Using either deflection magnetometer or vibration magnetometer, explain how will you compare magnetic moments of two given bar magnets.

Using Deflection Galvanometer:

We can use deflection galvanometer by setting it in end-on position or broad side-on position,
(i) By setting the magnetometer in end-on position : When the deflection magnetometer is placed so that the two arms of the magnetometer and 0°-0° line lie along east-west line, the magnetometer is said to be placed in end-on position.
So the horizontal component of earth’s magnetic field (B_H) is perpendicular to the magnetic field (B) produced by the bar magnet as shown in figure.

Magnetic moment can be compared by using deflection method or null method.
Consider two equal bar magnets A and B having magnetic moments M₁ and M₂ respectively.
Let l be length of the each magnet. Place magnet A on the arm of the magnetometer lengthwise r at a distance effect of an r from the centre of the magnetometer.
Let B₁ be magnetic field due to magnet at the centre of the magnetometer box.

If the magnetic needle ns of the magnetometer box deflect at an angle θ, then,
B₁ = B_H tanθ₁                                       ...(1)
Since, magnetic needle lies on the axial line of the magnet,

Place magnet B in place of magnet A at the same distance r from the centre of the magnetometer, magnetic needle deflects at an angle 0₂, then as obtained in case of magnet A, we have

By calculating θ₁ and θ₂ the ratio M_l/M₂ can be calculated.
ii) 

By setting the magnetometer in broad side-on position :
When the deflection magnetometer is placed, so that the arms of the magnetomer and 90°-90° line lie along the N-S magnetometer is said to be placed in broad side-on position.

The horizontal component of earth’s magnetic field to magnetic’s magnetic field.
Let M₁and M₂ magnetic moments of magnets A and B.
2l be length of each magnet.
Place magnet A on the arm of magnetometer breadthwise at a distance r from the centre of the box as shown in figure.

Let B₁ be the magnetic field due to the centre of the magnetometer box. If the magnetic needle ns deflects through angle θ₁, then

B = B_Htan θ₁                                   ...(6)
magnetic needle lies on the equitorial line of the magnet.
B₁ = 
Using B₁ in equation, we have