B field inside conductor with assymetric cavity

[Gauss M.D.]

Homework Statement

Infinite straight conductor, parallel with z axis, of radius R1 with a cylindrical cavity of radius R2. The axis of the cavity passes through the point <0,b,0>. A current I flows through the conductor. The current density is homogenous inside the cundoctor. Find the direction and magnitude of the B-field inside the cavity.

Homework Equations

The Attempt at a Solution

I think we're supposed to use

$\oint \textbf{B} \cdot \textbf{dl} = \mu _0 I$

Where we first do the outer line integral, and then subtract the inner line integral.

1) Am I on to something?
2) How do I do the inner line integral in the most convenient way?

 

[Simon Bridge]

See discussion:
https://www.physicsforums.com/showthread.php?t=278045