A long straight metal rod has a very long hole of radius 'a' drilled parallel to the rod axis as shown in the fiugre. If the rod carries a current I, find the value of magnetic induction on the axis of the hole, where OC=c

Explanation

In the rod current density `j = (i)/(pi(b^2 - a^2))`
On the hole axis, only the larger rod contributes magnetic field. Imagine an amperean loop of radius c and apply Ampere.s law.
`B_("Total") = underset(underset("solid")"complete")(vec(B_1)) + underset("cavity")(vec(B_2)) = (mu_0 j pi c^2)/(2 pi c) + O`
` = (mu_0 ic)/(2pi(b^2-a^2)) = (mu_0)/(2pi) (ic)/((b^2 - a^2))`