Question

A pair of parallel conducting rails lie at right angle to a uniform magnetic field of 2.0 T as shown in the fig. Two resistors 10$\Omega$ and 5$\Omega$ are to slide without friction along the rail. The distance between the conducting rails is 0.1 m. Then

• A. Induced current = $\frac{1}{150}A$ directed clockwise if 10$\Omega$ resistor is pulled to the right with speed $0.5m{s}^{-1}$ and 5$\Omega$ resistor is held fixed
• B. Induced current = $\frac{1}{300}A$ directed anti-clockwise if 10$\Omega$ resistor is pulled to the right with speed $0.5m{s}^{-1}$ and 5$\Omega$ resistor is held fixed
• C. Induced current = $\frac{1}{300}A$ directed clockwise if 5$\Omega$ resistor is pulled to the left at speed $0.5m{s}^{-1}$ and 10$\Omega$ resistor is held at rest
• D. Induced current =$\frac{1}{150}A$ directed anti-clockwise if 5$\Omega$ resistor is pulled to the left with speed $0.5m{s}^{-1}$ and 10$\Omega$ resistor is held at rest

Answer 1

The correct option is D Induced current =$\frac{1}{150}A$ directed anti-clockwise if 5$\Omega$ resistor is pulled to the left with speed $0.5m{s}^{-1}$ and 10$\Omega$ resistor is held at rest

When 5$\Omega$ resistor is pulled left at 0.5 m/sec induced emf., in the said resistor
$=e=vBl=0.5\times 2\times 0.1=0.1$V
Resistor $10\Omega$ is at rest so induced emf in it (e=vBl) be zero.
Now net emf., in the circuit=0.1V and Equivalent resistance of the circuit
R=$15\Omega$



Hence current $i=\frac{0.1}{15}$ amp=$\frac{1}{150}$amp
And its direction will be anti-clockwise (according to Lenz's law)