A magnetic compass needle oscillates 30 times per minute at a place where the dip is $45^{\circ}$, a

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\

Professor PC Thomas Classes · Answer

(a) : Frequency of oscillation\ $\frac{30}{40}=\sqrt{\frac{B_{1} \cos 45^{\circ}}{B_{2} \cos 30^{\circ}}}$\ $\propto \sqrt{\text { magnetic field }}$\[0pt] [Horizontal component of magnetic field $=B \cos \delta]$\ $\frac{B_{1}}{B_{2}}=0.7$\