Vibration Magnetometer
It is based on simple harmonic oscillations of a magnet suspended in uniform magnetic field .
Time period of vibrations is given by T = 2π √I / MH
where , I = moment of inertia of the magnet , M = magnetic dipole moment of the magnet and H = horizontal component of earth ’ s magnetic field .
When two magnets of unequal size are placed one above the other and north poles of both magnets are towards geographic north then time period of oscillations is given by
T 1 = 2π√I 1 + I 2 / ( M 1 + M 2 ) H
If north pole of first magnet and south pole of second magnet is towards geographic north , then time period of oscillations is given by
T 2 = 2π√ ( I 1 + I 2 ) / ( M 1 – M 2 ) H Then , M 1 / M 2 = T 2 2 + T 2 1 / T 2 2 – T 2 1