均匀带电球体激发电场分布解的修正分析

Correction Analysis of the Electric Field Excited by Uniformly Charged Sphere

均匀带电球体的电场分布是基本且重要的静电场模型之一。文章从已有常见的均匀带电球体的电场分布结果与界面两侧法向电场的矛盾出发,理论推导了均匀带电球体激发的静电场的修正表达,分析了均匀带电球体的电荷组成,给出了均匀带电球体激发电场的基本物理模型,并对其进行了物理解释。研究表明,均匀带电球体为介质球,其内的电荷包括自由电荷、体极化电荷和面极化电荷,其中体极化电荷和面极化电荷等量异号。均匀带电球体的电场为三种电荷单独存在时激发电场的叠加。采用介质中的高斯定理或考虑极化电荷的真空中的高斯定理,求出的均匀带电球体的法向电场在球面界面两侧满足界面两侧电场的不连续特征。

The electric field distribution of uniformly charged sphere is one of the basic electrostatic field models.In this manuscript,based on the contradiction between the electric field of uniformly charged sphere solved by Gauss’s theorem in a vacuum and the normal electric field on both sides of the interface,the modified expression of the electric field excited by uniformly charged sphere is theoretically derived.The charge composition of uniformly charged spheres is analyzed and the excited electric field is explained physically.The results show that the uniformly charged sphere is a dielectric sphere,and it contains free charge,volume polarized charge and surface polarized charge.The charge is equal but the sign is opposite among the volume polarized charge and surface polarized charge.The electric field of a uniformly charged sphere is the superposition of the excited electric field when the three types charge exist separately.The normal electric field of the uniformly charged sphere is discontinuous on both sides of the spherical interface by using Gauss’s theorem in dielectric or Gauss’s theorem in vacuum considering polarized charge.