Q: A magnet is suspended so as to swing horizontally make 50 vibration/min at a place where dip is 30°, and 40 vibration/min where dip is 45^o. Compare the earth’s total fields at the two place.

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

$\large \frac{\nu_1}{\nu_2} = \sqrt{\frac{B_1 cos\theta_1}{B_2 cos\theta_2}}$

$\large \frac{50}{40} = \sqrt{\frac{B_1 cos30^o}{B_2 cos45^o}}$

$\large \frac{5}{4} = \sqrt{\frac{B_1}{B_2} \times \frac{\sqrt{3}}{\sqrt{2}} }$

$\large \frac{B_1}{B_2} = \frac{25}{8 \sqrt{6}}$