Question

Consider a geometry of concentric spheres: There is a solid conducting sphere having a radius of a, with a charge of –3q applied to it. There is an insulating spherical shell having an inner radius of b and outer radius of c, with a charge of +2q uniformly distributed throughout its volume. There is a conducting spherical shell having an inner radius of c and outer radius of d, with a charge of +q applied to it. The radii are defined according to a < b < c < d, as shown at right, with regions outside of the sphere and shells being free space. You may assume that the permittivity everywhere is ߳epsilon  

(a) Derive expressions for the free surface charge densities on the three conducting surfaces, i.e., at radii of a, c and d. State your expressions as a function of a, b, c, d, q, and ߳epsilon.

Answer 1