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
Concept. Induced emf $\varepsilon = -\dfrac{d\phi}{dt}$; power $P = \dfrac{\varepsilon^2}{R}$.
Step 1. Emf. $\phi = BA_0(1 + \sin t) \Rightarrow \varepsilon = -BA_0\cos t$.
Step 2. Power.
$$P = \frac{B^2A_0^2}{R}\cos^2t$$
Step 3. Shape. Maximum at $t = 0$, zero at $t = \dfrac{\pi}{2}$, maximum again at $t = \pi$, never negative: graph (2).
Answer. Graph (2) (Option B).
Solution by Sreeraj P, M.Sc Physics