Consider two concentric spherical metal shells with radii a and b (a < b). The space between the shells is filled with (weakly conducting) material with conductivity σ. This "spherical resistor" is part of a circuit with the current I flowing through it. 

(a) Consider carefully the symmetries of the system.

(b) Find J and E everywhere between the shells. 

(c) Find the potential difference V between the shells, and the resistivity R of this resistor. 

(d) Is there any net charge between the shells?