Electric Potential within coaxial cylinder

[electrifice]

Homework Statement

A long metal cylinder with radius a is supported on an insulating stand on the axis of a long, hollow metal tube with radius b. Thew positive charge per unit length on the inner cylinder is $$\lambda$$, and there is an equal negative charge per unit length on the outer cylinder. Calculate the potential for r < a; a < r < b; r > b.

Homework Equations

EA=q/epsilon
Va - Vb = $$\int$$E.dl

The Attempt at a Solution

I really just need help figuring out why the answer for when r < a is:
[(lambda)/(2(pi)(epsilon))]*[ln(b/a)]
The reference point here is b. If we are looking for the potential INSIDE the smaller cylinder with radius a, then why are we only integrating from b to a? Shouldn't it be from b to 0? Or is the potential inside the smaller cylinder constant? Why would that be?

 

[blochwave]

Or is the potential inside the smaller cylinder constant? Why would that be?

Well what IS the potential inside a hollow conductor at equilibrium? The electric field is zero, right? so...

 

[electrifice]

The smaller cylinder is not hollow and I don't think its a conductor (and its supported on an insulating stand anyway)... unless being "metal" is synonymous with conductor? E inside a conductor is 0, but I don't think the smaller cylinder is a conductor.