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A conducting circular loop made of a thin wire, has area $3.5 \times 10^{- 3} m^{2}$ and $10 Ω$ resistance . It is placed perpendicular to a time dependent magnetic field $B (t) = (0.4 T) \sin (50 π t)$ . The net charge flowing through the loop during $t = 0 s$ and $t = 10 m s$ is close to:

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$7 mC$

$6 mC$

$21 mC$

$14 mC$

answer is A.

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Detailed Solution

We know that,

$Q = \frac{Δ ϕ}{R} = \frac{1}{10} A (B_{f} - B_{i})$

$= \frac{1}{10} \times 3.5 \times 10^{- 3} (0.4 \sin \frac{π}{2} - 0)$

$\begin{array}{l} = \frac{1}{10} (3.5 \times 10^{- 3}) (0.4 - 0) \\ = 1.4 \times 10^{- 4} = 0.14 mC \end{array}$

The net charge flowing through the loop is 0.14 mC.

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