Question

A magnetic dipole of magnetic moment $6\times {10}^{-2}{Am}^2$ and moment of inertia $12\times {10}^{-6}kg{m}^2$ performs oscillations in a magnetic field of $2\times {10}^{-2}T$. The time taken by the dipole to complete $20$ oscillations is $(\pi \simeq 3)$

• A. $6s$
• B. $12s$
• C. $18s$
• D. $4s$

Answer 1

The correct option is B $12s$

The time period of oscillation of a magnetic dipole is given by

$T=2\pi \sqrt{\frac{I}{MB}}$

where, $I$ is the moment of Inertia, $M$ is the magnetic dipole moment and $B$ is the magnetic field.

Therefore, $T=2\pi \sqrt{\frac{12\times {10}^{-6}}{2\times {10}^{-2}\times 6\times {10}^{-2}}}=0.2\pi$ $\text{Hz}$

Time required for 20 oscillations = $20T=20\times 0.2\pi =4\pi \approx 12s$