The Method of Images applied to the grounded sphere: The problem of the ground wire

The Method of Images poses an important difficulty when used to solve the problem of a charge in the presence of a grounded conducting sphere. This arises from the fact that the sum of the inducing charge and the image charge is different from zero. As a consequence, there is a monopole field far from the system, and any ground wire physically connected to the sphere will carry an electric current, changing the initial balance of charges until a new equilibrium is reached. The approach taken in this paper assumed an infinite straight wire connecting the sphere to ground. The charge distribution over the surface of the conductors was calculated, and the results analyzed. It was shown that the thinner the wire, the lower will be its total charge, and the closer will be the calculated charge density at the surface of the sphere to the conventional solution by the Method of Images.

► Method of images applied to a grounded sphere leads to a current in the ground wire.
► Two different methods were used to obtain the charge density on the ground wire.
► We show that even very thin wires can change significantly the charge on the sphere.
► The validity of the Method of Images is dependent on ground wire thickness.
► We show that, when the wire is thin, its charge approaches zero.