Ampere's Law with an open cylindrical shell

[gsquare567]

Homework Statement

A long, hollow conducting pipe of radius R and length L carries a uniform current I flowing around the pipe. Find expressions for the magnetic field (a) inside and (b) outside the pipe. Hint: What configuration does this pipe resemble?

Homework Equations

Ampere's Law: $$\oint$$B dr = $$\mu$$ Iencircled
(mu is the permeability constant, and the integral is over the dot product of B and dr)

The Attempt at a Solution

I am looking at the open cylindrical shell from an open end, having current going counter-clockwise.

(a) For r < R, Iencircled = 0, and therefore so must be the magnetic field.

(b) This is where I need help (particularly with using the hint given). Since the magnetic field is pointing into the page outside of the shell, my B (dot product) dr will always be 0, because dr is encircling the current, and B is going into the page, which makes the angle between them 90, and cos90 = 0. However, this cannot be because Iencircled = I.

How can I look at it to rightfully configure this integral? This is also making me question my answer for (a), because there should still be a B field coming out of the page on the inside of the shell, but the current is not inside the closed path =S

Thanks!

 

[kuruman]

Model this as a solenoid with infinitely thin wire wrapped around the cylinder.