Magnetism and Matter
10.0 Vibration Magnetometer
10.0 Vibration Magnetometer
It is based on simple harmonic oscillations of a magnet suspended in uniform magnetic field. Time period of vibrations is given by $$T = 2\pi \sqrt {\frac{I}{{MH}}} $$
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 $${T_1} = 2\pi \sqrt {\frac{{{I_1} + {I_2}}}{{\left( {{M_1} + {M_2}} \right)H}}} $$ If north pole of first magnet and south pole of second magnet is towards geographic north, then time period of oscillations is given by $${T_2} = 2\pi \sqrt {\frac{{\left( {{I_1} + {I_2}} \right)}}{{\left( {{M_1} + {M_2}} \right)H}}} $$ Then, $$\frac{{{M_1}}}{{{M_2}}} = \frac{{T_2^2 + T_1^2}}{{T_2^2 - T_1^2}}$$
