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A square metal of loop PQRS of side 10cm and resistance $1 Ω$ is moved with a constant velocity partly inside a magnetic field of $2 {Wbm}^{- 2}$ , directed into the paper, as shown in the figure. This loop is connected to a network ABCD of five resistors each of value $3 Ω$ . If a steady current of 1mA flows in the loop, then the speed of the loop is

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4 cms^-1

1 cms^-1

2 cms^-1

0.5 cms^-1

answer is C.

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Detailed Solution

As, Wheatstone bridge is balanced. Then, current through arm AC is zero. Then, effective resistance R of bridge , i.e,

$\frac{1}{R} = \frac{1}{6} + \frac{1}{6} = \frac{1}{3} \Rightarrow R = 3 Ω$

Total resistance, $R = 3 + 1 = 4 Ω$

So, induced emf, $i = \frac{e_{induced}}{R_{total}} \Rightarrow \frac{Blv}{4} = \frac{2 \times 0 .1 \times v}{4} = 1 \times 10^{- 3}$

$∴$ Speed of the loop, $v = 2 \times 10^{- 2} {ms}^{- 1} = 2 {cms}^{- 1}$

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