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 $B,\ l\ and\ v,\ where\ l$ is the width of each tube, will be
A) $Blv$
B) $- Blv$
C) Zero
D) $2$ $Blv$
Explanation
(d) Relative velocity $= v - ( - v) = 2v = \frac{dl}{dt}$
Now, $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ e = \frac{d\phi}{dt}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ e = \frac{Bldl}{dt}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( \frac{dl}{dt} = 2v \right)$
Induced emf $e = 2\ Blv$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.