Capacitance and Other Traits of a Coaxial Cylinder

[plot]

This is for an electromagnetic theory class.

Homework Statement

Prompt can be seen here

Homework Equations

J = I/A, J = σE, V = Ed, C = εA/d

The Attempt at a Solution

I'm having trouble mostly with parts i and ii, as the rest are fairly simple to acquire after figuring out those two. Here's what I have so far:

A = (b-a)L
J = I/((b-a)L)
dE = (I/((b-a)L))d∅ (Here I'm honestly not sure what to integrate with, however my best guess is d∅, so after integrating nothing changes)
E = V/d
I = (Vσ(b-a)L)/((π/2)r)

At this point I'm not sure if that is the total current, or just a segment of current that needs to be integrated. Hence I don't know what to do with r.

Any help would be greatly appreciated.

 

[K^2]

Current density in steady state is just J=σE, and you should have no trouble computing E based on the fact that E=-∇V and the form they give you. Note that this part of the problem doesn't depend on ε at all. It's only when you get to surface charges that it will matter.