A conducting sphere of 4.0 cm radius has a cavity of 1.0 cm radius (sharing the same center). The conducting sphere has a total charge of + 15 nC. In addition, a - 12.0 nC point charge is located at the center of the cavity.

a) How much charge is on the inside surface of the cavity? Justify your answer using Gauss' Law, to get any credit

b) How much charge is on the outer surface of the sphere? Justify your answer to get any credit.

c) Calculate and show the direction of the net electric field at 0.5 cm, and at 5.0 cm from the center. Use Gauss Law adapted to spherical symmetry to derive your answers, to get any credit.