Question

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 :

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

Answer 1

Answer: (D)

2 Blv

Answer 2

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 $e=2\,Blv$