Magnetic field between non-coaxial cylinders with Ampere's law

[Merrank]

The question is:

Between two long parallel cylinders of radius "a" and "b" (non-coaxial) and an axal separation of "c", a steady current of "I" flows. (See attachment below) Show that the inner cylinder (radius "a") has a constant magnetic field. Use Ampere's Law. [Hint: 0 = 1 + (-1)]

Could someone please show me step by step how to do this, I am completely lost.

Thank You

 

[Theelectricchild]

This is interesting, I would suspect the simple fact that i(t) is constant would tell us that H(x,y,z,t) is also constant... wouldn't this fact come from using amperes law to show that the H field around the wire is simply

$$H=\frac{\mu_0i(t)}{2{\pi}R}$$ ?

 

[Theelectricchild]

And btw try not to double post :D