1. Tardigrade
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  4. A conducting circular loop of area 2.5× 10- 3m2 and resistance 10Ω is placed perpendicular to a time varying magnetic field B(.t.)=0.6Tsin(.50π t.). The field is uniform in space. The net charge flowing through the loop during t=0s and t=10ms is (k/2)mC . Find the value of k .

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Q. A conducting circular loop of area $2.5\times 10^{- 3}m^{2}$ and resistance $10\Omega$ is placed perpendicular to a time varying magnetic field $B\left(\right.t\left.\right)=0.6Tsin\left(\right.50\pi t\left.\right).$ The field is uniform in space. The net charge flowing through the loop during $t=0s$ and $t=10ms$ is $\frac{k}{2}mC$ . Find the value of $k$ .

NTA AbhyasNTA Abhyas 2022

Solution:

Net charge $=\frac{\Delta \phi}{ R }=\frac{ A \left( B _{2}- B _{1}\right)}{ R }$
$=\left(2.5 \times 10^{-3}\right)(0.6)\left[\sin \frac{50 \pi(10)}{10^{3}}-\sin 0\right]$
$=1.5 \times 10^{-3}\left[\sin \frac{\pi}{2}-\sin 0\right]$
$=1.5 \times 10^{-3} C =\frac{3}{2} mC$