Question

The figure shows a conducting loop, being pulled out of a magnetic field, with a uniform speed $v$. Which of the following graph represents the correct graph of power $P$ delivered by the pulling force, as a function of the speed $v$ ?

Assume loop wire has some resistance.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The emf induced across the loop is,

$E=Bvl$

$\therefore$ Electrical power generated in the loop is,

$P=\frac{E^2}{R}$

Here, $R$ is the resistance of the loop

$\Rightarrow P=\frac{(Bvl{)}^2}{R}$

$\Rightarrow P=\left(\frac{B^2{l}^2}{R}\right)v^2$

This is the power delivered by the external force.

Here, $P\propto v^2$.

Therefore, the graph between power and velocity will be a parabola with open upward as $\frac{B^2{l}^2}{R}>0$.


Hence, option $\left(D\right)$ is the correct answer.