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A current I=3.36I+2t×10-2A increases at a steady state in a long straight wire. A small circular loop of radius 10-3 m has its plane parallel to the wire and is placed at a distance of 1 m from the wire. The resistance of loop is8.4×10-4Ω. Find the approximate value of induced current in the loop.

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a
5.024×10-11A
b
3.8×10-11A
c
2.75×10-11A
d
1.23×10-11A

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detailed solution

Correct option is A

As the loop is very small the distance of every point in its plane can be taken to be equal to d = 1 mI=3.361+2t×10-2amperedIdt=2×3.36×10-2m/secMagnetic induction at every point on the loop'), B=μ0I2πdMagnetic flux linked with loop at any instant,ϕ=BA=μ0I2πd.πr2Induced emf, e=dϕdt=μ0r22ddIdtInduced current , I=eR=μ0r2R×2d(dIdt)=4π×10-7×(10-3)2×2×3.36×10-28.4×10-4×2×1=5.024×10-11amp

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