Charge Simulation Method

Abstract

According to the uniqueness theorem of electromagnetic fields, if a solution satisfies Laplace’s equation or Poissons equation and all the corresponding boundary conditions, no matter how that solution is obtained — even if guessed — it is the only solution of the specified boundary value problem. For example, the field distribution of an isolated charged spherical conductor equals the field distribution of a point charge if it is located at the centre of the sphere and its charge equals the total amount of surface charge of the sphere. This point charge is called the equivalent charge or simulated charge of the original charged conductor. Thus the distributed charge on the conductor surface is replaced by a lumped fictitious point charge. It should be noted that the region of interest is now the region outside the sphere. In other words, the fictitious simulated charges must be placed outside the space in which the field is under consideration.