(a) Using the law of cosines, show that Eq. 3.17 can be written as follows where r and θ are the usual spherical polar coordinates, with the z axis along the line through q. In this form it is obvious that V = 0 on the sphere, r = R.

(b) Find the induced surface charge on the sphere, as a function of θ. Integrate this to get the total induced charge. (What should it be?)

(c) Calculate the energy of this configuration.