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Q.

A very small circular loop of area 5×10−4 m2 ,resistance 2Ω  and negligible inductance is initially coplanar and concentric with a much larger fixed circular loop of radius 0.1m.  A constant current of 1 ampere is passed in larger loop and smaller loop is rotated with a angular velocity '' ω rad/s   about its diameter.  The induced emf is  ___ ×10−9V

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a

πω2sinωt

b

πω2sinωt

c

πω8cosωt

d

πωsinωt

answer is D.

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Detailed Solution

Induced emF in smaller loop     e=BANωsinωte=μ0i2rAω sinωt            B=magnetic induction at the centre of larger loope=4π×10−7×1×5×10−4×ω sinωt2×(0.1)                  B=μ0i2re=πω sinωt
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A very small circular loop of area 5×10−4 m2 ,resistance 2Ω  and negligible inductance is initially coplanar and concentric with a much larger fixed circular loop of radius 0.1m.  A constant current of 1 ampere is passed in larger loop and smaller loop is rotated with a angular velocity '' ω rad/s   about its diameter.  The induced emf is  ___ ×10−9V