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  4. One conducting U-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v, then the emf induced in the circuit in terms of B, I and v, where l is the width of each tube, will be :

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Q. One conducting U-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field $B$ is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed $v$, then the emf induced in the circuit in terms of $B, I$ and $v$, where $l$ is the width of each tube, will be :Physics Question Image

AIEEEAIEEE 2005Electromagnetic Induction

Solution:

Relative velocity $=v-\left(v\right)=2v=\frac{dl}{dt}$
Now, $e= \frac{d\phi}{dt}$
$e=\frac{Bldl}{dt}\,\left(\frac{dl}{dt}=2v\right)$
Induced emf
$e=2\,Blv$