Urgent: Help Needed on Ampere's Law Probolem (Totally Lost)

AI Thread Summary
To solve the problem involving two long parallel cylinders with a steady current, Ampere's Law can be applied to demonstrate that the magnetic field around the inner cylinder remains constant. The magnetic field intensity, H, can be expressed as H = μ₀I/(2πR), where R is the distance from the center of the cylinder. Since the current is steady, the magnetic field does not vary with time, confirming its constancy. The hint provided suggests that the contributions to the magnetic field from both cylinders can be balanced, leading to a net effect of zero at certain points. Understanding these principles is crucial for accurately applying Ampere's Law in this context.
Merrank
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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
 

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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} ?
 
And btw try not to double post :D
 
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