Conducting Spheres in Electrostatic Fields

The problem of finding the resulting electrostatic potential outside a conducting sphere when the sphere is introduced into a known field is usually attacked by placing suitable image charges and dipoles at specially chosen points within the sphere. Thus, for example, to determine the field due to a point charge e outside an earthed conducting sphere, the standard procedure is to place a point charge é at the corresponding inverse point and to determine é by making the surface potential of the sphere zero. To the student, this method seems very indirect and not very obvious, and it has the additional disadvantage of depending on special geometrical properties of inverse points in a sphere.