Question

A conducting rod moves towards right with constant velocity $v$ in uniform transverse magnetic field. Graph between forcer applied by the external agent $v/s$ velocity and power supplied by the external agent $v/s$ velocity.

Answer 1

It is given that a conducting rod moves towards right with constant velocity v in uniform transverse magnetic field. Let force F is applied in forward direction and it covers a distance x. (from figure)

Area of the is $A=lx$ ,l is the length of coil.

Flux $\varphi =Blx$

Induced emf $e=\frac{d\varphi }{dt}=\frac{d\left(Blx\right)}{dt}=Blv$

Current $I=\frac{e}{R}=\frac{Blv}{R}$

Force

$F=BIl$

$F=\frac{B^2{l}^{2}v}{R}$

$so,F\propto v$

Graph between force and velocity is a straight line passing through origin.

$\because power=force\times velocity$

$P=\frac{B^2{l}^{2}v}{R}\times v$

$P=\frac{B^2{l}^2{v}^2}{R}$

$P\propto v^2$

So, the graph between power and velocity is parabola.