# A charged solid spherical conductor with a charged solid spherical shell

A solid spherical conductor has charge + Q and radius R. It is surrounded by a solid spherical shell with charge − Q, inner radius 2R, and outer radius 3R. The objects are isolated in space and the electric potential is zero as the distance from the spheres approaches infinity. Point A is at the center of the inner sphere, Point B is located at R, Point C is located at 2R and point D is located at 3R. All distances are from the center of the inner sphere.
Where is the electric potential maximum?
Where is the electric field maximum?

###### Solution.

The electric field in the interior of conductors is zero. The charge of +Q is on the surface of radius R and all of the charge –Q of the solid spherical shell is on the inner surface of radius 2R. There is no electric field from 2R to infinity and from 0 to R. Hence, the electric field only exists between R and 2R with the field strongest at B.

EB = kQ/R2 + kQ/R2 = 2kQ/R2.

The electric potential is zero at all points from infinity to C, at which point the magnitude increases up to point B. From zero to R, there is no electric field and hence no change in potential.

VB = kQ/R – kQ/2R

Thus, the electric potential and electric field achieve a maximum magnitude at point B.