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The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $1.0\times10^{-2}\ A\,m^2$ and $\dfrac{10^{-6}}{\pi^2}\ kg\,m^2$. If it completes 10 oscillations in 10 s, the magnitude of the magnetic field is
A
0.4 T
B
4 T
C
0.4 mT
D
4 mT
Detailed Solution
Time period $T=2\pi\sqrt{\dfrac{I}{MB}}$. $T=\dfrac{t}{n}=\dfrac{10}{10}=1$ s. $1=2\pi\sqrt{\dfrac{10^{-6}/\pi^2}{1.0\times10^{-2}\times B}}\Rightarrow B=0.4\times10^{-3}\ T=0.4$ mT.