Answer
$q = 29.5~mC$
Work Step by Step
We can find an expression for the magnitude of the induced emf:
$\mathscr{E} = \frac{d\Phi}{dt}$
$\mathscr{E} = NA\frac{\Delta B}{\Delta t}$
$\mathscr{E} = NA\frac{\Delta B}{\Delta t}$
We can find an expression for the induced current:
$i = \frac{\mathscr{E}}{R}$
$i = \frac{NA~\Delta B}{R~\Delta t}$
We can find the charge that flows through a point in the circuit:
$q = i~\Delta t$
$q = \frac{NA~\Delta B}{R}$
$q = \frac{(100)(1.20\times 10^{-3}~m^2)~(3.20~T)}{13.0~\Omega}$
$q = 29.5~mC$
