Answer
$E = 3.75\times 10^{-6}~J$
Work Step by Step
We can find an expression for the induced emf:
$\mathscr{E} = \frac{d\Phi}{dt}$
$\mathscr{E} = A~\frac{\Delta B}{\Delta t}$
We can find an expression for the induced current:
$i = \frac{\mathscr{E}}{R}$
$i = \frac{A~\Delta B}{R~\Delta t}$
We can find an expression for the power:
$P = i^2~R$
$P = \frac{A^2~(\Delta B)^2}{R~(\Delta t)^2}$
We can find the thermal energy that is produced:
$E = P~\Delta t$
$E = \frac{A^2~(\Delta B)^2}{R~\Delta t}$
$E = \frac{(2.00\times 10^{-4}~m^2)~(-17.0\times 10^{-6}~T)^2}{(5.21\times 10^{-6}~\Omega)~(2.96\times 10^{-3}~s)}$
$E = 3.75\times 10^{-6}~J$
