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  4. A conducting circular loop made of a thick wire, has area 3.5 × 10-3 m2 and resistance 10 Ω . It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T) sin(50 π 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:

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Q. A conducting circular loop made of a thick wire, has area $3.5 \times 10^{-3} m^2$ and resistance $10 \Omega$ . It is placed perpendicular to a time dependent magnetic field $B(t) = (0.4T) \sin(50 \pi t)$. 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:

JEE MainJEE Main 2019Electromagnetic Induction

Solution:

$Q = \frac{\Delta \phi}{R} = \frac{1}{10} A\left(B_{f} -B_{i}\right) = \frac{1}{10} \times3.5 \times10^{-3} \left(0.4 \sin \frac{\pi}{2} -0\right) $
$ = \frac{1}{10} \left(3.5 \times10^{-3}\right)\left(0.4 - 0\right)$
$ = 1.4 \times10^{-4} = 0.14\, mC $