Question

In the figure, a rod closing the circuit moves along a $U-$shaped wire at a constant speed $v$ under the action of the force $F$. The circuit is in a uniform magnetic field perpendicular to its plane. Calculate $F$, if the rate of generation of heat is $P$.

• A. $\frac{P}{v}$
• B. $\frac{2P}{v}$
• C. $0$
• D. $\frac{P}{2v}$

Answer 1

The correct option is A $\frac{P}{v}$

EMF induced across the ends of the rod is,

$E=Blv$

$\therefore$ Current in the circuit is,

$I=\frac{E}{R}=\frac{Blv}{R}$

Magnetic force on the conductor,

$F^{\prime }=IlB$, directed towards left

$\because$ Acceleration of the rod is zero,

$\Rightarrow F^{\prime }=F$

$\Rightarrow IlB=F$

or, $I=\frac{F}{Bl}$

Now, power, $P=EI$

$\Rightarrow P=Blv\times \frac{F}{Bl}=Fv$

$\Rightarrow F=\frac{P}{v}$

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