Question:
A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4 \mathrm{~mm}$ and a total length of $30 \mathrm{~cm}$. The magnetic field changes with time at a steady rate $\mathrm{dB} / \mathrm{dt}=0.032 \mathrm{Ts}^{-1}$.The induced current in the loop is close to
(Resistivity of the metal wire is $1.23 \times 10^{-8} \Omega \mathrm{m}$ )
Correct Option: 1,
Solution:
$\mathrm{q}_{\mathrm{i}}=\frac{\mathrm{d}\left(\mathrm{Ba}^{2}\right)}{\mathrm{dt}}=\mathrm{a}^{2} \frac{\mathrm{dB}}{\mathrm{dt}}$
$\mathrm{i}=\frac{\mathrm{q}}{\mathrm{R}}=\frac{\mathrm{a}^{2} \mathrm{~dB} / \mathrm{dt}}{\frac{\rho(40)}{\pi \mathrm{r}^{2}}}$