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  4. A conducting circular loop of resistance 20 Ω and crosssectional area 20 × 10-2 m 2 is placed perpendicular to a spatially uniform magnetic field B, which varies with time t as B=2 sin (50 π t) T. Find the net charge flowing through the loop in 20 ms starting from t =0

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Q. A conducting circular loop of resistance $20\, \Omega$ and crosssectional area $20 \times 10^{-2} \,m ^{2}$ is placed perpendicular to a spatially uniform magnetic field $B$, which varies with time $t$ as $B=2 \sin (50 \pi t) T$. Find the net charge flowing through the loop in $20\, ms$ starting from $t =0$

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Solution:

$\Delta q=\frac{\Delta \phi}{R}=\frac{\phi_{2}-\phi_{1}}{R}=0$
$\Rightarrow \Delta q=0$
$\left[\phi_{1}=\phi_{2}=0\right.$ at $t =0$ and $\left.t =20 ms \right]$