Magnetic Fields: I don't understand cylindrical current systems

[Strawberry]

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This is a really bad picture, but it should kind of give the idea.
How do I deal with a system where a current is running in a cylinder surrounded by a cylindrical shell? I know this sounds like a homework question, and it is related to a few of them, but it's the whole concept of the system I don't really understand. Basically I need to know how to find the magnetic field inside the cylinder, between the cylinder and the shell, in the shell, and outside the shell. Is it basically just a sum of the two independent fields? Also do the fields cancel outside of the shell if the currents are opposite?

 

[Mike Cookson]

So we are talking about a cylinder inside another one of a greater radius, like a piece of coaxial cable?

 

[Meir Achuz]

If the cylinders are much longer than their radii, you can use Ampere's law for the inner current.

 

[KnowPhysics]

Yes, What clem said is correct. using ampere law you can easyly find magnetic field inside and outside the cylinder. Assume your radius of the cylinder is R. then if you want to find the magnetic field outside the cylinder assume its outside radius(distance) is r then the formula is B(magnetic field)=(Permiabilityof the space*Current)/(2*pi*r). if you want to find the magnetic field inside the cylinder assume its inside radius(distance) is r then the formula is B(magnetic field)=(Permiabilityof the space*Current*r)/(2*pi*R*R).