Question

A magnetic compass needle oscillates $30$ times per minute at a place where the dip is $45^{\circ}$, and $40$ times per minute where the dip is $30^{\circ}$. If $B_1$ and $B_2$ are respectively the total magnetic field due to the earth at the two places, then the ratio $B_1/B_2$ is best given by :

• A. 2.2
• B. 1.8
• C. 0.7
• D. 3.6

Answer 1

Answer: (C)

0.7

Answer 2

$f_{1} = \frac{1}{2\pi} \sqrt{\frac{\mu B_{1} \cos45^{\circ}}{I}} f_{2} = \frac{1}{2\pi } \sqrt{ \frac{\mu B_{2} \cos30^{\circ}}{I }}$
$\frac{f_{1}}{f_{2}} = \sqrt{\frac{B_{1}\cos 45^{\circ}}{B_{2} \cos30^{\circ}}} \therefore \frac{B_{1}}{B_{2}} = 0.7$