Question

Magnetic field of the earth is $0.3\, G$ . A magnet is oscillating with the rate of $5$ oscillations/min. How much the magnetic field of the earth is increased, so that the number of oscillations becomes $10$ per minute?

Answer 1

$f=\frac{1}{2 \pi} \sqrt{\frac{M B_{H}}{I}} \propto \sqrt{B_{H}}$
$B_{H} \propto f^{2}$
$\frac{B_{H_{2}}}{B_{H_{1}}}=\left(\frac{f_{2}}{f_{1}}\right)^{2}=\left(\frac{10}{5}\right)^{2}=4$
$B_{H_{2}}=4 B_{H_{1}} $
$\Rightarrow B_{H_{2}}=4 \times 0.3=1.2 G$
$\Delta B=1.2-0.3=0.9\, G$