{"id":100012,"date":"2020-03-26T05:38:12","date_gmt":"2020-03-26T05:38:12","guid":{"rendered":"https:\/\/martinphysics.club\/?p=100012"},"modified":"2026-08-20T15:36:52","modified_gmt":"2026-08-20T07:36:52","slug":"find-the-force-on-a-uniformly-charged-rod-on-an-infinitely-long-charged-wire-in-a-vacuum","status":"publish","type":"post","link":"https:\/\/martinphysics.club\/?p=100012","title":{"rendered":"\u6c42\u4e00\u5747\u5300\u5e26\u7535\u68d2\u5728\u771f\u7a7a\u4e2d\u65e0\u9650\u957f\u5e26\u7535\u5bfc\u7ebf\u7684\u53d7\u529b"},"content":{"rendered":"<p>\u9898\u76ee\uff1a\u771f\u7a7a\u4e2d\u6709\u4e00\u65e0\u9650\u957f\u5e26\u7535\u5bfc\u7ebf\uff0c\u5176\u7535\u8377\u7ebf\u5bc6\u5ea6\u4e3a\u3002\u76f8\u8ddd\u5bfc\u7ebf\u957f\u5ea6a\u5904\u6709\u4e00\u957f\u4e3aL\u7684\u5747\u5300\u5e26\u7535\u68d2AB\uff0c\u7535\u8377\u91cf\u4e3aQ\uff0c\u6c42AB\u68d2\u7684\u53d7\u529b\u3002<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-100018\" src=\"https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/1-e1586271199552-300x242.png\" alt=\"\" width=\"300\" height=\"242\" srcset=\"https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/1-e1586271199552-300x242.png 300w, https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/1-e1586271199552-768x620.png 768w, https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/1-e1586271199552.png 787w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u601d\u8def\uff1a\u5fae\u5143\u6cd5\uff0c\u5148\u6c42\u573a\u5f3a\u5206\u5e03\uff0c\u518d\u6c42\u68d2\u4e0a\u7684\u529b\u5143\uff0c\u518d\u79ef\u5206\u3002<\/p>\n<h3>\u89e3\uff1a<\/h3>\n<h6>1.1\u3001\u5fae\u5143\u6cd5\u6c42\u573a\u5f3a<\/h6>\n<p>\u5982\u56fe\u6240\u793a\uff0c\u5efa\u7acb\u5750\u6807<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-100020\" src=\"https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/3-e1586271158219-300x220.png\" alt=\"\" width=\"300\" height=\"220\" srcset=\"https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/3-e1586271158219-300x220.png 300w, https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/3-e1586271158219-768x564.png 768w, https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/3-e1586271158219.png 896w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u53d6\u5e26\u70b9\u5bfc\u7ebf\u4e0a\u4e00\u70b9\u7ebf\u5143\uff08P\u70b9\uff09\u5bf9X\u8f74\u4e0a\u4efb\u610f\u4e00\u70b9\uff08Q\u70b9\uff09\u7684\u7535\u573a\u5f3a\u5ea6\u4e3a<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\vec{E}=\\frac{1}{4\\pi&amp;space;\\varepsilon&amp;space;_{0}}\\frac{\\lambda&amp;space;l}{r^{2}}\\vec{e_{r}}\" alt=\"\\vec{E}=\\frac{1}{4\\pi \\varepsilon _{0}}\\frac{\\lambda l}{r^{2}}\\vec{e_{r}}\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<p>\u770b\u5f97\u51fa\u6765\u7535\u573a\u5e94\u8be5\u662f\u4e2a\u5bf9\u79f0\u573a\uff0c\u770b\u4e0d\u51fa\u6765\u522b\u505a\u4e86\u3002\u73b0\u5728\u8981\u6c42\u7684\u5c31\u662f<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\vec{E_{x}}(x)\" alt=\"\\vec{E_{x}}(x)\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<p>\u6570\u5b66\u51c6\u5907\uff1a<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sin&amp;space;\\varphi&amp;space;=\\frac{l}{r}=\\frac{1}{\\csc&amp;space;\\varphi&amp;space;},tan\\varphi&amp;space;=\\frac{x}{l}=\\frac{1}{\\cot&amp;space;\\varphi&amp;space;}\" alt=\"\\sin \\varphi =\\frac{l}{r}=\\frac{1}{\\csc \\varphi },tan\\varphi =\\frac{x}{l}=\\frac{1}{\\cot \\varphi }\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<p>\u63a8\u8bba\uff1a<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?r=a\\csc&amp;space;\\varphi&amp;space;,l=a\\cot&amp;space;\\varphi\" alt=\"r=a\\csc \\varphi ,l=a\\cot \\varphi\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<p>\u7269\u7406\u51c6\u5907\uff1a<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/svg.image?dq=\\lambda&amp;space;dl,dl=acsc^{2}\\varphi&amp;space;d\\varphi&amp;space;\" alt=\"\" width=\"184\" height=\"19\" border=\"0\" \/><\/p>\n<p>\u6765\u4e86\uff1a<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\vec{E_{x}}=\\int&amp;space;d\\vec{E_{x}}=2\\int_{\\frac{\\pi&amp;space;}{2}}^{0}\\frac{\\lambda&amp;space;\\vec{i}}{4\\pi&amp;space;\\varepsilon&amp;space;_{0}x}\\sin&amp;space;\\varphi&amp;space;d\\varphi&amp;space;=\\frac{\\lambda&amp;space;}{2\\pi&amp;space;\\varepsilon&amp;space;_{0}}\\frac{1}{x}\\vec{i}\" alt=\"\\vec{E_{x}}=\\int d\\vec{E_{x}}=2\\int_{\\frac{\\pi }{2}}^{0}\\frac{\\lambda \\vec{i}}{4\\pi \\varepsilon _{0}x}\\sin \\varphi d\\varphi =\\frac{\\lambda }{2\\pi \\varepsilon _{0}}\\frac{1}{x}\\vec{i}\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<h6>1.2\u3001\u9ad8\u65af\u5b9a\u7406\u6c42\u573a\u5f3a<\/h6>\n<p>\u5982\u56fe\u6240\u793a\uff0c\u5efa\u7acb\u5750\u6807<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-100019\" src=\"https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/2-e1586271263747-300x204.png\" alt=\"\" width=\"300\" height=\"204\" srcset=\"https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/2-e1586271263747-300x204.png 300w, https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/2-e1586271263747-768x522.png 768w, https:\/\/martinphysics.club\/wp-content\/uploads\/2020\/03\/2-e1586271263747.png 913w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u7531\u9ad8\u65af\u5b9a\u7406\u5f97\uff1a<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\oint_{s}&amp;space;\\vec{E}d\\vec{s}=\\frac{\\sum&amp;space;q_{i}}{\\varepsilon&amp;space;_{0}}\" alt=\"\\oint_{s} \\vec{E}d\\vec{s}=\\frac{\\sum q_{i}}{\\varepsilon _{0}}\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<p>\u53d6\u67f1\u9762\u5750\u6807,\u95ed\u5408\u5706\u67f1\u9762\u4e3a\u9ad8\u65af\u9762\uff0c\u91c7\u7528\u56fe\u793a\u7684\u6b63\u65b9\u5411\uff0c\u770b\u5f97\u51fa\u6765\u662f\u5bf9\u79f0\u573a\uff0c\u53ef\u5f97\uff1a<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\oint_{s}\\vec{E}(x)d\\vec{s}=\\frac{\\lambda&amp;space;l&amp;space;}{\\varepsilon&amp;space;_{0}}\\Rightarrow&amp;space;\\vec{E}(x)=\\frac{\\lambda&amp;space;}{2\\pi&amp;space;\\varepsilon&amp;space;_{0}}\\frac{1}{x}\\vec{i}\" alt=\"\\oint_{s}\\vec{E}(x)d\\vec{s}=\\frac{\\lambda l }{\\varepsilon _{0}}\\Rightarrow \\vec{E}(x)=\\frac{\\lambda }{2\\pi \\varepsilon _{0}}\\frac{1}{x}\\vec{i}\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<h6>2\u3001\u6c42AB\u6240\u53d7\u7684\u529b<\/h6>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\vec{F}=\\int&amp;space;\\vec{E}(x)dq=\\int_{a}^{a+L}&amp;space;\\vec{E}(x)\\frac{Q}{L}dx=\\frac{\\lambda&amp;space;Q}{2\\pi&amp;space;\\varepsilon&amp;space;_{0}L}\\vec{i}\\int_{a}^{a+L}\\frac{1}{x}dx\" alt=\"\\vec{F}=\\int \\vec{E}(x)dq=\\int_{a}^{a+L} \\vec{E}(x)\\frac{Q}{L}dx=\\frac{\\lambda Q}{2\\pi \\varepsilon _{0}L}\\vec{i}\\int_{a}^{a+L}\\frac{1}{x}dx\" align=\"absmiddle\" border=\"0\" \/><\/p>\n<p>\u6545\uff1a<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\vec{F}=\\frac{\\lambda&amp;space;Q}{2\\pi&amp;space;\\varepsilon&amp;space;_{0}L}\\ln&amp;space;(1+\\frac{L}{a})\\vec{i}\" alt=\"\\vec{F}=\\frac{\\lambda Q}{2\\pi \\varepsilon _{0}L}\\ln (1+\\frac{L}{a})\\vec{i}\" align=\"absmiddle\" border=\"0\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u771f\u7a7a\u4e2d\u6709\u4e00\u65e0\u9650\u957f\u5e26\u7535\u5bfc\u7ebf\uff0c\u5176\u7535\u8377\u7ebf\u5bc6\u5ea6\u4e3a\u3002\u76f8\u8ddd\u5bfc\u7ebf\u957f\u5ea6a\u5904\u6709\u4e00\u957f\u4e3aL\u7684\u5747\u5300\u5e26\u7535\u68d2AB\uff0c\u7535\u8377\u91cf\u4e3aQ\uff0c\u6c42AB\u68d2\u7684\u53d7\u529b\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"wpai_generated_summary":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-100012","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":7}},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ 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