A short bar magnet with its north pole facing north forms a neutral point at $P$ in the horizontal plane. If the magnet is rotated by $90^{\circ}$ is the horizontal plane, the net magnetic induction at $P$ is : (Horizontal component of earth's magnetic field = $B_H$ )

Question

( A ) zero
( B ) $\sqrt{5} B_H$
( C ) $\frac{\sqrt{5}}{2} B_H$
( D ) $2B_H$