A long straight metal rod has a very long hole of radius \( a \) drilled parallel to the rod axi...

A long straight metal rod has a very long hole of radius \( a \) drilled parallel to the rod axis as shown in the figure. If the rod carries a current \( I \), find the magnetic field on axis of hole. Given \( C \) is the centre of the hole and \( O C=c \).
(A) \( \frac{\mu_{0} i c}{\pi\left(b^{2}-a^{2}\right)} \)
(B) \( \frac{\mu_{0} i c}{2 \pi\left(b^{2}-a^{2}\right)} \)
(C) \( \frac{\mu_{0} i\left(b^{2}-a^{2}\right)}{2 \pi c} \)
(D) \( \frac{\mu_{0} i c}{2 \pi b^{2}} \)