Question

One conducting U-tube can slice inside another as shown in the 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 $\text{v}$ where $l$ is the width of each tube, will be

• A. $Bl\text{v}$
• B. $0.5Bl\text{v}$
• C. $\text{Zero}$
• D. $2Bl\text{v}$

Answer 1

The correct option is D $2Bl\text{v}$

According to faraday's Law of electromagnetic induction, an emf is induced in a moving conductor is given by,

$E=\overrightarrow{l^{\prime }}.(\overrightarrow{\text{v}}\times \overrightarrow{B})$

Here, $l^{\prime }=l=$Effective length between the ends points of the conductor.


$\because b,l$ and $\text{v}$ are mutually perpendicular in the arms $AD$ and $BC$,

$E_{AD}=Bl\text{v}$ and $E_{CB}=Bl\text{v}$

Net induced emf,

$E=Bl\text{v}+Bl\text{v}=2Bl\text{v}$

Hence, option $\left(D\right)$ is correct.

Why this Question: To understand the concept of induced emf in an arbitrary shaped conductor in a magnetic field.