关键词: 导体球, 镜像法, 电荷分布, 电荷量, 面电荷密度

Abstract: In this paper, the charge distribution of two charged conductor spheres at equal potential is solved by multiple image method. We mainly focus on the charge quantity distribution and the average surface charge density distribution as function of the radius and spacing of the two spheres. By choosing suitable coordinates, this paper gives the general formula of n-order mirror charge’s charge quantity and position, and the analytical expression of total charge quantity, when two conductor spheres are in contact. It is found that when two conductor spheres are in direct contact, the charge of the two spheres can be solved strictly, and the expression of the ratio of charge of the two spheres is given. As the distance between two equally potential conductor spheres increases, the ratio of the charges tends to the ratio of the radius. Considering the limiting case where the radius of one of the conductor spheres tends to 0, we find that the charge ratio of the small sphere to the large sphere tends to 0, and the ratio of the average surface charge density tends to infinity when the two spheres are not in direct contact, but tends to π2/6 when the two spheres are in direct contact.

Key words: conductor sphere, image method, charge distribution, charge quantity, surface charge density