Question

In the diagram shown, the wires $P_1{Q}_1$ and $P_2{Q}_2$ are made to slide on the rails with the same speed of $5\text{m/s}$. In this region, a magnetic field of $1\text{T}$ exists. The electric current in $9\Omega$ resistor is

• A. zero if both wires slide towards left
• B. zero if both wires slide in opposite direction
• C. $20\text{mA}$ if both wires move towards left
• D. $20\text{mA}$ if both wires move in opposite direction

Answer 1

Answer: (B), (C)

$20\text{mA}$ if both wires move towards left

The emf induced in each wire is given by

$E=Bvl$

$E=1\times 5\times 0.04$

$E=0.2\text{V}$

When both wires move in the opposite direction, the equivalent circuit can be drawn as


In this case, the net emf across $9\Omega$ resistance is zero.
Hence, no current will flow through $9\Omega$ resistor when wires move in opposite direction.

When both wires move towards the left, the equivalent circuit can be drawn as


Hence, current flowing through the $9\Omega$ resistor is

$i=\frac{0.2}{9+1}$

$i=\frac{0.2}{10}=0.02\text{A}$

Or, $i=20\times {10}^{-3}\text{A}=20\text{mA}$

Hence, options $\left(\text{B}\right)$ and $\left(\text{C}\right)$ are the correct answers.