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long solenoid of radius R carries a time...

long solenoid of radius R carries a time –dependent current `I(t) = I_(0) (12t - t^(3))` . A ring of radius 2R is placed coaxially near its middle. During the time interval ` 0 le t le 2 sqrt(3)` , the induced current `(I_(R))` and the induced EMF `(V_(R))` in the ring change as :

A

At t=1 sec direction of `I_(R)` reverses and `V_(R)` is maximum

B

At t=2 direction of `I_(R)` reverses and `V_(R)` is zero

C

Direction of `I_(R)` remains unchanged and `V_(R)` is zero

D

Direction of `I_(R)` remains unchanged and `V_(R)` is maximum

Text Solution

Verified by Experts

The correct Answer is:
B
`phi` in ring `=[mu_(0)n" "I_(0)(12t-t^(3))]xxpiR^(2)`
`(d phi)/(dt)=mu_(0)nI_(0)(12-3t^(2))piR^(2)`
Emf in Ring `=mu_(0)n I_(0)(12-3t^(2))piR^(2)`
`i=(mu_(0)nI_(0))/(R_(0))(12-3t^(2))piR^(2)`
i is + vec for `t lt 2`
is - ve for `t gt2`
So at t-2 sec current through ring reverses its direction.
And at t=2 EMG `(V_(R))=0`
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