A solid conducting sphere of radius $$a$$ and charge $$Q is concentric with a spherical

conducting shell of inner radius $$b$$ and outer radius $$c$.$ The net charge on the shell is

$+3$Q$.$ Take the zero of electric potential to be at some point at infinity. $(25$ pts$)$

a$)$ Use Gauss$$s Law to find the charge on the inner and outer surface of the shell.

b$)$ Use the superposition principle for potential to find the potential at all points in

space.

c$)$ Using the results of part $($b$)$ find the electric field at all points in space.

d$)$ Find the potential difference between the surface of the sphere and the inner

surface of the shell. Which point is at a higher potential?

e$)$ Find the work required to move a $+$q charge from the surface of the sphere to the

surface of the outer shell.

f$)$ If a charge $+$q is released from rest at the inner surface of the shell, how fast will

it be moving when it reaches the surface of the central sphere?

g$)$ Draw the graph of V vs$.$ r and E vs$.$ r