Q: When a short bar magnet is kept in tan A position on a deflection magnetometer, the magnetic needle oscillates with a frequency ‘ f ’ and the deflection produced is 45°. If the bar magnet is removed find the frequency of oscillation of that needle?

Sol: $\large \nu \propto \sqrt{B}$

$\large \frac{\nu_1}{\nu_2} = \sqrt{\frac{B_1}{B_2}}$

Where $\large B_1 = \sqrt{B^2 + B_H^2}$

$\large B_1 = \sqrt{(B_H tan45^o)^2 + B_H^2} = \sqrt{2}B_H$

And , B_{2} = B_{H}

$\large \frac{\nu_1}{\nu_2} = \sqrt{\frac{\sqrt{2}B_H}{B_H}} = 2^{1/4}$

$\large n_2 = \frac{n_1}{2^{1/4}} = \frac{f}{2^{1/4}}$