(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We are given an infinitely long cylinder of radius b with an empty cylinder (not coaxial) cut out of it, of radius a. The system carries a steady current (direction along the cylinders) of size I. I am trying to find the magnetic field at a point in the hollow. I am told that the answer is that the magnetic field is uniform throughout the cavity. and is proportional to [itex]d\over b^2-a^2[/itex] where [itex]d[/itex] is the distance between the centers of the cylinders.

3. The attempt at a solution

I have found by using Ampere's law that the magnetic field at a point at distance r from the axis in a cylinder of radius R carrying a steady current, I, is given by [itex]\mu_0 I r\over 2\pi R^2[/itex]. So I thought I would use superposition. But what I get is [itex]{\mu_0 I \sqrt{(x-d)^2+y^2}\over 2\pi b^2}-{\mu_0 I \sqrt{(x)^2+y^2}\over 2\pi a^2}[/itex]. However this is not the given answer!

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# Magnetic field in a cavity

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