Answer
The magnitude of $\mathscr{E}$ is $~~6.00~mV$
Work Step by Step
$B = (6.00\times 10^{-2}~T/s)~t~\hat{k}$
Note that the magnetic field changes over time and the magnetic field is in the +z direction.
Thus, the magnetic flux through the loop also changes over time
We can find the induced emf in the loop:
$\mathscr{E} = -\frac{d\Phi}{dt}$
$\mathscr{E} = -A~\frac{dB}{dt}$
$\mathscr{E} = -(0.400~m)(0.250~m)~(6.00\times 10^{-2}~T/s)$
$\mathscr{E} = -6.00~mV$
The magnitude of $\mathscr{E}$ is $~~6.00~mV$
