I've been working on some exercises and I'm in doubt if my procedure with this one is correct. We have a hollow cylinder with internal radius $r_a$, external radius $r_b$, resistivity $\rho$ and length $L$. A difference of potential $V$ is then applied on the extremes paralel to the axis of the cylinder.
First I'm asked to find the resitance. Well, for this one I've just used that $R=\rho L/A$ and calculated $A=\pi(r_b^2-r_a^2)$. Second, I'm asked to find the current density when $V$ is applied. Well, what I did was suppose that the cylinder is an ohmic resistor so that $V=Ri$ holds, and then I've got $i=V/R$. Then the current density should be $J=i/A$ and so we have $J=V/RA$ which gives $J=V/\rho L$. Is this correct? Can I assume that the cylinder is ohmic?
Third I'm asked to find the electric field. Now I've used that $\rho = E/J$ so that we must have $E = \rho J$ so that $E = V/L$, this says tha that the field is uniform, but I'm a little unsure about it. Finally the fourth one asks to find the resitance again if now the current flows radially from inside to ouside. In this final case I think that it'll change just the cross sectional area, but I didn't find some easy way to write this down.
Can someone give a little help with this?