偏心球形电容器的近似解

The approximate values about an eccentric spherical capacitor

借鉴近年来利用电磁场能量在求解不同电磁问题的研究,结合最小作用原理,构造一个满足偏心球形电容边界条件的势函数,求得形式上的电场和电场能量,经求极值获得该场能的极小值。根据最小作用原理,在各种可能的能量中,真实能量应为最小值,因此所求的这个极小值与真实场能的近似值相对应,这样得到电容的近似解。在偏心距为一级小量,内、外半径a∶b比1∶1.5条件下,近似解与所求理论值相对误差不超过0.3%。不失一种方法,对任何形状的电容,都能构件一个近似场,调节参数,获得最小值,得到近似解。

Based on the recent reports on applying electromagnetic energy to the solution of various electromagnetic problems as well as the principle of least action, a potential function that satisfies the boundary conditions of an eccentric spherical capacitor is formed to obtain the formal electromagnetic field and its energy and the minimum values of such a field. According to the principle of least action, the approximate value of the capacitor can be obtained since of all the possible energies, the real energy should be the minimum value that corresponds to the approximate value of the electromagnetic field. When the eccentric distance is first order and the ratio of the radii is 1:1.5, the result is satisfactory with the relative error between the approximate value and the real value being no more than 3%. As a method for calculating capacitors of all shapes, an approximate field with some unknown parameters can be formed and adjusted to get a minimum value as well as the approximate value. 