1. The problem statement, all variables and given/known data Two concentric metal shells of radius a and b respectively ( a < b) are separated by weakly conducting material of varying conductivity σ(r) = kr where k is a constant and r is the distance from the common center. If the metal shells are maintained at a constant potential difference V and a steady current flows between the shells, what is the value of this current? 2. Relevant equations J=σE I = ∫J da 3. The attempt at a solution I = ∫σE da Since the current is the same everywhere I set up a guassian surface inbetween the two shells. Here sigma is constant since r does not vary so I pulled it out of the integral. Now the integral is gausses law and can be replaced with q/ε I = σq/ε The final step is putting q in terms of the potential difference. That's easy enough however this seems to show that the current is dependent on sigma which is dependent on the distance from the center. The problem specifically says steady current. Where did I go wrong?