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A long solenoid of radius R carries a ti...

A long solenoid of radius R carries a time dependent current `I = I_(0) t(1 – t)`. A ring of radius 2R is placed coaxially near its centre. During the time interval`0 le t le 1`, the induced current `I_(R)` and the induced emf VR in the ring vary as:

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
B
`I = I _(0) t ^(2) - I _(0) t ^(3 )`
`phi = BA = mu _(0) pi //pi R ^(2)`
` V _(R)= (d phi )/(dt) =- mu _(0) pi R ^(2) (dl )/(dt) =- mu _(0) pi R ^(2) I _(0) ( 2t - 3t ^(2))`
`I _(R) = (V_(R))/(R_(0)) =- (mu _(0)pi R ^(2) I _(0))/(R_(0)) ( 2t -3t ^(2)`
`I _(R) =-(1)/(R _(0)) mu 0 pi R ^(2) I _(0) ( 2-3 t )`
`I _(R) =0 at t =0 t = 2/3`
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