Определим напряженность электрического поля = - grad В сферической системе координат
. Благодаря осевой симметрии .
- вектор не зависит от угла α (поле обладает осевой симметрией) и имеет две составляющие. Картина силовых линий поля диполя
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GeQhQptw5hSEe9QWKGS32T3VOKLpYFvZlKc0aNkWNTnQMZqAl7SYj7BqnRufus6PZo6syanRaQ+zL77M9RUBSjT6cwTAbyX9FIaujbyNuckVu9ode2fe7vrIiIGBSC3KUiqWfUYUjxMifclqR5DPKkGpFUlBj8afZVtZeBGg4LMenWIEtJyKsTYv9RS/4rWmgWVhjyQb2qoAJ909VWXTQe7JBv5ekAxoTcIyaGK3d6RG4Y0nmZHFXbPPuInzQH6sxOiLGvvTDUfLZQoFXqGxtJiF5MgXTfDZrzo5lGHVVv8+wjQdC8xBlom7cwMlRptnWrJUl68803v/KVrwwNDW3cuHH//v2lr581a9amTZssFMys1pMQvVgWs4I6SXN+tPAwpDk9iH3EZ3G7FXWHrZbCkOeVc8IJJzzzzDO9B9/97ne/973v9R785Cc/uemmm+IXjI6OjoyM7Ny5c8uWLZdddtmCBQuclbWBdpMQq8Gz6OI7THNKkOd9X3uIQeFqGAK60eZlhqG+V199tf/g5JNPTj4/ZcLhhx8+Z86cXuFPO+00F6Vrqq0kxLT2XHTxnUcYKlIag1gkH4raM1qyg6a1382V0jBUb3fOVk7/GX8qZ82aNf0HqSSUNDIycuqpp9oqkUmtJCFiUK5wd35Uoj+NWk4YqhGDul0hARkw9/sYuTEiuMZvYWQo8mxiSS/irF+/vvfgqKOOmjVrluJlJKEcYbVva6gWIUp7TA8X6LaNGBQECzfRCZqdb+HPXvDaa6+NjY31Hnzyk59UvGznzp22SmSY+STESrFcVItwRSe+zZfR+k/d+Bkr9Uq2HRrfKMk3DLfxtxGGcu9S5gOdS2NB435CNnjYsmFfaXcf4vGgVOmkivhx9757EDyZvBhi42/7Mpk/dVI0XbozDCchRj6y6Os94UPjFDVhSDFf0JPLYT40Cd9YrorQG383LvaVUowJPfPMM4sXL37vvfesF8okxoTsCW4n7wa3/ZTY2dP+x6AkmZHI4FToJkJv/C1dJvNqWEgxJvTggw8GOks6yWQSktmbKEg4V7DMSJVWfRPjq2Zyhwlzl9E2/1wnFOOgLcUgU/tajfcJazP52SkRhhScV8ju3bvfeeedaGLh2MyZM5P/1CvYQw89dO211zoqmjHGkpCfO5hDVEhnmOqJSpcQZ5fRBndISFHEoNC/WiyIzZSbrb0qdpfCkJHy+1Mha9eu7X/68PDwpEmTsi8I9L7SSWaSUCc7uNo8mYEYLg9DpKmb/uWuDUmFoeQLWu0BrbVJs+NAHW4ebQjo7m7+HPvrMT4y5EmFxJfGvva1r/3sZz9L/tOqVauuvvpqktC/EYOSAup3gtZkuWmljdLS/WRTb556n7Z7wFabZelGaTUGGdy4pR9R+uduD+ceRsZKCEORH2FIMUlo8uTJkyZNUt9kKAiNkhBH/RRCYT01+o4m3Y3ZrqrJgIeimwt0TUrpLtB2UrFQaZU+wkmfYOGeQHaEOGGu7TAUWa8QxcKxXhI6/vjjp06darM8bTA2TyisxtoGYlA9il6jdLKtK+oRqUqnbj6c85mSuwvU3i9KG4Zv7SFFPSfMOA9X5NWQ22yC2y/aGMR1WCGKMaH/m2CtJO0xk4TCaqZtozaMyF1q3n/gycJ4Uyd/gQ7/KDSPQTpv7py6JA43qz9VVJtvYdc5VxWyffv2jRs39h7MmGD5063hfkJmcAeBqppcWm0YiQxuo+xbxXcBqfSJubcP8e2eImrZXaBeDNKvuuZ10nb7Sb6yXsMoFbcN/1tIDWHtAp2keXfpxx57bNmyZe+++66VQplHEjKAE5eqTNWYJ6NEpSr147kv9vxIkHslKH5cOwZ5pY36r7dZfa6l9ni+C3SVZhJ68MEHzz77bCslagVJqCmmB5VqdTFR6h2cHySKromUjhpm50Vm38FUAzM77zJ7U4Dk/yo+xULDaM7gRT11wyj9rNyt5kMVtapLE+lCpPPbq6Ojow8//PDNN99sq1Dm1U9Czg85vmEXraqNGvMhEmWviSQpevPSmSVmjwS9d3v77bePPfbYj3zETD+QLX+90vqwK7XaOKPqYVfyGRdhyCGdMaEnn3zygw8+kDgmJHm3hD79dWHG+RCJiih2n9x5ke0to/34xz/+2muvnXjiiTX+tjT0aK6o0vkra5z3ZtkjvYcN2L7urSpoyFoijMeEUjcNGh0d3bt3765du7Zu3Xr33Xf3ynPWWWdZKE9L6iQhYlCMnVPBk2W9biNRvWGAbB5yu4y2VG6Bq/65Q/YLoIg78cbtzG2BYIqdRLhnz55rrrlmw4YNQ0NDO3bs6D+Z+sWxlPnz50+fPr3tgrWn0TwhdssYVVHKeRU5L0BD3q4r1hwN0v9za7xtEpxtooiF9XSHHXbYo48+2sY7e6tyEmK5eIyqUKByshRL7nNrKZQlxJpzg4wvIO8Sb2OuP0LZHRAi1o7VRJ+lQOVUVdq5+9b7V93ENAm1/vbNXvvwbbt7Qni1EAqNIwlVxqltrtxDHZWjlrtyPllpilUzTjrB3LlfRZdyHM6XD0LRLkMYKtLe0gEIRxJqhP1QgcrRUXrky4Yhf1YUV41BNIlI47ZA2Stlzje0PzxfOmANw0JmkYTqo/31ebJGLFy5YShKVGPu0FH8vw5rmxhUSZPhZIZAYsypSiEMNVctCdH4qIEUYpARuUv9kx2cYvVspX5wypQpY2NjyWdOOumk5P++8cYbxx9/fNEHFb1tUQyiMfTV6Ddyj/cc8xDzang4dBWSEB0cNZBCDDIudfxLTh5SnArr94PHHXdcLwm9/fbb8TPHHHNMLx7F/1t0v+miY7nidk00htILYfXek4pNklwh3HDSFN0kRAhIogYimkSbFJOHivo+zePBm2++GR287Z566ql695iOlNudJmFkB8kdbJN87I8xIpIk/Os3V3meEDWOiBjUvhphyDJGg4q0tHU49qd4siP4gPbQkFYS4i55ETOEEohBdijWEFk+BiiyDjEoKXtAMlsbhCGgDawdq4zeJ0ZVOGTtxjOKyEUMsr9KjoEQJLGc3ojyJMSAUEQlJFAVluXOoS6q/Eq9Ye+VkyZNUr9GMwbRGPrs1AMHvxhVASMYEwLCo+j3dQ4JzY8ZxKCB//4+hg/FcFsGT4itCuJgcyQhaGFA3jeebBFRPa8ndR7xuxMJzJ1CcyVJyJ893yEqAc4pbl3YXvssfWcJR52inOHbd5ccAmyGoXXr1i1dunRoaGjTpk2pm5TmmjVrVu+V7ZUHRqiSEAPgEZXALyf4R/HjG/GTmhvowIEDRf9EDIr4ueVwWJtIPn/+/Geffbb3YMmSJffdd1/vwUMPPXTFFVfEL9i3b9/IyMjOnTu3bNly0UUXnX766RZKhYa0ro6x/0dUwn9RDz4o7fcbnhkTg/wfCVbcyAAWvPLKK/0Hp5xySvL5QyZMnz79mGOO6f3vaaedZqEwTBVqiHlCqIB9zB/JMKT4IQ5Tn5V8/243g7bvCYQO6DWJtWvX9h4ceuihRb/T1zMyMmInCaEhkhB0cTzwTepEMDVQpF5fFimX4qc+Jep6DAr6xkiMB9j31ltv7dmzJ5q4WKa4FcW+ffusJSGaQRMkIRWGnamBUOR2f+o+kR4zV9B1wja149VXX+0/SF0aS9m7d6+V4qTRDKoiCeVjpmTEbPEQlM6ebq7badiT2wI1xEryJAs1ECehk08+udUPqoT7j9dGEionvFuJqAG/me3+Ot+TdvULEoZs1kDRdOme559//sorr3zvvffa+3QYRxIqIbBDQXAUM6YrHRI6vGQslNsCNcGQgLUaUIwJrVixYsGCBRbKAINIQjmE9yZ9VEJnGDk/DjoxcJ0XBo2Ojr7++uu9B9OmTZs7d27yn3qta+XKlYsXL3ZTMtRVmIS6vVREgU4zohJwsHDbgNhAL/MCWVJ7NbBu3br9+/f3HuzevTt34RhjQsFhTKiQ8H6kj0oISMO7ChX9YaBtQOZtgZgtZKEG4ktj119//b333pv8p9WrVy9atEi9oAweyk9CYgeEgE6qdAOhpIB6AH4Wpo8fZ217tpBiuvTkyZN7H61eUDY8PHzLLbc88cQTe/bsWbhw4a233trGAjSZObg2xoSQJvaCQjcoDgNVO8ege9KgC28WB0WzFDcT6iWhuXPnTps2rehvX3755YsvvnjKlCm//OUv58yZ841vfOOss8666667vvzlLxspG4OC9ZCEcBBmCHWAkXPigLZ+N+4JhFDEY0LZsZxLL710/fr1RX+4devWyy+/fMuWLX/9618/9alP9Z757W9/e+qppy5dunT+/PnnnHOOkeKxhLAGkhD+hxjUGQ17Q/+3Pn29Aj/O2p5du3YNDQ31HgwODvZ/Y1XfHXfcsWHDhjPPPLMfg3qOOOKIL3zhCz/60Y+++tWv/u1vfzNfXOghCSGH/wdC1JM6NAY3fp478SWsr4CgrVmzpt/eSif3PP744zfeeGM/NkUTC83uvvvu3oOrr746+bIrr7yyl4T+/ve/v/DCC6aGhVAVSQjoJs1hoVCGDfgBHPhAMV065f777z/vvPPi/33uued27NjRe/CZz3wm+bKzzjprypQpo6Ojq1atIgm5QhLCf4RyRIQ0tEz4Q/O3V3ft2vXwww/fdttt8TN//vOf+w9mzZqVfGWvec+YMWPTpk0vvvii6cJCF0noIGJvH8AMIcT8aQAy7wnUhuAug3pLMV06aeXKlR9++GFyTCj+w6OPPjr14t4zvST08ssvGy0pKshJQpyBSUZ32SU15k07bwDZAjsvUrhYU21c0ZjQ2NjY6OhoL/3s3Llz69at99xzz9SpU88444z4BcPDw73/Tpky5aMf/WjqPWfOnBm/AE6kk5DksQGxA0LosEo3nnbV8iX8PKorwtdUG7m3ZO/Pr7rqqvXr1w8NDW3fvr3/ZD++KCxcuHDy5Mnx/77//vvRxG+W5f5AR8+BAwd27dp1+OGHNylqCvFXU+HVMaoPgAVMhYZxqfzXMBD0/nzVqlXNi9R/q3nz5qX+6d133929e3c0kZMafkr8WYwFVsI8IQD/Zr+7lDxWgbY1/Bk+44488shoojxr1qxJDQtdcMEFTz/9dO/JwcFBUx8nfCywKpIQ0H2+dYtMhYY0s2fPjiYugQ0PD8+YMSP5T5s3b44m5k17tZOKQhICYANToSHZueeeu2LFimgi96SS0JYtW/ovcFMykIQA2EcGgjQXXHBB/8G6deuSK/D/9a9/bdu2rffgwgsvdFMykIQAtI1fSAUWLFiwcOHCZ5555te//vVVV10VP/+b3/wmmvgVsy996UvuSicdSUg6rkzDOBqVn1hG5Nbtt9/+uc997pFHHnn33Xc/9rGP9Z7Zv3//L37xi96DW2+9NXufIVhDEgLQLo6+/iAMOXTuuef2cs8NN9xwySWX3HvvvTNnzrz55ptfeumlm2666Zvf/Kbr0olGEsL/0EWiIS6EAQrXXXfdOeecs3z58kWLFu3YseOMM8549NFHL7vsMtflko4khP/g6IV6uBbmOd/urCPcCSec8MADD0QTK+qL7jcNy0hCAGritkBAbcQgf5CEAOjKHVcg/QAIGkkIQE1kIAAdQBICUI6p0AC6iiQEIB9zbAFIQBICUI7RIABdRRICcJB4RRjpB4AEJCEA/8a1MAAykYQAHIShIACikIQA/BsBCIBMJCEA/5a6Olb0Ew29590+qVlU/SdzP6u9r69fVONfv69jm0/zyf5jm1/KYetFVSQhADmKfrRc8+Da3pPZUjV8Mvez2vv6+kVt+Of6g3xBb76GG9rIk3Y2X6UvhUpIQviPSl0nOq+oMfgwJmT2ydzPau/r6xfV+NevWtQgNp8PX1//gzSL2vxLoRKSkHTJvYgwJJaik/XtSecFsFZ+U18/3sHHi2+O4OHXN/Jk6ru39EG5z7v9+mSjSkhC4JQCAKCre4cMkhAAAND19NNPb9y48brrrnNdEGNIQgAAdFMbEx4+8YlPXHjhhe+8887y5cuNv7kTJCFAnO4NbgNoz7XXXpt98pZbbumFoZ///OeTJ0+2XySzSEKALMQgoNuM7+ArVqzIff5Xv/rVkiVLzj77bLMfZx9JCOi+0p6RZYMAivzlL39J/u/evXs/+9nPzpo165FHHjnzzDNdlcqgdBKKzxfpGQFR2OUB5ErFnZdeemn+/PmPPfbY3LlzHZXIMMaEAACArkMPPfT5558fHBx0XRBjcpIQw0JAlzArSDLJW1/yd2/V/PnzXRfBMMaEckiOgJK/e/do3u8/9XoaQGckG4Cozar52ylAH0nofyT/7oTk744UGkD3SN6gkr87NJGEDiJ5gbHk744UwhC6gWYMHSQhoJt0cm3qFzpTf85RJGic2ACaSELIwXyR0HEUlIxZMkAlJKF89B0RowJA+NiFgVIkoXyEAHQPTVoatrhAjAfXQBLC/8T9JvtSuIq2neKgWLTdOR8AIAFJKI0bS6J7ardk9oLgcBojuQYkf/cmSEJQ4UAYkJY6QdpAQMTeSjFGDaCG/CQkfFxE+NdPoRJAGwgO24sagD7GhICwlQ4FFR0SOFQAQKRIQoyLSKa44R7CkrvzKrIRGz1cbDtqAPUwJgTgf4rCEGdEAWFLUQOohCSEQowLhsXUSB5hKETxJhO7jagB1EYSghaOgn7K3gGo7Y+jGQDoGJJQCeG/wJUcHuAo6JvUguFsDKq9vRQThjjz9g2TY4CGVElI8sWR1JFAYA3ECEN+ahKDauT77EfQGOAP4mBEJTTAmFAh1k/FUmEoYjzAtdKLYjobqFKUYeZQEGRuDu6mmNo9WQRaVUkSkjwsBAXag0PtXRTTwXCpVwgBSdRARCXUwpiQLnr8FCrECctTpPuyg4LZMtAYLMsOA7gqCfxBM6iHJFSCWTJ9uT9XLrlCnCgdDTIo2/LVn05jsIkYFOMyEJqrkITE9nRcc4UPNK+DGNxJS9MPnJPZJ+eiKlBbeRJiUARJTCS3rNI0IJu7Z3aYkP7BDm5kEKMqYITWmBBhCHBCEYMsT5TWRP/QNk5CkNJqk1i+fPmPf/zjffv2JZ88/PDDd+zY0d6H2qd7dYyB8T46+hQqpD2VYpDlwii2O02iDX4GXzjX9uLBH/7wh8PDwwsXLvziF7/Ye/89e/YMDQ0tWrTI+Ae5xYxpLYyKpVAhbVN0cDZjkPpm0/2CZS+Y0iTaRvVGDI8drL0msW3btqOOOiqaqPBp06bNmzdvzpw5LX2WKyQhXRz7U6iQ9tSIQe3Vv2JmmHpkqO2CSZBb7VRpxI2UJtjZy4aHh/tJqG9sbIwkJBrH/hQqpA1exaDUR+TeTKhoZCj1AhhBZUbEILviMaG+XhKaPXu2w/K0gSRUDfOlUqgQszRjULLanRwJ2O5OcNSPiEH/Za0HSI0JTZ069c4772z1E+2rkIT45Q3kSjaM+BmnJQpP6XxYRQz69Kc//cILLxS98+c///nf/e53psqZ3dbx4+TIUKrM3IS6Bu6dmIsYlKU+J2k+1/79998fHBysWqqw1BwTIgxBgebRUKU7Bs2ZM+e4444rev3MmTONFUupdKPTKvQx3laKtmTHyMjIlClTJk2a1P/fG2644Z577nFbpDZUS0IMiSdxphvL/e2FiMpR0pz0U7rHrVq1yliZNOisJitCGNLBgnlUUum4XLUtDQ8PH3nkkfH/bty4sdKfh6LymBDXyFLNTmw9pOROmKVyqtKJQc7PRhS/wpHc4kVXymgSClz9UXDe8v1hrSqS06XHxsa2bt1q53MtY8Z0HamjPp27ApOHYqWdV9UY1LBKm/y5ZhgqekHzAnQM40ClyIgxm1UxPDz84osvxlfHzj///FY/zpU6SYhhoT7WkGflDgPE/yu5ihQxKLdainKG+q80tb0hSsOQ4mUCEYNKEYNyJcdfdUaJalRdLwldffXVDzzwQP/xsmXLqr5DEBgTaoSJUwpFk4fif7VeImcaxiDNv3JF/6aL6iYRv8Zs8fxUtUlIJrbfyGV5SDV5daz30cnl9F1CEkKL4n1V8g33mvTj2dlX/lRaNtboXDVWNAnFX3UMd46uhyqyL3kzIZJQIQndliaqQiF38Kyr80Vq3wm67YlBxuVGH82rxuo1aMn37xhiEGpT7BqlFyjqtbFt27bNmDGj/3hwcPD222+v8Sb+q5mEmCIToyo0CRkfkhODYtldQD8MJf+32w2jL4gN6hWmH8ScVMXw8PC8efPsf65l9ceEmCIToyqgVu+YN37wvaSNlsiw3Ctl7BQKnm9QDwmvMVcZOvVTGz3f//73b7nlFmsFsKPR1TEWkcWSVRE/47RE/sodCQj0XLn2CFDR++QuvjNeIZbve6n5caUNI/dlfmrjOoVAdKd9mt2j4vSjdgWmfn41mshG9d7KZ8yYbgvpsDZpVefq9omW69nUx0lrHmIxpphlv+Vnx4RIQjkYFopxOaAe9WTq1CutlCit6matVM7cs71AR8j6FF1BpV5CZ0p19k8039ygVpuHTLlrEuFEakxo165do6OjDsvTEpNjQoSh7Jpn6FDcjzHJSQPT3Jr1CtalGJQ7bzr+13qrCrKvVG8O+y2ktHkEtAU9QQxqIvf8oUkdxmNCBw4c2L59++OPPz5nzpxGRfSSgSTE4qkilmdjdIN6aM3PlGkqBoV+DFB0Bal/ip9s8hG5vGohwW1B5wI9DWiVq8lSr7/++uWXX753797DDjss+fwdd9xhsxh2mBkTIgwlpTprKqSq3Opye4Rrac6y4s0DbTOaYSj3Bfofkfu8wxYS6MbyDTHIK/PmzfvHP/7huhSWGLs6RhhKyr3jnNMSBc/hlUdT205/8lPQrcVCGCr9XJuC3lg+CHR5oB01BoRSOwKVqcPkPCGmDKeQDo0Ltw5LY1CX9h11GIqfz31Bw8818j5wiI0Y61Kf4DnDq+hZSpZCOkSRoh2kGztO6WkAuwayutH4jaNa2sb9hFpHOkTpEHcn7yCnPybKroGoW42/OSMLC6hSTeaTEAd+BepEoNKRjw4PjRCGoNbhxt8E1WIZY0I2mFpCjIBozgPt/NxG/cbPWaw0nW/89VAt9rWShBgWymp11Qx8QwxKKmr8uTeTZL8QQkjjr8pUtVCllbQ+JsR5Xiz3eBBROZ1DDMpSnwlk7zqRfB6doX8jCYFCv7Fq0NpKQtxdMBcnwZ2nmW9ExaC+0vXzjJt2GzFIH9ViWYtjQtxdUIHK6ZKqXbwnMcjVR1e99WLyX+2UEMZx+0Q1xkHdav3qGHcXVKByOiDEGOS8pVW69WKMfSRQPrR5QMHG2jFuoaZA5XSP5zHIE6Utn12je4S3+SIMCDlnaRU9q8kUkpUTP+O0RChXY3ojMSiltFvI/hoJHUhw6NbgPwf3E6IvK0UVea7GWAUxSE2/zbN3BIRRvVIkRR/YS0LMiVFgoqj/FH166QZiaxbJ3ndR8XNsLLMPAmvE9JEUPWF1TIgwpMBEUZ816dyJQWr6d9xgmb3nio7rbKNc9Az+sH11jFmQpVIL7Pvo8Z1oMg6UfQd/tqBvt/TUv6mEevQ0+W6wo7Q/Z3Pk8rNnEMvBPCFmT+sovQ0d2tb8EOt5Z+dbi9IcM1aMnpb+LcziQlg9nvcMAvELrL5jFM0T/AaQBZVaO7uGW4zG1UMM8pCbJMSwUCUss7epya//cIrcXKXOIfsC9pS2EYCaIAb5yf2YEGGoBiqtDQ0HGBifMK55O2dPMYsY1AQxyFvOkhDryCphomgbTE32bD6xGklNOgduSNEe+pwmaIc+czkmRBiqhImiZpla8dvkahqKNAxD8R+m/ol9pDYO5LXRRfjP8dUxwlANiomiTI8oZfaWJxwe2qN/00Wdd4hxzxs1VsUbxChaKNzPEyIM1VA0UTT5v9RkltmOiRjUNv2bLireIfnnileyy0TEIKMYCgqI+yQUEYZM0JlIFL/SSolc0py8TAzyn/5NF3XeqjQMJT9UDgv7iyhkoOB4kYQiwpAJpROJ4n/tdvVaOK8lBlnW/EpZ/D65z0seUuUKjlnEoBD5koQiwpA5+ue+yT9ps0QtqrR23cjXJAY5kb1Slvwns28elbWrELc7Az8W0DkEyqMkFJk784PmuW/y+RCr2vLydc723EpdKYsZab2aQ6oGP9EmJgBZQAwKl19JKDIxRxIKpevOQqlt+7fwIQZ5IjcPGewoBP6IB43ZLOozON4loShvjmRE2zJHve7MhyH0qsehttsGGchD2SEcs2FI8a+pH/So/T6m6O8vNN32iJ1u3w0+JqE+BoesKbrooNDe5rA/70eNGOQ5ny+pWyiPtOErD7EJOsDfJBQZXUCLUlUvCjjf/y3HoO61vc58o9zJ1O19u+D2lL7ObG5/dGnpiXBeJ6E+1pRZo1m3Fnp2H7Zyh2NQx75OlDeu2Wpf4c+e0te9Deo/Rou7JIAkFBGGPNP2lFK325fzvHD5NopcaT1aw4+ATR0+TZIpjCQU+T0bQKBOVn7u4aqT37TbPDxx8qEMMIUY1D3BJKGIOdRoEzGoSwSuhIcdxKBOCikJRSywRwu43t9JcRjilAmmEIO6KrAk1MfgEEwhBknAKRMaoqPotiCTUOTf1EiESOwZnpBkoPipskjA14cRLKGQINQk1Ofh1EgEgYNiJGOXUdw1VMLXR0N0FEKEnYSivDVlqX+1XiL4yP7vlMEfRavZCUNQEDtmLFDwSSgq+1VRWrBwZCDEcn+tLKIl4GAMBUnThSQUEYaQhwyEIkwhQha30hCrI0koUv7EOmFIII5tUGMKEZKYXCFZd5JQFrelRsRGh5JiClFE4xGJjS5Ql5NQxJ2HpIo3OpsbmnIjET1G5zF4jKjzSSjizkPy8DMLaIIeQwg6CsS6n4T6uPNQVzEtGm3g9hxdRY+BLClJKGLaUOeoT+nYuGiIFandQ6hFLkFJKGLpbPh0BrTZjjCFMNQl3CkRRWQloahs6WzEHuKrogMS2wutUt+eI/cF8A0nvVATl4T6ipbORpw3eIaL+vANQ8s+Kx02ZgMhS2gSiiX3iqJUxJ7jChf14SeGlv3E3EHUIz0JJRX1btycxhougSEgpXko9/UwSHMlPDUPNZJQmmKUiDmSrSIGWUbFGpGqRsWxmQ7ELHoMmEISUuGXq62hU7OJWm2PYqAIFtC2UQNJSItijiQ7nibGsSFH0YozplfXxskS2kMS0qWeRcTeqEYMArLoPXQwwIa2kYSqKbrTGou9U2p0XjIrCkKob9Ko+KvWSuQv/d5DZv3AOJJQZfoTJJMvkLPH0q0DuRQ3aSxC7xGTUwmwjyTUlOYEydD38OYD1EF8TcAmxS1ek0LvPaJmHUgo3xHhIgmZodhXdUKS57s6l7o6RtpIg/+KtkU3Bo2qdiCefx10D0modTqDRkF0Zzo68BXk8D+CQ3/QyM9NSQZCEEhCluic83m+RIJOCnCltAPxvPeI6EDgMZKQY9yHDUBtiiVp/iADwXMkIS/4353RlwF+8vxsiq4D/iMJ+YL+AkBtdCBAbSQhAAAgF0kIAADIRRICAABykYQAAIBcJCEAACAXSQgAAMhFEgIAAHKRhAAAgFwkIQAAIBdJCAAAyEUSAoTi9xkAICIJAQKRgQAgRhICAABykYQAAIBcJCEAACAXSQgAAMhFEgIAAHKRhABxBgYGIlaQAcAEkhAgVC8PEYYAgCQEAADkIgkBAAC5SEIAAEAukhAAAJCLJAQAAOQiCQEAALlIQgAAQC6SEAAAkIskBAAA5CIJAQAAuUhCAABALpIQAACQiyQEAADkIgkBAAC5SEKAUOPj466LAADukYQAcchAABAjCQEAALlIQgAAQC6SEAAAkIskBAAA5CIJAQAAuUhCgDgDAwMRK8gAYAJJCBCql4cIQwBAEgIAAHKRhAAAgFwkIQAAIBdJCAAAyEUSAgAAcpGEAACAXCQhAAAgF0kIAADIRRIChOK2igAQkYQAgchAABAjCQEAALlIQgAAQC6SEAAAkIskBAAA5CIJAQAAuUhCAABALpIQAACQiyQEAADkIgkBAAC5SEIAAEAukhAAAJCLJAQAAOQiCQEAALlIQgAAQC6SEAAAkIskBAAA5CIJAQAAuUhCAABALpIQAACQiyQEAADkIgkBAAC5SEIAAEAukhAAAJCLJAQAAOQiCQEAALlIQgAAQC6SEAAAkIskBAAA5CIJAQAAuUhCAABALpIQAACQiyQEAADkIgkBAAC5SEIAAEAukhAAAJCLJAQAAOQiCQEAALlIQgAAQC6SEAAAkIskBAAA5Pp/LQ3tuEC+Qj8AAAAASUVORK5CYII=)
4. Поле точечного заряда, расположенного над идеально проводящей плоскостью. Рассмотрим влияние точечного заряда на проводящую плоскость. В результате электростатической индукции на границе должен появиться некий заряд, создающий дополнительное поле, которое, налагаясь на первоначальное поле источника, приведет к удовлетворению граничных условий. Задача определения поля точечного заряда, расположенного над проводящей плоскостью, эквивалентна задаче определения поля двух зарядов: заданного q и некоторого фиктивного заряда (-q), являющегося зеркальным изображением первого, находящихся в неограниченном диэлектрике.
![](data:image/png;base64,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) Поле в верхнем полупространстве удовлетворяет граничному условию Е = 0, граница раздела – эквипотенциальная поверхность. Плоскость АВ, расположенная симметрично относительно зарядов, - эквипотенциальная поверхность с нулевым потенциалом, в точках этой плоскости вектор |