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A uniform but time varying magnetic fiel...

A uniform but time varying magnetic field `B(t)` exist in a circular region of radius `a` and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point `P` at a distance `r` form the centre of the circular region.

A

a) is zero

B

b) decreases as `1/r`

C

c) increases as r

D

d) decreases as `1/r^2`

Text Solution

Verified by Experts

`intE.d1=|(dphi)/(dt)|=S|(dB)/(dt)|` or `E(2pir) =pia^2|(dB)/(dt)|`
For `rgea`
`:. E=a^2/(2r)|(dB)/(dt)|`
`:.` Induced electic field `prop1//r`
For `rlea`
`E(2pir)=pir^2|(dB)/(dt)| or E=r/2 |(dB)/(dt)|` or `Epropr`
At `r=a, E=a/2 |(dB)/(dt)|`
Therefore variation of `E` with `r` (distance from centre) will be as follows

`:.` The correct option is b
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