Physics - Magnetism Question with Solution | TestHub

Here, magnetic moment is given in weber-meter, which is the unit of${\mu }_0 M$.

$\therefore {\mathrm{\mu }}_0 M=5\times {10}^{-5}$Wb-m

$M=\frac{5\times {10}^{-5}}{{\mathrm{\mu }}_0}\mathrm{A}{\mathrm{m}}^2$

Also,$B=8\pi \times {10}^{-4}={\mathrm{\mu }}_{0}H$

$\therefore H=\frac{8\pi \times {10}^{-4}}{{\mathrm{\mu }}_0}$

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

$I=\frac{MH{T}^2}{4{\pi }^2}=\frac{5\times {10}^{-5}\times 8\pi \times {10}^{-4}\times {15}^2}{4{\pi }^2{\mathrm{\mu }}_0^2}$

$=\frac{5\times {10}^{-5}\times 8\pi \times {10}^{-4}\times 225}{4{\pi }^2{\left(4\pi \times {10}^{-7}\right)}^2}$

$I=\frac{2250\times {10}^{-9}}{\pi \left(16{\pi }^2\right)\times {10}^{-14}}=4.54\times {10}^5\mathrm{ k}\mathrm{g}\mathrm{ }{\mathrm{m}}^2$