A thin spherical shell with radius R₁ = 3.00 cm is concentric with a larger thin spherical shell with radius R₂ = 5.00 cm. Both shells are made of insulating material. The smaller shell has charge q₁ = +6.00 nC distributed uniformly over its surface, and the larger shell has charge q₂ = -9.00 nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells.

(a) What is the electric potential due to the two shells at the following distance from their common center:

(i) r = 0;

(ii) r = 4.00 cm;

(iii) r = 6.00 cm?

(b) What is the magnitude of the potential difference between the surfaces of the two shells? Which shell is at higher potential: the inner shell or the outer shell?