Question

A conducting circular loop of area $2.5\times 10^{- 3} \, m^{2}$ and resistance $1 \, \Omega $ is placed perpendicular to a uniform time varying magnetic field $B\left(t\right)=0.6sin\left(50 \pi t\right) \, T$ . What is the net charge (in $mC$ ) flowing through the loop during $t=0$ and $t = 10 \, \text{ms}$ ?

Answer 1

Net charge $=\frac{\Delta \phi}{R}=\frac{A \left(B_{2} - B_{1}\right)}{R}$
$=\left(2 . 5 \times \left(10\right)^{- 3}\right)\left(\right.0.6\left.\right)\left[sin \frac{50 \pi \left(\right. 10 \left.\right)}{\left(10\right)^{3}} - sin 0\right]$
$=1.5\times 10^{- 3}\left[sin \frac{\pi }{2} - sin 0\right]$
$=1.5\times 10^{- 3}C=1.5mC$