Question

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

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

Each wire can be replaced by a battery whose emf is equal to $\begin{array}{cc}B\ell v& =1\times 4\times {10}^{-2}\times 5\times {10}^{-2}\\ & =20\times {10}^{-4}V\end{array}$
The polarity of the battery can be given by Fleming's right hand rule. When both wire move in opposite direction, the diagram looks like as shown in the figure.


The effective emf of the two batteries shown in the diagrams is zero.
So, choice (b) is correct and choice (d) is wrong.
When both wires move towards left, the circuit diagram looks
like as shown.

Effective emf of two batteries shown is $E(=20\times {10}^{-4}V)$ and internal resistance is 1$\Omega$ . Hence, current in the circuit is
$i=\frac{20\times {10}^{-4}}{10}=0.2mA$