A conducting loop of finite resistance lies on the $x$ - $y$ plane. There is a constant magnetic field in the $z$ direction. The area of the loop varies with time $t$, as $A = A_0(1 + \sin t)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power $P$ dissipated in the loop as a function of time is :
Answer: (B) see figure
Flux: $\phi = BA_0(1 + \sin t)$. Induced emf:
$$\varepsilon = -\frac{d\phi}{dt} = -BA_0\cos t$$
Power dissipated:
$$P = \frac{\varepsilon^2}{R} = \frac{B^2A_0^2}{R}\cos^2 t$$
$P$ is maximum at $t = 0$, falls to zero at $t = \pi/2$, rises to the maximum again at $t = \pi$, and so on. It never becomes negative.
This is option (2), which starts at a maximum and dips to zero.
Solution by Sreeraj P, M.Sc Physics