Question

On conducting U tube can slide inside the other as shown in figure 25.28 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 induced emf in terms of $B$, $l$ and $v$ where $l$ is the width of each tube, will be

• A. $Blv$
• B. $-Blv$
• C. $2Blv$
• D. zero.

Answer 1

The correct option is C $2Blv$

The total emf induced across each of the U tube is:${\int }_0^{\pi }BvR\sin \theta d\theta$$=2BvR=Bv\left(2R\right)=Bvl$ (since $l=2R$)

The positive terminal of induced emf of u tube on left is at the top while that of right is at bottom.

Hence, the net emf induced is $2Bvl$.