Inside a long staight unifrom wire 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 1. A direct current of density `j` flows along the wire. Find the magnedtic induction inside the cavity. Consider, in particular , the case `l= 0`.

Explanation

We can think of the given current which will be assumed uniform, as arsining due to a negative current, flowing in the cavity, superimposed on the true current, everywhere including the cavity. Then from the problem by superposition.
`vec(B) = (1)/(2) mu_(0) vec(j) xx (A vec(P) - B vec(P)) = (1)/(2) mu_(0) vec(j) xx vec(l)`
if `vec(l)` vanishes so that the cavity is concentric with the conductor, there is no magnetic field in the cavity.