Question

A pair of parallel conducting rails lies at right angle to a uniform magnetic field of $2.0T$ as shown in the figure. Two resistors $10\Omega$ and $5\Omega$ are to slide without friction along the rail. The distance between the conducting rails is $0.1m$. 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 $10\Omega$ 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 $10\Omega$ resistor is held fixed
• C. Induced current $=\frac{1}{300}A$ directed clockwise if $5\Omega$ resistor is pulled to the left at $0.5m{s}^{-1}$ and $10\Omega$ resistor is held at rest
• D. Induced current $=\frac{1}{150}A$ directed anti-clockwise if 5A resistor is pulled to the left at $5m{s}^{-1}$ and $10\Omega$ resistor is held at rest

Answer 1

Answer: (D)

When $5\Omega$ resistor is pulled left at $0.5m/s$, induced emf in the said resistor $=e=vBl=0.5\times 2\times 0.1=0.1V$ Resistor $10\Omega$ is at rest so induced emf in it $(e=vBl$ ) is zero.

Now net emf in the circuit $=0.1V$
and equivalent resistance of the circutit $R=15\Omega$
Hence, current, $i=\frac{0.1}{15}A=\frac{1}{150}A$
And its direction will be anti-clockwise (according to Lenz's law)