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

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0.5 cms^–1

1 cms^–1

2 cms^–1

4 cms^–1

answer is C.

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Detailed Solution

Magnetic Flux, ϕ=BLx
Induced EMF, E=dϕ/dt= $B l v_{o}$
Total resistance of the loop, R=1Ω+3Ω=4Ω

$\begin{aligned} i = \frac{V}{R} \\ 10^{- 3} = \frac{{BLv}_{o}}{4} \\ v_{o} = 0.02 m / s \end{aligned}$

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