A point charge with a charge of -3Q is placed at the center of a conducting spherical shell. The shell has an inner radius a, an outer radius b, and a net charge of +2Q.

What is the electric field as a function of r?

For r > b, E = kQ/r² and points toward the center

For a < r < b, E = 0

For r < a, E = 3kQ/r², directed toward the center

What is the electric potential as a function of r?

To find the total potential we can simply use superposition. The net potential is the potential from the different pieces, the point charge, the +3Q charge on the inner surface of the conductor, and the -Q on the outer surface of the conductor.