A compass needle placed at a distance ‘r’ from a short magnet in tan A position shows a deflection of  600, if the distance is increased to r(3)1/3 . Then the deflection of the compass needle is

The magnetic field at a point along the axial line of a bar magnet is perpendicular to the horizontal component of Earth's magnetic field. If a magnetometer and a bar magnet are placed in such way that this condition is satisfied, then this arrangement is called Tan A position.In the  tan A position tanθ = BaxialBH⇒μ04π.2Mr3=BH tanθ ⇒r1r23=tanθ2tanθ1 Given : r1r2=rr(3)1/3=131/3∴tanθ2=tanθ1r1r23  ⇒tanθ2=tan600131/33⇒tanθ2=3.13=13 ⇒θ2=300 .