Magnetic Field Intensity Question

[sillucius]

This is for an assignment that is due next Monday for me. I'm kind of confused here for how to calculate the magnetic field intensity at all points for the conductor(s) in the diagram I have attached. First, there is a cylindrical conductor of radius a, then surrounding it is another conductor from radius b to c. They call this the outer shell. The question also states that there is a current, I, flowing in the inner conductor and outter conductor but in opposite directions. I have an idea for how to do this, but there are still a lot of things I can't figure out.

Firstly, how does the current effect each region? In the regions where there is only a conductor (ρ > a and b < ρ < c), do I only consider the current by the one conductor? For example, would the conductor of radius a's current affect the magnetic field intensity where ρ is in the conductor between radius b and c? And oppositely, would the current of the outter shell's conductor effect the magnetic field intensity of the inner conductor?

Also, for the region where a < ρ < b, where it's free space, do both conductors affect the magnetic field intensity in this region? Or just the inner conductor?

And on the outside, where ρ > c, would the magnetic field intensity be 0? I'm guessing because because I think the net current be 0 since the current are in equal but in opposite directions in the conductors, however I am not too confident in my answer.

I know this is quite lengthy, but the book I am using doesn't offer much insight into this question. Any help would be greatly appreciated, thanks.

 

[jdavel]

sillucius,

Think about electric current, the magnetic filed it creates, and the line integral of that magnetic field around a closed loop.

Does that help?

 

[sillucius]

Oh, I know how to do the calculations themselves and derive the equations for Magnetic Field Intensity. It's just that I don't know exactly how the current will affect each region. Like in between region a < ρ < b, does the current from both conductors affect it, or just one?

 

[jdavel]

sillucius,

What does the principle of superposition say about the field from two sources?

 

[Burrito]

i believe at a< p <b you would only consider the inside current, since for everything we seem to use the current enclosed. so i would also guess at p>c the net current enclosed would be 0. I'm just not sure what to do to get the current enclosed...