偏心球形电容器电容的理论分析与应用探讨  

Theoretic analysis and application of the eccentricspherical capacitor's capacitance

作　　者：康东[1] 

机构地区：[1]成都理工大学应用核技术与自动化工程学院,四川成都610059

出　　处：《西安科技大学学报》2004年第3期365-368,共4页Journal of Xi’an University of Science and Technology

摘　　要：在对偏心球形电容器的电容进行理论计算时,现有的文献大都采用在球坐标系下分离拉普拉斯方程并且假定其偏心率较小采用一阶近似得到了偏心球形电容器电容的近似解。这些计算的局限是它们只能用于小偏心率的情况,当偏心率增加时,就会带来极大的误差甚至是错误。为此本文通过在双球坐标系下分离拉普拉斯方程的方法经推导严格求解了偏心球形电容器的电容,得到了它的级数解,并通过编制程序对级数解进行计算获得了偏心球形电容器的电容大小与偏心率之间的数值关系,发现偏心球形电容器电容大小是随偏心率的增加而增加的,但是在偏心率很小的情况下电容的改变量相当小,可近似认为不发生变化,最后对这种电容器应用的前景进行了探讨。When it comes to the issue of computing the eccentric spherical capacitor's capacitance, the current articles are mostly based on spherical coordinate system to separate Laplace equation,and suppose the eccentriccity is small to get its solution.The weakness of these calculations is that they can only be used for the small eccentriccity, but when the eccentriccity increases, they will bring the tremendous error margin and mistakes. So we based on the bispherical coordinate system and strict derivation to get the series solution of the eccentric spherical capacitor's capacitance and through making programe to compute to get the numerical relation between the capacitance and the eccentrity,discovering that the eccentric spherical capacitor's capacitance increases with the increases of the eccentriccity but when the eccentriccity is small this changes very small, pionted out the mistakes in some related articles and also discussed the application of the eccentric spherical capacitor.

关 键 词：球形电容器 偏心率 电势分布 双球坐标系 

分 类 号：TM53[电气工程—电器]