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Q.

A long solenoid of radius R carries a time (t) - dependent current  It=I0t1−t. A ring of radius 2R is placed coaxially near its middle. During the time interval  0≤t≤1, the inducted current IR  and the induced EMF (VR) in the ring changes as:

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a

Direction of  IR remains unchanged and VR is maximum at t=0.5

b

At t=0.5 direction of IR  reverses and VR  is zero

c

Direction of IR  remains unchanged and  VR is zero at t=0.25

d

At t=0.25 direction of IR reverses and VR  is maximum

answer is B.

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Detailed Solution

Current, I=I0t−I0t2           ​Magnetic flux,  ϕ=BA=μ0nIA​Induced emf, VR=−dϕdt=−μ0nAI01−2t Hence, VR=0 at t=12     And ​IR=VRResistance of loopSo, 0
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A long solenoid of radius R carries a time (t) - dependent current  It=I0t1−t. A ring of radius 2R is placed coaxially near its middle. During the time interval  0≤t≤1, the inducted current IR  and the induced EMF (VR) in the ring changes as: