Question

In figure, the wires $P_1{Q}_1$ and $P_2{Q}_2$ are made to slide on the rails with same speed of $5cm$ $s^{-1}$. In this region, a magnetic field of $1T$ exists. The electric current in the $9\Omega$ resistance is

• A. zero if both wires slide toward left
• B. zero if both wires slide in opposite directions
• C. $0.2mA$ if both wires move toward left
• D. $0.2mA$ if both wires move in opposite directions

Answer 1

Answer: (B), (C)

The correct options are
B zero if both wires slide in opposite directions
C $0.2mA$ if both wires move toward left

EMF induced according to Faraday's Law: $E=\frac{d\varphi }{dt}$
$\varphi =BLx$ , where $x$ is the distance from the origin
For a single slider: $|E|=BvL=1\left(0.05\right)\left(0.04\right)=2mV$
The sign depends on the direction of velocity.
If same direction, $E_{eq}=E=Bvl=2mV$
$i=\frac{V}{R_{eq}}=\left(2/10\right)=0.2mA$
If velocities in opposite direction: $E_{eq}=0$
$\Rightarrow i=0$