静电屏蔽效应的理论与模拟研究

Research on theory and simulation of electrostatic shielding effect

在静电屏蔽效应中,无论金属壳是否接地,壳外电场不影响壳内电场.然而,由于电场的叠加原理,并不能从高斯定理直接得到壳外电场不影响壳内任意位置的电场.本文利用静电场的唯一性定理,以及唯一性定理的证明方法,对静电屏蔽效应进行了严格的证明.此外,利用数值模拟进一步验证了静电屏蔽效应,如外电场改变时,金属壳作为等势体电势发生变化,导致壳内整体电势改变,但壳内任意位置的电场不发生变化.最后,数值计算了接地金属壳在外电场中感应电荷的分布,金属尖端靠近带电体会产生很大的电荷面密度.

For the electrostatic shielding effect,the electric field inside the metal shell is not affected by that outside the shell whether the metal shell is grounded or not.However,it cannot be obtained directly from Gauss theorem that the electric field outside the shell does not affect the electric field at any position inside the shell.In this paper,the electrostatic shielding effect is proved strictly by the uniqueness theorem of electrostatic field.In addition,the electrostatic shielding effect is further verified by numerical simulation.For example,the electric potential of the metal shell changes with the external electric field,which results in the change of the overall electric potential inside the shell while the electric field does not change.Finally,the distribution of the induced charge in the grounded metal shell is numerically calculated,and a large surface density of charge is generated when the metal tip is near the charged objects.