A deflection magnetometer is arranged with its arms oriented in the north–south direction. At what distance and in which orientation must a short magnet having M/B_H = 40 A m ^2 T ⁻¹ be placed on the arms so that the compass needle can rest in any arbitrary position?

Step-by-step solution

For the compass needle to rest in any arbitrary position, the net magnetic field at the center of the magnetometer must be zero. This means the magnetic field produced by the short magnet ( B ) must be equal and opposite to the horizontal component of the Earth's magnetic field ( B _H ). Since B _H is directed towards the geographic North, the magnetic field B due to the magnet at the location of the needle must be directed towards the geographic South. The arms of the deflection magnetometer are along the North-So