Question

Figure shows a conducting loop being pulled out of a magnetic field with a speed v. Which of the four plots shown in figure (b) may represent the power delivered by the pulling agent as a function of the speed v?

Answer 1

(b) b

The emf developed across the ends of the loop is given by
$e=Bvl$
If R is the resistance of the loop, then the power delivered to the loop is given by
$$\begin{gathered} P=\frac{e^2}{R}=\frac{B^2{v}^2{l}^2}{R} \\ \Rightarrow P\propto v^2 \end{gathered}$$

This relation is best represented by plot b in the figure.