均匀带电介质球空间电场及极化电荷分布解析

DISTRIBUTION OF ELECTRIC FIELD AND POLARIZATION CHARGE OF A UNIFORMLY CHARGED DIELECTRIC SPHERE

静电学中导体与电介质在某种程度上具有一定的相似性,比如:它们都可以带电,并且都会受到外电场的影响,并随之产生感应电荷。学生在学习过程中往往没有充分认识到它们之间的差别,容易产生混淆。现有大学物理教材中很少涉及电介质带电的情况,将带自由电荷的电介质放置于外电场中的问题几乎没有讨论过。本文针对这一现状,特别设计了三个问题,讨论了均匀带电的介质球在三种不同情形下空间电场分布的问题,详细给出极化体电荷和极化面电荷的分布,并进一步计算了空间电场能量密度分布以及总能量的大小。

Conductors and dielectrics in electrostatics share some similarities to an extent,for example,they can be both charged,and would be affected by the external electric field following with induced charges.Usually in the learning process,students do not pay enough attention to the differences between them,resulting in great confusion.The issue of charged dielectrics is rarely involved in the existing college physics textbook,and the problem of placing a charged dielectric in the external electric field has hardly been discussed.In view of this situation,three problems are specially designed in this paper.The spatial electric field distribution of a uniformly charged dielectric sphere is discussed in three different cases.The distributions of bulk polarization charge and surface polarization charge are given in detail.Moreover,the energy density distribution and the total energy of spatial electric field are calculated.