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If the magnetic field is a function of time given by $B = 2 t + 4 t^{2}$ applied perpendicular to the plane of a circular wire of radius r and resistance R
and all the units are in Sl, what is the electric charge that flows through the circular wire during t = 0 s to t = 2 s

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$\frac{6 {πr}^{2}}{R}$

$\frac{20 {πr}^{2}}{R}$

$\frac{32 {πr}^{2}}{R}$

$\frac{48 {πr}^{2}}{R}$

answer is B.

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Detailed Solution

$ΔQ = \frac{Δϕ}{R}$

$= \frac{{πr}^{2} (B_{2} - B_{1})}{R} = \frac{{πr}^{2} [2 \times 2 + 4 \times 4]}{R} = \frac{20 {πr}^{2}}{R}$

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