Figure shows a conducting rod of negligible resistance that can slide on smooth U-shaped rail made of wire of resistance 1Ω/m. Position of the conducting rod at t = 0 is shown. A time t dependent magnetic field B = 2t tesla is switched on at t = 0.
At t = 0, when the magnetic field is switched on, the conducting rod is moved to the left at constant speed 5cm/s by some external means. The rod moves perpendicular to the rails. At t = 2s, induced emf has magnitude

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0.08V

0.02 V

0.04V

0.12V

answer is B.

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Detailed Solution

$\begin{aligned} B = 4 T, \frac{dB}{dt} = 2 T / s \\ a = 20 \times 30 {cm}^{2} \\ = 600 \times 10^{- 4} m^{2}; \\ \frac{dA}{dt} = - (5 \times 20) {cm}^{2} / s \\ = - 100 \times 10^{- 4} m^{2} / s \\ E = - \frac{d ϕ}{dt} = - [\frac{d (BA)}{dt}] = - [\frac{B (dA)}{dt} + \frac{adB}{dt}] \\ - [- 0.04 + 0.120] = - 0.08 V \end{aligned}$