$A$ magnetic field $B = 2t + 4t^{2}$ (where $t$ is time) is applied perpendicular to the plane of a circular wire of radius $r$ and resistance $R$. If all units are in $SI$, the electric charge that flows through the circular wire during $t = 0 \ s$ to $t = 2 \ s$ is:
- A$\frac{6 \pi r^{2}}{R}$
- B$\frac{20 \pi r^{2}}{R}$
- C$\frac{32 \pi r^{2}}{R}$
- D$\frac{48 \pi r^{2}}{R}$
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