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Question

Figure below shows a conducting rod of negligible resistance that can slide on a smooth U-shaped rail made of a wire of resistance 1 Ω m1. Position of the conducting rod at t=0 is shown. A time 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 a constant speed of 5 cms1 by some external means. The rod moves perpendicular to the rail. At t=2s, induced emf has magnitude

A
0.12 V
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B
0.08 V
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C
0.04 V
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D
0.02 V
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Solution

The correct option is B 0.08 V
From Faraday's law induced emf, E=dϕdt
Since flux, ϕ=B.A
After t sec if rod is moving with velocity v area, A=0.2×(0.4v×t)
Also magnetic field, B=2t
Therefore flux, ϕ=B.A=2t×0.2×(0.4v×t)
ϕ=0.16t0.4vt2
dϕdt=0.160.8vt
At t=2 sec and v=5 cm/s = 0.05 m/s
dϕdt=0.160.8×0.05×2=0.08
E=dϕdt=0.08 V
Since only magnitude is asked, therefore induced emf is 0.08 V

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