explain in detail

Comprehension III
A long cylindrical conductor of radius R having a cylindrical cavity of radius R/2 through out its length is lying with its axis parallel to x-axis. The distance between the axes of the cylinder and the cavity is R/2. A constant current I is passed through the cylinder along its length in the positive x direction. The cross-sectional view of the cylinder is shown in the figure.
Figure
Problem 1.
The magnetic induction at point on the cavity is
(A) $\frac{{\mu }_0\mathrm{I}}{3\mathrm{\pi R}}\left(-\hat{\mathrm{k}}\right)$
(B) $\frac{{\mu }_0\mathrm{I}}{3\mathrm{\pi R}}\left(\hat{\mathrm{k}}\right)$
(C) $\frac{{\mu }_0\mathrm{I}}{6\mathrm{\pi R}}\left(\hat{\mathrm{j}}\right)$
(D) $\frac{{\mu }_0\mathrm{I}}{6\mathrm{\pi R}}\left(-\hat{\mathrm{j}}\right)$