**Magnetic Moments of Two Bar Magnets in Null Deflection Method:**

The deflection magnetometer is placed in Tan A position (Figure). A bar magnet of magnetic moment M_{1} and length 2Ɩ_{1} is placed on one side of the compass box at a distance d_{1} from the centre of the magnetic needle.

The second bar magnet of magnetic moment M_{2} and length 2Ɩ_{2} is placed on the other side of the compass box such that like poles of the magnets face each other. The second magnet is adjusted so that the deflection due to the first magnet is nullified and the aluminium pointer reads 0^{o} – 0^{o}.

The distance of the second magnet is x_{1}. The first magnet is reversed pole to pole and placed at the same distance d_{1}. The second magnet is also reversed and adjusted such that the aluminium pointer reads 0^{0} – 0^{0}. The distance of the second magnet is x_{2}.

The experiment is repeated by interchanging the magnets. Two more distances x_{3} and x_{4} are noted. The mean of x_{1}, x_{2}, x_{3} and x_{4} is taken as d_{2}.

As the magnetic fields due to the two bar magnets at the centre of the magnetic needle are equal in magnitude but opposite in direction, B_{1} = B_{2}

**(μ _{0}/4π) * {2M_{1}d_{1}/(d_{1}^{2}-Ɩ_{1}^{2})^{2}} = (μ_{0}/4π) * {2M_{2}d_{2}/(d_{1}^{2}-Ɩ_{2}^{2})^{2}}**

**(M _{1}/M_{2}) = [(d_{1}^{2}-Ɩ_{1}^{2})^{2}/(d_{2}^{2}-Ɩ_{2}^{2})^{2}] * (d_{2}/d_{1})**

If the bar magnets are short, Ɩ_{1} and Ɩ_{2} are negligible compared to the distance d_{1} and d_{2}

so, **M _{1}/M_{2} = d_{1}^{3}/d_{2}^{3}**

It is the equation for magnetic moments of two bar magnets in Null deflection method.