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A plane loop is shaped as two squares (figure) and placed in a uniform magnetic field at right angle to the loop's plane. The magnetic induction varies with time as B=B0 sin ωt, where B0=10 mT and ω = 100 rads-1. The wires do not touch at point A. If resistance per unit length of the loop is 50mΩ/m, then amplitude of current induced in the loop is

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a
1.5 A
b
1.0 A
c
0.5 A
d
2.0 A

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detailed solution

Correct option is C

Induced emf's in the two loops will oppose each other. So net induced emf:e=ddtb2-a2B=b2-a2dBdt=0.202-0.102ωB0 cos ωt=0.04-0.01×100×10×10-3 cos ωt=30×10-3 cos ωtResistance: R=50×10-34×0.20+4×0.10=60×10-3ΩI=eR=0.5 cos ωtSo amplitude of current = 0.5 A

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