A conducting circular loop made of a thin wire has area $3.5\times10^{-2}\ \text{m}^2$ and resistance $10\ \Omega$. It is placed perpendicular to a time-dependent magnetic field $B(t) = (0.4\ \text{T})\sin(50\pi t)$. The field is uniform in space. Then the net charge flowing through the loop during $t = 0$ s and $t = 10$ ms is close to
Answer: (A) $1.4\ \text{mC}$
Charge through the loop depends only on the change in flux: $q = \dfrac{\Delta\Phi}{R}$.
At $t = 0$, $B = 0$. At $t = 10\ \text{ms}$, $50\pi t = \pi/2$, so $B = 0.4\ \text{T}$ (the field rises steadily in this interval, so the current does not reverse).
$$q = \frac{AB}{R} = \frac{3.5\times10^{-2}\times0.4}{10} = 1.4\times10^{-3}\ \text{C} = 1.4\ \text{mC}$$
Solution by Sreeraj P, M.Sc Physics