Questions

A current $I=3.36\left(I+2t\right)\times {10}^{-2}A$ 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 is$8.4\times {10}^{-4}\Omega $. 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

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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