Inside a long straight uniform 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 l. A direct current of density j flows along the wire. Find the magnetic induction inside the cavity. Consider, in particular, the case `l=0`.

Explanation

Consider a cross section of the cylinder perpendicular to its
axis. The cylindrical cavity is shown at a distance l from O the
axis point of the cylinder. Let us calculate the megnetic field at
pointP inside the cavity. The cavity means an absence of current
which is equilivalent to an opposite current density j in the cavity
plus the true current through the cross section of the wire.
By superposition theoram
`vecB_P=1/2 mu_0hatjxx(vec(OP)-vec(CP))=1/2 mu_0hatjxxhatl`
It is a uniform field.
In case l vanishes, point C coincides with the point O, then there
is no magnetic field in the cavity.