一个点电荷 [tex=1.286x1.143]XjKdZcMPBzOQweZnPXoVVw==[/tex] 位于 [tex=4.0x1.357]ARPkVlj26+ww5Rfaw7bgNQ==[/tex] 处, 另一点电荷 [tex=1.786x1.214]Um2WbBqM4Ud+EMa50hTbCw==[/tex] 位于 [tex=2.929x1.357]H/jUf3DzFJmiq+60sKORAw==[/tex] 处, 求电位等于零的面; 空间有电场强度等于零的点吗?[img=265x222]17a89fa5a244e87.png[/img]

2022-07-01

一个点电荷 [tex=1.286x1.143]XjKdZcMPBzOQweZnPXoVVw==[/tex] 位于 [tex=4.0x1.357]ARPkVlj26+ww5Rfaw7bgNQ==[/tex] 处, 另一点电荷 [tex=1.786x1.214]Um2WbBqM4Ud+EMa50hTbCw==[/tex] 位于 [tex=2.929x1.357]H/jUf3DzFJmiq+60sKORAw==[/tex] 处, 求电位等于零的面; 空间有电场强度等于零的点吗?[img=265x222]17a89fa5a244e87.png[/img]

答案：

解 根据点电荷电位叠加原理, 有[tex=9.929x2.786]d+ve3qe0nNSJAINNZuSJWmzGY4IpxCeJjlzjtz1cSXg2sggUZSaN0AdvTwIeBpi2j82/neOQS6iLDZzKdA2fG8SO6JYrum7HHsfTLaItOyHlk+G5Okv9fuAh5JnADVyF6nFIJ5NZjqVUX0qSKD7sUg==[/tex]式中[tex=13.214x6.5]rZM5/OPAdr7aX+kNl9iwpHlDZL8WatGHoy5R/Vts5BhnsXUoR/QHNga7wV5vhHsUMV44QTSCZy95LSyxxeAooF5g6jIiO5OZQD+QvhhPWwDE6kysFr4nY/VBm+eYgx+o6vaizQ4W0yo6avgxevTW1HmQC4OKApqi9doB8mKKYelOF5gYVK1scLwqlbVzTk4DgBZKWW6Je4hfqhCX0xJFzDJ15FO5uwa5Vlo4NcZeioAAa9HYOpKq1xLcOR2N3dg1msHQWQpa6dl+o7YTm1bNiVw/ws8TIiiTDWQG6Z6Cse+67lXqoT4A3FYKdmOLev+mZ4UBD3nGiHYLX+2KEU1aYs2zLoUR1S0ArblxiTHGiOk6D40RXg04v+07cDdS5/mJLhQcypbPIjPaDdc1rSzUGQ==[/tex]代入得到[tex=22.786x3.357]d+ve3qe0nNSJAINNZuSJWr3HfDZsu+c+4YQ5HokKeicgxK5ruj08xH4Vos5JF7ZEgrIlNzS+C2QVHzVSoMvUJAdcwIxB4p4S9Pvxcws0WuJQWt7NcC8/zgF8mGXVlWqEvUHtuq0eAWV9LUfxHyhZ6Z9LOhyu+Jf7AFDPvHRH88pRrrPU3n+m8o974RnNa02Q[/tex]电位为零, 即令[tex=24.214x3.357]d+ve3qe0nNSJAINNZuSJWr3HfDZsu+c+4YQ5HokKeicgxK5ruj08xH4Vos5JF7ZEgrIlNzS+C2QVHzVSoMvUJAdcwIxB4p4S9Pvxcws0WuJQWt7NcC8/zgF8mGXVlWqEvUHtuq0eAWV9LUfxHyhZ6Z9LOhyu+Jf7AFDPvHRH88qag+QrXorfaQErnHbC+uDx[/tex]简化可得零电位面方程为[tex=12.0x1.5]s9mwO+A12K2ty6CF8APPmQkcjWTyatLKxDpuBStgvYZcRO084XAZt48XiQRpE3vz[/tex]根据电位与电场强度的关系，有[tex=37.786x9.071]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[/tex]要是电场强度为零, 必有[tex=9.714x1.286]VvYsz+/8hyfWZYshrAdGs80JdDEqsp3ujWDNRi9Y/fhEXqhROwamLUrYcRjOuzk6[/tex]即[tex=27.714x6.357]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[/tex]此方程组无解, 因此, 空间没有电场强度为零的点。

举一反三

内容

0
如图所示真空中，电荷量为[tex=1.786x1.214]i98pJ3QE8Gq9wzvWzQ+yWw==[/tex]的点电荷在[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]点，而电荷量为[tex=1.786x1.214]ue/bfJs0R1Qzu2vl11A89w==[/tex]的点电荷在[tex=0.786x1.0]YEkxBRWVe8SyiK/VG6WTCQ==[/tex]点，线段[tex=3.071x1.0]M+EPA1xYGjvxPwNNL2ddkg==[/tex],现将一个单位正电荷从[tex=0.786x1.0]ri6gmnf1+J9dGqG5/1sV6A==[/tex]点沿半径为[tex=0.786x1.0]as0RCzgUx1oS48cKHRAVVg==[/tex]的半圆弧形轨道[tex=2.357x1.0]c5hPBX2K9wBLr+hRlo3MDA==[/tex]移到[tex=0.857x1.0]m2DKAQtGuc1DyN3zyNlILg==[/tex]点，求电场力所做的功。[img=385x150]17978ff0c133bf1.png[/img]
1
[img=308x130]17a8b8965bba268.png[/img]如图所示，在点电荷[tex=1.286x1.143]XjKdZcMPBzOQweZnPXoVVw==[/tex]的电场中，若取图中点[tex=0.857x1.0]zkVuLx/VQ1XnCvAv90B7dQ==[/tex]处为电势零点，则点[tex=1.0x1.0]0KCelhZna0R9EGhYF1VZHA==[/tex]的电势为多少？
2
如图所示, 一根绝缘细胶棒弯成半径为 [tex=0.786x1.0]AOSTmhvIsOwsdZlGoks7dg==[/tex] 的半圆形。其上一半均匀带电荷 [tex=1.286x1.143]XjKdZcMPBzOQweZnPXoVVw==[/tex],另一半均匀带电荷 [tex=1.286x1.143]LPSLxLAra1efnOoLajObnQ==[/tex] 。求圆心 [tex=0.786x1.0]5SeCOJOzMwSNbX8MGx2Qsg==[/tex]处的场强。[img=276x300]17ac7c1d909476e.png[/img]
3
如图所示，一绝缘细棒被弯成半径为 [tex=0.786x1.0]AOSTmhvIsOwsdZlGoks7dg==[/tex] 的半圆环。其左半部分均匀带有电荷量 [tex=1.286x1.143]XjKdZcMPBzOQweZnPXoVVw==[/tex]，右半部分均匀带有电荷量 [tex=1.286x1.143]3ZXX1a0roXxpxBNG4nK4nw==[/tex]。求环心处的电场强度。[img=316x232]179843076e5d45e.png[/img][br][/br]
4
如图所示，一个电荷量为[tex=0.5x1.0]NSsYk+dfiqXGkmCPT5DyRg==[/tex]的点电荷,位于真空中立方体的[tex=0.786x1.0]Yn3GgEZev6SOu2r4v1WnCw==[/tex]角上，求通过侧面[tex=1.929x1.0]OE+pSGoAIKeuWnO6LTso9Q==[/tex]的电场强度通量[img=202x216]17978a777d406f3.png[/img]