![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/gfleareth.png\")
<\/center>\n\u6700\u8fd1\u5728\u8bb2\u7535\u573a\uff0c\u7ff0\u94ee\u540c\u5b66\u5206\u4eab\u4ed6\u770b\u5b66\u4e60\u5fc3\u5f97\uff0c\u8bf4\u6709\u8001\u5e08\u7528\u201c\u81ed\u811a\u4e2b\u201d\u7c7b\u6bd4\u7535\u8377\uff0c\u81ed\u5473\u662f\u770b\u4e0d\u89c1\u7684\u90a3\u79cd\u7269\u8d28…\u540e\u6765\u5728\u65e5\u8bed\u73ed\u4e0a\u8bfe\uff0c\u8fd8\u7279\u5730\u8ba9\u6253\u7bee\u7403\u7684\u82cf\u540c\u5b66\u62d6\u978b\uff0c\u5982\u679c\u4ed8\u51fa\u95fb\u70b9\u5473\u9053\u7684\u4ee3\u4ef7\u5c31\u80fd\u5f88\u597d\u7406\u89e3\u201cfield\u201d\u5012\u4e5f\u5408\u7b97\u3002
\n\u540e\u6765\u6211\u89c9\u5f97\u7528\u69b4\u83b2\u4ee3\u8868\u5e26\u7535\u7269\u4f53\u53ef\u80fd\u66f4\u597d\uff0c\u6709\u4eba\u5bf9\u69b4\u83b2\u7684\u5473\u9053\u559c\u6b22\u7684\u4e0d\u5f97\u4e86\uff0c\u800c\u6709\u4eba\u5219\u552f\u6050\u907f\u4e4b\u4e0d\u53ca\uff0c\u76f8\u5f53\u4e8e\u540c\u4e00\u70b9\u6b63\u8d1f\u7535\u8377\u53d7\u529b\u76f8\u53cd…
\n\u5c3d\u7ba1\u6211\u672c\u4eba\u4e0d\u66fe\u5403\u8fc7\u69b4\u83b2\uff0c\u5f88\u591a\u5e74\u524d\u8fd8\u5199\u8fc7\u5173\u4e8e\u5b83\u7684\u5fc3\u5f97\uff1a
\n@qiusir:\u69b4\u83b2\u4f3c\u4e4e\u53ef\u4ee5\u7528\u6765\u5f62\u5bb9\u4e00\u79cd\u4eba\uff0c\u7c97\u786c\u591a\u523a\u7684\u5916\u8868\u5374\u88f9\u7740\u67d4\u8f6f\u4e30\u5b9e\u7684\u5fc3\u3002\u4e0d\u5c11\u4eba\u88ab\u5176\u5916\u8868\u6240\u62d2\uff0c\u800c\u80fd\u89e6\u53ca\u5176\u5185\u5728\u7684\u4e5f\u672a\u5fc5\u53d7\u5f97\u90a3\u6c14\u5473\uff0c\u4f46\u5bf9\u6562\u80fd\u4eab\u98df\u8005\u6765\u8bf4\u5374\u591a\u6709\u6c34\u679c\u4e4b\u738b\u4e4b\u7f8e\u8a89.
\n@qiusir:\u6709\u7684\u77e5\u8bc6\u4e5f\u5982\u69b4\u83b2\uff0c\u4e0d\u754f\u5176\u8868\u4e0d\u60e7\u5473\uff0c\u80fd\u6562\u98df\u4e4b\u65b9\u77e5\u5176\u7f8e\u5473.
\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/GravitationalPotentialEnergy.png\")
<\/center>\n\u7535\u573a\u548c\u5f15\u529b\u573a\u4e2d\u7684\u52bf\u80fd\u95ee\u9898\u662f\u53e6\u4e00\u4e2a\u96be\u70b9\u3002\u5728\u5b66\u4e60\u8fd9\u4ef6\u4e8b\u4e0a\uff0c\u4e5f\u5f88\u80fd\u4f53\u73b0\u56f0\u96be\u6e90\u81ea\u7f8e\u5fb7\uff08\u6df1\u7a76\u6089\u8ba8\uff09…
\n1\u3001\u5f15\u529b\u52bf\u80fd
\n$\\int\\frac{1}{r^2}dr=-\\frac{1}{r}$
\n$E_p=-\\int F\\cdot dx$
\n$E_p(r)=-\\int_{\\infty }^{r}-\\frac{GMm}{r^2}dr$
\n$E_p(r)=-\\frac{GMm}{r}$
\n2\u3001\u91cd\u529b\u52bf\u80fd
\n\u4ee5\u5730\u9762\u4e3a\u96f6\u52bf\u9762\uff08\u901a\u5e38\u662f\u4ee5\u4fdd\u5b58\u529b\u4e3a\u96f6\u7684\u4f4d\u7f6e\u4e3a\u96f6\u52bf\u9762\uff0c\u8fd9\u91cc\u662f\u4e3a\u4e86\u8868\u8fbe\u5f0f\u7b80\u6d01\u548c\u65b9\u4fbf\uff0c\u5c31\u5982\u901a\u5e38\u4ee5\u5730\u9762\u4e3a\u53c2\u7167\u7269\u4e00\u6837\uff09
\n$E_p=-\\frac{GMm}{h+R}-(-\\frac{GMm}{R})$
\n$E_p=\\frac{GMm}{R}-\\frac{GMm}{R+h}$
\n$E_p=\\frac{GMm}{R}(1-\\frac{1}{1+\\frac{h}{R} })$
\n\u5982\u679c\u7269\u4f53\u5728\u5730\u7403\u8868\u9762\u9644\u8fd1\uff0ch$\\ll$R\uff0c$\\frac{1}{1+\\frac{h}{R} } \\approx 1-\\frac{h}{R}$
\n$E_p\\approx\\frac{GMm}{R^2}h$
\n\u6240\u4ee5\u6709$E_p\\approx mgh$\uff0c\u4e5f\u5c31\u662f\u6709\u5fc3\u529b\u573a\u5c40\u90e8\u8fd1\u4f3c\u4e3a\u5300\u5f3a\u7684\u5f15\u529b\u573a\u3002
\n3\u3001\u7535\u52bf\u80fd
\n\u7c7b\u6bd4\u4e07\u6709\u5f15\u529b$F=\\frac{GMm}{r^2}$\u548c\u5e93\u4ed1\u5b9a\u5f8b$F=\\frac{kQq}{r^2}$
\n\u4e0d\u96be\u5f97\u51fa\u5bf9\u4e8e\u5f02\u79cd\u7535\u8377\u95f4\u7684\u7535\u52bf\u80fd\u548c\u5f15\u529b\u52bf\u80fd\u5177\u6709\u76f8\u540c\u8868\u8fbe\u5f0f\uff0c$E_p(r)=-\\frac{kQq}{r}$\uff08\u6b64\u5904Q,q\u4ec5\u6307\u7535\u91cf\u5927\u5c0f\uff09
\n\u5982\u679c\u8003\u8651\u5230\u7535\u8377\u7684\u6b63\u8d1f\u95ee\u9898\uff0c\u4ee5\u53car\u7684\u65b9\u5411\u95ee\u9898\uff0c\u5e93\u4ed1\u5b9a\u5f8b\u66f4\u4e00\u822c\u8868\u8fbe$\\mathord{ \\buildrel{ \\lower3pt \\hbox{$ \\scriptscriptstyle \\rightharpoonup$}} \\over F} = k \\frac{{Qq}}{{{r^2}}} \\hat{r} $\uff0cQq\u662f\u5305\u542b\u7535\u6027\u6b63\u8d1f\u7684…\uff08$\\mathord{ \\buildrel{ \\lower3pt \\hbox{$ \\scriptscriptstyle \\rightharpoonup$}} \\over F} =-G \\frac{{Mm}}{{{r^2}}} \\hat{r} $\uff09
\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/electric_fieldlines2-005.png\")
<\/center>\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/electric_fieldlines2-006.png\")
<\/center>\n\u7535\u52bf\u80fd\u7684\u8868\u8fbe\u5f0f\uff1a$E_p(r)=\\frac{kQq}{r}$
\n\u7531\u7535\u52bf\u7684\u5b9a\u4e49\u5f0f$\\varphi =\\frac{E_p}{q}$\uff0c\u4e5f\u5c31\u65b9\u4fbf\u5f97\u51fa\u70b9\u7535\u8377\u7684\u7535\u52bf\u51b3\u5b9a\u5f0f\uff1a$\\varphi =\\frac{kQ}{r}$
\n\u5982\u6b64\u5bb9\u6613\u7406\u89e3\uff0c\u6b63\u7535\u8377\u7684\u7535\u573a\u7535\u52bf\u4e3a\u6b63\uff0c\u8d1f\u7535\u8377\u7684\u7535\u573a\u7535\u52bf\u5c0f\u4e8e\u96f6\uff1b\u8d1f\u7535\u8377\u5728\u8d1f\u7535\u8377\u7535\u573a\u7684\u7535\u52bf\u80fd\u5927\u4e8e\u96f6…\u5bf9\u7b49\u91cf\u5f02\u79cd\u7535\u8377\u4e2d\u5782\u7ebf\u4e3a\u96f6\u52bf\u80fd\u9762\uff0c\u9664\u4e86\u7528\u7535\u573a\u529b\u65b9\u5411\u7406\u89e3\uff0c\u7528$\\varphi =\\frac{kQ}{r}+\\frac{-kQ}{r}=0$\u7406\u89e3\u66f4\u76f4\u63a5…
\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/landfe2003.png\")
<\/center>\n\u5957\u7528\u70b9\u7535\u8377\u7535\u52bf\u7684\u65b9\u7a0b\uff0c\u53ef\u4ee5\u5f97\u51fa\u5173\u4e8e\u4e24\u4e2a\u5173\u4e8ey\u8f74\u5bf9\u79f0\u7684\u70b9\u7535\u8377\u5728\u5e73\u9762\u67d0\u70b9\u7684\u7535\u52bf\uff1a
\n$\\varphi_n=\\frac{k_0Q_1}{\\sqrt{(x+l)^2+y^2}}+\\frac{k_0Q_2}{\\sqrt{(x-l)^2+y^2}}$
\n\u7535\u573a\u662f\u4fdd\u5b88\u529b\u573a…\u7535\u573a\u7ebf\u65b9\u7a0b\u548c\u7b49\u52bf\u9762\u65b9\u7a0b\u4e92\u4e3a\u5171\u8f6d\u8c03\u548c\u51fd\u6570\uff08\u4e0d\u61c2\uff0c\u5b89\u6392\u8fdc\u5353\u7b49\u540c\u5b66\u66b4\u529b\u6c42\u89e3\u53bb\u4e86\uff09…
\n$\\psi_n=\\frac{k_0Q_1(x+l)}{\\sqrt{(x+l)^2+y^2}}+\\frac{k_0Q_2(x-l)}{\\sqrt{(x-l)^2+y^2}}$
\n\u6839\u636e\u4e0a\u5e74\u7684\u4e24\u4e2a\u65b9\u7a0b\uff0c\u7528GeoGebra\u7684\u66f2\u7ebf\u201c\u5e8f\u5217\u201d\u5c31\u53ef\u4ee5\u7ed8\u5236\u4e0a\u56fe\u4e86…
\n\u53e6\uff0c\u6700\u8fd1\u8fd9\u91cc[?<\/a>]\u53d1\u73b0\u8fd9\u5f20\u56fe\uff0c\u6309\u7167\u8fd9\u91cc\u7269\u7406\u91cf\u8868\u8fbe\u4e60\u60ef\u7565\u5fae\u505a\u4e86\u4fee\u6539\uff08\u65e5\u672c\u6559\u6750\u4e2d\uff0cU\u4ee3\u8868\u52bf\u80fd\uff0c\u800c\u7535\u52bf\u7528V\u8868\u793a\uff09\uff1a
\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/fomulae.png\")
<\/center>\n\u5173\u4e8e\u7535\u52bf\u7684\u9ad8\u4f4e\uff0c\u7528\u5730\u52bf\u7684\u9ad8\u4f4e\u7c7b\u6bd4\uff0c\u800c\u7b49\u52bf\u9762\u548c\u5730\u91cc\u7684\u7b49\u9ad8\u7ebf\u7c7b\u540c…
\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/41pns2.png\")
<\/center>\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/ephipn3.png\")
<\/center>\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/4ycm.png\")
<\/center>\n
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/4fchargesf.png\")
<\/center><\/p>\n![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/twhlwlxc63.png\")
<\/center><\/p>\n\u4e2d\u5b66\u9636\u6bb5\u53ea\u8bb2\u7535\u52bf\u80fd\uff0c\u662f\u7535\u8377\u76f8\u4e92\u4f5c\u7528\u7684\u52bf\u80fd\uff0c\u7b80\u79f0\u201c\u4e92\u80fd\u201d\u3002
\n\u70b9\u7535\u8377Q\u4e5f\u662f\u7531\u4f17\u591a\u66f4\u5c0f\u7684\u7535\u8377\u805a\u96c6\u8d77\u6765\u7684\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u9700\u8981\u514b\u670d\u7535\u573a\u529b\u505a\u529f\uff0c\u56e0\u6b64\u8981\u6d88\u8017\u5916\u754c\u7684\u80fd\u91cf\uff0c\u8fd9\u4e9b\u80fd\u91cf\u603b\u548c\u79f0\u4e3a\u201c\u81ea\u4f5c\u7528\u52bf\u80fd\u201d\uff0c\u7b80\u79f0\u201c\u81ea\u80fd\u201d\u3002
\n[Q]\u6c42\u5747\u5300\u5206\u5e03\u7684\u7535\u91cf\u4e3aQ\u534a\u5f84r\u7684\u7403\u5916\u8868\u9762\u7684\u5e26\u7535\u4f53\u7684\u201c\u81ea\u80fd\u201d
\n$W_1=0$
\n$W_2=k\\frac{e}{r}e$
\n$W_3=k\\frac{2e}{r}e$
\n\u79fb\u52a8\u7b2cn\u4e2a\u5143\u7535\u8377e\u6240\u9700\u8981\u514b\u670d\u7535\u573a\u529b\u7684\u529f$W_n=k\\frac{(n-1)e}{r}e$
\n$E=\\sum W=\\frac{1}{2}k\\frac{Q^2}{r}$<\/p>\n","protected":false},"excerpt":{"rendered":"
\u6700\u8fd1\u5728\u8bb2\u7535\u573a\uff0c\u7ff0\u94ee\u540c\u5b66\u5206\u4eab\u4ed6\u770b\u5b66\u4e60\u5fc3\u5f97\uff0c\u8bf4\u6709\u8001\u5e08\u7528\u201c\u81ed\u811a\u4e2b\u201d\u7c7b\u6bd4\u7535\u8377\uff0c\u81ed\u5473\u662f\u770b\u4e0d\u89c1\u7684\u90a3\u79cd\u7269\u8d28…\u540e\u6765 … \u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[5],"tags":[247,252,263],"class_list":["post-27438","post","type-post","status-publish","format-standard","hentry","category-physics","tag-physics","tag-students","tag-teach"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/27438","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=27438"}],"version-history":[{"count":3,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/27438\/revisions"}],"predecessor-version":[{"id":44051,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/27438\/revisions\/44051"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=27438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=27438"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=27438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}