$A$ 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
  $\frac{48 \pi r^{2}}{R}$