^Vibration magnetometer

^Vibration magnetometer

A magnet free to vibrate about vertical axis passing through its CM is first kept in a non- magnetic hook along B_H.

On deflecting it slightly by an amount θ, it experiences a restoring torque due to horizontal component of earth’s field B_H

τ = M B_H sinθ

≈M B_{H θ}   [As sinθ ≈ θ, for small angle deflection.

Due to inertia of the magnet it start oscillating simple harmonically. We know from the theory angular SHM that linear frequency, angular frequency & time period of oscillations is,

Thus for this situation we have

Here, I = MI of the magnet

Uses:

For two dissimilar magnets using

Here T_s = time period for the sum position & T_d = time period for the difference position.