Consider a solid conducting sphere inside a hollow conducting sphere, with radii and char...

Consider a solid conducting sphere inside a hollow conducting sphere, with radii and charges specified Take V = 0 as r → ∞. Use the electric field calculated in Problem to calculate the potential V at the following values of r.  (a) r = c (at the outer surface of the hollow sphere): (b) r = b (at the inner surface of the hollow sphere): (c) r = a (at the surface of the solid sphere): (d) r = 0 (at the center of the solid sphere).

Problem:

A Sphere in a Sphere. A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net charge. (a) Derive expressions for the electric field magnitude in terms of the distance r from the center for the regions r < a, a < r < b, b < r < c, and r > c. (b) Graph the magnitude of the electric field as a function of r from r = 0 to r = 2c. (c) What is the charge on the inner surface of the hollow sphere? (d) On the outer surface? (e) Represent the charge of the small sphere by four plus signs. Sketch the field lines of the system within a spherical volume of radius 2c.