On the Interaction Force between a Point Charge and a Charged Conducting Sphere

• 1、Xiamen University Tan Kah Kee College, Zhangzhou 363123, China
• 2、Key Laboratory of Intelligent Manufacturing Equipment and Industrial Internet Technology, Fujian Provincial Department of Education, Zhangzhou 363123, China

Abstract：This paper investigates the electrostatic interaction between a point charge and a charged conducting sphere using the image charge method. The polarization effect on the conductor surface is equivalently represented by two image charges inside the sphere, whose positions and magnitudes are analytically derived. The explicit expression for the net force on the external point charge is then obtained. The results show that when the point charge and the conducting sphere carry like charges, the system can exhibit a non-monotonic transition from repulsion to attraction as the distance decreases, with the critical condition determined by the charge ratio and a dimensionless distance parameter. When they carry opposite charges, the net force is always attractive, and no repulsion occurs under any parameter settings. In particular, when the two charges are equal in magnitude, the ratio of the sphere radius to the distance from the sphere center to the point charge at the zero force equilibrium position is exactly the golden ratio. These findings correct the common misconception that "like-charge attraction implies opposite-charge repulsion" found in some previous literature.

Keywords： Method of image charge Like-charge attraction Coulomb\'s law Charged conducting sphere