Figure (i) shows a conducting loop being pull | vedclass

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(B) When a conducting loop of resistance $R$ and length $l$ is pulled out of a magnetic field $B$ with speed $v$,an induced $EMF$ $\varepsilon = Bvl$

Vedclass · Accepted Answer

$b$

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(B) When a conducting loop of resistance $R$ and length $l$ is pulled out of a magnetic field $B$ with speed $v$,an induced $EMF$ $\varepsilon = Bvl$ is generated.This $EMF$ drives an induced current $I = \frac{\varepsilon}{R} = \frac{Bvl}{R}$.The magnetic force acting on the loop is $F = Bil = B \left( \frac{Bvl}{R} ight) l = \frac{B^2 l^2 v}{R}$.To pull the loop at a constant speed $v$,the external pulling agent must apply an equal and opposite force $F_{ext} = F = \frac{B^2 l^2 v}{R}$.The power delivered by the pulling agent is $P = F_{ext} 	imes v = \left( \frac{B^2 l^2 v}{R} ight) 	imes v = \frac{B^2 l^2 v^2}{R}$.Since $B$,$l$,and $R$ are constants,we have $P \propto v^2$.$A$ graph of $P$ versus $v$ where $P \propto v^2$ is a parabola opening upwards,which corresponds to curve $b$.

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

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