System of equations describing charges of multiple conductors immersed in electrostatic fields

Abstract

Problems of electrostatic fields involving multiple conductors arise in various scientific fields. It is known that the relation between the electric potentials and the charges of multiple conductors can be expressed by a system of linear equations. However, the well-known system of equations holds true only when no other charge exists external to the conductors. In this paper, we derive an extended system of equations that is valid even if the conductors are immersed in electrostatic fields due to external charges.