vec{E}(\\vec{r}) = \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\sigma(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dS<\/span>\n<p>\u5c06\u8be5\u8868\u8fbe\u5f0f\u79ef\u5206\u540e\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\iint_{\\mathcal{A}} \\sigma(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dS<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span> \u662f\u63cf\u8ff0\u5e26\u7535\u4f53\u5f62\u72b6\u7684\u8868\u9762\u7684\u53c2\u6570\u5316\u8868\u793a\u3002<\/p>\n<h4>\u4f53\u79ef\u5206\u5e03<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=KWwRfJ9ZRrA&amp;t=1054s\" target=\"_blank\" rel=\"noopener\"><strong>\u5728\u4f53\u79ef\u7535\u8377\u5206\u5e03\u4e2d\uff0c<\/strong><\/a>\u5e26\u7535\u4f53\u7684\u6bcf\u4e2a\u4f53\u79ef\u5143\u7d20\u5177\u6709\u4f53\u79ef\u7535\u8377\u5bc6\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\rho(\\vec{r}^\\prime)=dq(\\vec{r}^\\prime)\/dV<\/span>\uff0c\u56e0\u6b64\u7535\u573a\u7684\u5fae\u5143\u8868\u793a\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle d\\vec{E}(\\vec{r}^\\prime) = \\frac{dq(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3} = \\frac{\\rho(\\vec{r}^\\prime)}{4\\pi\\epsilon_0} \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dV<\/span>\n<p>\u5c06\u8be5\u8868\u8fbe\u5f0f\u79ef\u5206\u540e\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{E}(\\vec{r}) = \\frac{1}{4\\pi\\epsilon_0} \\iiint_{\\mathcal{V}} \\rho(\\vec{r}^\\prime) \\frac{\\vec{r} - \\vec{r}^\\prime}{\\|\\vec{r} - \\vec{r}^\\prime\\|^3}dV<\/span>\n<p>\u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{V}<\/span> \u662f\u63cf\u8ff0\u5e26\u7535\u4f53\u5f62\u72b6\u7684\u4f53\u79ef\u7684\u53c2\u6570\u5316\u8868\u793a\u3002<\/p>\n<p><a name=\"3\"><\/a> <\/p>\n<h2>\u7ec3\u4e60\uff1a<\/h2>\n<h3>\u5e26\u7535\u6746<\/h3>\n<p>\u8003\u8651\u4e00\u6839\u957f\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">L<\/span> \u7684\u6746\uff0c\u5176\u4e0a\u5747\u5300\u5206\u5e03\u6709\u7535\u8377 <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span>\uff0c\u5e76\u7ad6\u76f4\u653e\u7f6e\u3002\u6c42\u8be5\u6746\u5728\u8ddd\u5176\u4e2d\u5fc3\u6c34\u5e73\u8ddd\u79bb\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u5904\u7684\u7535\u573a\u3002<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/PEi3xjHDyxM\" title=\"YouTube \u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h3>\u5e26\u7535\u73af<\/h3>\n<p>\u8003\u8651\u4e00\u4e2a\u534a\u5f84\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">R<\/span> \u7684\u73af\uff0c\u5176\u4e0a\u5747\u5300\u5206\u5e03\u6709\u7535\u8377 <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span>\uff0c\u5e76\u4f4d\u4e8e xy \u5e73\u9762\u5185\u3002\u6c42\u8be5\u73af\u5728\u8ddd\u5176\u4e2d\u5fc3\u9ad8\u5ea6\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">z<\/span> \u5904\u7684\u7535\u573a\u3002<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/kPVAhlzvgKA\" title=\"YouTube \u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h3>\u65e0\u9650\u5e26\u7535\u5e73\u9762<\/h3>\n<p>\u8003\u8651\u4e00\u4e2a\u65e0\u9650\u5e73\u9762\uff0c\u5176\u4e0a\u5747\u5300\u5206\u5e03\u6709\u8868\u9762\u7535\u8377\u5bc6\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\sigma<\/span>\u3002\u6c42\u8be5\u5e73\u9762\u5728\u8ddd\u5176 <span class=\"katex-eq\" data-katex-display=\"false\">L<\/span> \u5904\u7684\u7535\u573a\u3002<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/IQeDWxVT7eM\" title=\"YouTube \u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7535\u573a\u7684\u6982\u5ff5 \u572819\u4e16\u7eaa\uff0c\u8fc8\u514b\u5c14\u00b7\u6cd5\u62c9\u7b2c\uff08Michael 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