长 [tex=4.143x1.0]W1rSyremLkOInnZ1Tkp4kl5HoVCLAJCn+Za3ykk/VeY=[/tex] 的直导蛲线上均匀地分布着线密度[tex=7.429x1.5]mGOdEt4rfzX2iG4YqbX0QSmr+M/+1BZJMmA8aS2niZKqJxQQhLhh5680t9KDx517fvHS1ydHev02LpzYAvrbDg==[/tex]的正电荷。试求:(1)在导线的延长线上与导线 [tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]端相距 [tex=4.214x1.214]S/bNVXmvEF+uQOKXi74NomvLEW5vYSMiuck9CWmigvk=[/tex]处 [tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex] 点的场强；(2)在导线的垂直平分线上与导线中点相距 [tex=4.786x1.286]x5mawgfDbPOlQQTCTcAGwpW5aO79bsEWMVY23h2mK1g=[/tex] 处 [tex=0.857x1.214]to/MrMoO1ux8UhZHnpEvBg==[/tex] 点的场强。[img=530x242]17e4bd65a02a72b.png[/img]

2022-05-26

长 [tex=4.143x1.0]W1rSyremLkOInnZ1Tkp4kl5HoVCLAJCn+Za3ykk/VeY=[/tex] 的直导蛲线上均匀地分布着线密度[tex=7.429x1.5]mGOdEt4rfzX2iG4YqbX0QSmr+M/+1BZJMmA8aS2niZKqJxQQhLhh5680t9KDx517fvHS1ydHev02LpzYAvrbDg==[/tex]的正电荷。试求:(1)在导线的延长线上与导线 [tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]端相距 [tex=4.214x1.214]S/bNVXmvEF+uQOKXi74NomvLEW5vYSMiuck9CWmigvk=[/tex]处 [tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex] 点的场强；(2)在导线的垂直平分线上与导线中点相距 [tex=4.786x1.286]x5mawgfDbPOlQQTCTcAGwpW5aO79bsEWMVY23h2mK1g=[/tex] 处 [tex=0.857x1.214]to/MrMoO1ux8UhZHnpEvBg==[/tex] 点的场强。[img=530x242]17e4bd65a02a72b.png[/img]

答案：

如题图所示(1)在带电直线上取线元 [tex=1.143x1.0]hJUtCV/z/Za8eEtC0L0rnA==[/tex], 其上电量 [tex=1.0x1.214]ZOoAJZWJ/o8t1zeE5xKzAw==[/tex]在 [tex=0.786x1.286]dSWbQCTjdbLxKy7q0ps2gg==[/tex]点产生场强为[tex=8.071x2.714]wZXtcrNOptuwHElm5FYBQKoHr31MZtnuOqq8WqS66FxyqOKe8Ooccek8maPt//bmRxhwZ8JYHRoRSJpdXTEiVotJT5TDqYX12V8MW4kbbcWYD/tPcN6V8r45Hwt2/n6zdk0XGO6FkXvJyep9MOWMuksfFDBjkhZBi/Zo1fP5Vec=[/tex][tex=13.214x3.143]75kE60RkyMtQrSoZ8kWa5zKmtMfFeo35Nz62tJMJYPkfgj1BkIF6GqdnaHf8Pa152BNpy2XarevXkDEZL2JIijhalLeQKALqT7jJgCkVJNV9ZcE4kXiiUdz5efLR+cIT9F2dOIWxrhByLCsWm1L5ZziohLvA7v4fZDJQl/6D490=[/tex][tex=10.143x3.357]nDxhd4l4EyQy511tQUhzA7HG3cwWVsPV77cOIi52D5LbtRW0BUuCnT2cclyA42obWOrvY7jOn7Bn+In2nbWJEwhGOKzj9jmJliN0YnJmLHC67G9T9lemE519fyJ8WGudusLv3+0hLbnKs94KZBTwnA==[/tex][tex=6.643x2.714]H+YecY3MITtR1RGcH/EUMovH9u9UAtkh5Io5FsvHiazIJNmM3v87E/3IQmP62V+zBZ9oOsW+zBE5XF1MCc/uq2MVjyeOYwiaqLuNW1A/JDI=[/tex]用 [tex=15.357x1.5]BBK6h9lZWAfb8nH0A4dLyqSKjmrsYTiIr95inw8ZfPD7+6oeFktdjUMh4PkFHS40wf9fnb1sJBcaZUH887PIBxkpahYPFSeXC3Y87fzSXwCbREIGmDko4dMeznOENsf9uqhgqmW1n+RzTQqHnVdjhw==[/tex]，代入得[tex=9.0x1.5]R9TCmfw5W9aplBp208dyXGiPIaZVk/58907CO1ZxiF4rUSIOsaajDx4AokpQ92HDJKonJ8J+2Yi9SjBBqVL2tQ==[/tex]方向水平向右(2) 同理 [tex=7.929x2.714]wZXtcrNOptuwHElm5FYBQJPinFMz31CPQ34/zdnsyAje1RF02HRjd33Hk/8b9Ws1ioHSAsJUxHF2tboA/wZpgVoDcqyRHunz8X8EqSGpFbBM34SdMTBXAqESbnRvsrk2[/tex]方向如图所示由于对称性[tex=4.643x2.643]9XgwmCyziOXduviCAy4kniMeGHHYXBdbToaQEUy7o28=[/tex], 即 [tex=1.357x1.429]5vrF/sZLBOVMHK9KiRj5CA==[/tex] 只有 [tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex]分量,[tex=12.214x2.929]arzB3oR5jX51fFuX+LE1goesC5JTR1fhNLuXNma48VJ3wlHPA9rlamIta6Zoaoth58FlfiCgt2r1e9KEzimIIZjBDYqd70A4zjRPignjqrs8GIK55IJHJwBjNC3iKkIUDneULewuy17rI7zFqM4zTA==[/tex][tex=15.286x3.429]rTOPnPqTVqxGCgLblX8TZ3eoBwyvUBM1nLfNphyYTmfK5xMRmidjs2YsG1o6YD7buyRmrDAsK3V451Pt5RbnPPLBlqNu2fhL1JfJQrBsh2HKA2BkGRj1J0Yq2bXzARWWmCYDSh8EaOIuK3GOYPiBo9WXOkvHLYlYHkDdTu8ONUFqVOKCQWsGUei8IDhPWuX99RA8qON8AckJ5t58vrkK5WEuTwA0j+ReLhnT9BVPFZMy8y9O7mk1jxv6L+fqcWGD[/tex][tex=7.286x3.5]H+YecY3MITtR1RGcH/EUMsPCV9UqOjDjplU4QXYF8X2Vd7wThNTNG0FqBTVKO90s+/vK8H5tdK7sneiSq3WmaB4EeHdfV5XAtEKVEiYz47c=[/tex]以 [tex=15.857x1.5]mGOdEt4rfzX2iG4YqbX0QSmr+M/+1BZJMmA8aS2niZKqJxQQhLhh5680t9KDx517CavL4dyEJ5k2q6cSaB2pWEwoO3iQbPkaAjazhgIFldqw5upb0pLX/STsKt7kZfzxFko7XFSyWOvCNsN7a8C8FpRC/4UaoTRCgckiujxM410=[/tex] 代入得[tex=12.0x1.5]hPN5emY1eKR67go5FIu38X/El7M/f5oIbqJgtoi8bNQLN71FKiOKYMGMVFtbSysWOxf132ThrhB13ENuv4ou1vSoeuzAZJHSTiL0i9kXNNR2ZAlDNV63oEE2PkJuS19p[/tex], 方向沿[tex=0.571x1.0]xmABzkfH1dI7hTnxCUH55g==[/tex] 轴正向

举一反三

内容

0
长 [tex=4.214x1.0]RzB3/GF7R4sBwM8Z9qqhcw==[/tex]的直导线 A B 上均匀地分布着线密度 [tex=7.929x1.5]mGOdEt4rfzX2iG4YqbX0QT4BiiGO790n5K27yoSEILlLhkzR6mGHtYT3thDcuqAR[/tex]的正电荷. 试求:在导线的垂直平分线上与导线中点相距[tex=4.286x1.214]cvU2MGpNs6UMuJ3sc6zCEg==[/tex]处 Q 点的场强.
1
长 [tex=4.357x1.0]p3In2IhLW2F2OdQeZ8nLSA==[/tex] 的直导线[tex=1.571x1.0]JLMbVw4e37VvhkU494+8Ew==[/tex]上均匀地分布着线密度为[tex=7.143x1.5]S0J7wkSsDMBbCtsQeXMedE9x/3nHSLGUO0dopjLqyohTzzqb1DLHwK85bXMrVJV4[/tex] 的电荷。求：在导线的延长线上与导线一端 [tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex] 相距 [tex=3.714x1.0]VN1peBY1mtoH4t0giRk1ng==[/tex] 处 [tex=0.643x1.0]WUJ/JHItsc3Bqx1WYNJcrg==[/tex] 点的场强。
2
长为 [tex=0.357x1.0]Le5Jr6QhXJv1Yp4NjrbGVA==[/tex] 的直导线[tex=1.571x1.0]mCjAngcIqtveplNftuY0BQ==[/tex] 均匀地分布着线密度为[tex=0.643x1.0]+D9NhKovEP8INGz+KZnr1A==[/tex]的电荷. 求在导线的垂直平分线上与导线中点相距[tex=0.571x0.786]HXNXn3AXpwdIpZt8+6oCEw==[/tex]处 [tex=0.857x1.0]sKuuIgoU/ynFEIl8B2/CpA==[/tex] 点的场强.
3
长[tex=4.214x1.0]RzB3/GF7R4sBwM8Z9qqhcw==[/tex]的直导线[tex=1.571x1.0]mCjAngcIqtveplNftuY0BQ==[/tex]上,设想均匀地分布着线密度[tex=9.143x1.357]0WN4LRZSsaFbXcsix/4HuC8B4WuJcNBFdvnh4OIK7hizstw9yL9rKiEUJx6ZrUxw[/tex]的正电荷. 求在导线的延长线上与导线[tex=0.786x1.0]sHo1pKm+gjxjcUAJjHrarQ==[/tex]端相距[tex=4.286x1.214]pnKp0PrC/IGJMz4V07Xwxg==[/tex]处[tex=0.643x1.0]WUJ/JHItsc3Bqx1WYNJcrg==[/tex]点的场强;
4
长 [tex=4.214x1.0]RzB3/GF7R4sBwM8Z9qqhcw==[/tex]的直导线 A B 上均匀地分布着线密度 [tex=7.929x1.5]mGOdEt4rfzX2iG4YqbX0QT4BiiGO790n5K27yoSEILlLhkzR6mGHtYT3thDcuqAR[/tex]的正电荷. 试求:在导线的延长线上与导线 B端相距[tex=4.286x1.214]fVlCn1BdvFFJZYnC/xxuSw==[/tex]处 P点的场强