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Question

Inside a long straight uniform with of round cross-section there is a long round cylindrical cavity whose axis is parallel to the axis of the wire and displaced from the latter by a distance l. A direct current of density j flows along the wire. Find the magnetic induction inside the cavity. Consider, in particular, the case I=0.

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Solution

We can think of the given current which will be assumed uniform, as arising due to a negative current, flowing in the cavity, superimposed on the true current, everywhere including the cavity. Then, by superposition,
B=12μ0j×(APBP)=12μ0j×l
If l vanishes so that the cavity is concentric with the conductor, there is no magnetic field in the cavity.

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