Calculating Magnetic Fields in Cylinders w/ Currents

[Jimmy84]

Homework Statement

Consider two infinitely long cylinders with radius a and b and currents:

J =

(Jo r)/a for r less than a

-Jo for a less than r less than b
Find the magnetic field in

1) r less than a

2) a less than r less than b

3) r greater than b

Homework Equations

The Attempt at a Solution

I think I was able to compute the magnetic field for r less than a

using Ampere's law

H 2 pi r = (the integral from 0 to a of) (Jo r) /a 2 pi r dr the result that I found for H was H = (Jo r squared )/3aIn the other cases I am confused about the integration limits and the addition of magnetic fields.
How can I find the magnetic field for a less than r less than b, and for r greater than b ?I would appreciate some help, thanks a lot.

 

[Jimmy84]

Can anyone give me an idea how to solve this please? I ll truly appreciate it.