Question

Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10^-5 Wb/m². The magnet has moment of inertia 3 × 10^-6 kg/m2 and magnetic moment 3 A-m².

Answer 1

Given:  B =1.6 x 10^-5 T, I = 3 x 10^-6 Kg/m², m =3 A-m²

The period of oscillation, T = 2π\(\sqrt{\frac{I}{μB}}\)

∴ The frequency of oscillation is

η = \(\frac{1}{2π}\sqrt{\frac{μB}{I}}\)

The number of oscillations per minute

60η =\(\frac{60}{2π}\sqrt{\frac{(3)(1.6×10^{-5})}{3×10^{-6}}}\)

=\(\frac{60}{2π}\sqrt{16}\)

= 38.19 per minute