a) Consider two point charges q and q'=-uq (0u1), separated by a distance d. Show that the equipotential surface V=0 is a sphere, and find...

a) Consider two point charges q and q'=-uq (0<u<1), separated by a distance d. Show that the equipotential surface V=0 is a sphere, and find expressions for its center and radius in terms of u and d.

b) Now consider a point charge q a distance a from the center of a grounded conducting sphere of radius R (R < a). Use the result from part a to show that the potential outside the conducting sphere can be obtained using the method of images, and find expressions for the charge and location of the image charge in terms of q, a, and R.