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

Deflection magnetometer works on the principle of tangent law. According to tangent law when two uniform magnetic fields act at right angles to each other on a magnetic needle, it comes to rest in the way of resultant field. The deflection magnetometer is placed in Tan A position (Figure). A bar magnet of magnetic moment M_{1} and length 2Ɩ_{1} is placed at a distance d_{1} from the center of the magnetic needle, on one side of the compass box. Since the sensitivity of the magnetometer is more at 45°, the distance of the bar magnet should be chosen such that the deflection lies between 30° and 60°.

The readings corresponding to the ends of the aluminum pointer are noted as θ_{1} and θ_{2}. The magnet is reversed pole to pole and kept at the same distance. Two more readings θ_{3} and θ_{4} are noted. By placing the magnet on the other side of the compass box at the same distance, four more readings θ_{5}, θ_{6}, θ_{7, }and θ_{8} are noted as above. The mean of the eight readings gives a value θ_{I}.

The experiment is repeated as above for the second bar magnet of magnetic moment M_{2} and length 2Ɩ_{2} by placing at a distance d_{2}. Now the mean of the eight readings gives a value of θ_{II}.

Applying tangent law, for the first magnet,

**(μ _{0}/4π) * {2M_{1}d_{1}/(d_{1}^{2}-Ɩ_{1}^{2})^{2}} = B_{h} tan θ_{I}** …. …. …. (1)

and for the second magnet.

**(μ _{0}/4π) * {2M_{2}d_{2}/(d_{1}^{2}-Ɩ_{2}^{2})^{2}} = B_{h} tan θ_{II}** …. …. …. (2)

From the above equations (1) and (2), we get

(M_{1}/M_{2}) = [**(d _{1}^{2}-Ɩ_{1}^{2})^{2}/(d_{2}^{2}-Ɩ_{2}^{2})^{2}] * (d_{2}/d_{1}) * (tan θ_{I}/ tan θ_{II})**

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

Deflection magnetometer is an apparatus used to determine the magnetic moment and polar potency of a bar magnet. It is also used to contrast the pole strengths of two bar magnet.

Deflection magnetometer is used to –

- compare magnetic moments
- compare earth’s magnetic inductions
- verify inverse square law and
- determine the horizontal constituent of the earth’s magnetic induction.

**About the Apparatus –**

Fig: Deflection magnetometer apparatus

Deflection magnetometer is a box-type vibration magnetometer, timer, bar magnet. This magnetometer consists of a huge compass box with a little magnetic needle pivoted at the center of a round scale so that the needle is liberated to rotate in a horizontal plane.

A large aluminum pointer is rigidly set at right angles to the magnetic needle. The spherical scale is graduated in degrees. The compass box is placed at the middle of a wooden board one meter long. The wooden board has a millimeter scale along its axis. The zero of this scale is in the middle of the compass box.