The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $1.0 \times…
The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $1.0 \times 10^{-2} \mathrm{~A} \mathrm{~m}$ and $\frac{10^{-6}}{\pi^2} \mathrm{~kg} \mathrm{~m}^2$. If it completes 10 oscillations in 10 s , the magnitude of the magnetic field is
0.4 T
4 T
0.4 mT
4 mT
Solution
Time period of oscillation of magnet inside the magnetic field $T=2 \pi \sqrt{\frac{1}{M B}}$
$T=\frac{t}{n}=\frac{10}{10}=1 \mathrm{~s}$
$1=2 \pi \sqrt{\frac{10^{-6}}{\pi^2 \times 1.0 \times 10^{-2} \times B}}$
$\frac{1}{4}=\frac{10^{-4}}{B} \Rightarrow B=0.4 \mathrm{mT}$
