A uniform but time-varying magnetic field B (t) exists 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 from the centre of the circular region is

Options

A. is zero.
B. decreases as `(1)/(r )`.
C. increases as r.
D. decreases as `(1)/(r^(2))`.

Answer

B

Explanation

`int vecE.vecd vecl =|(dphi)/(dt)|=A|(dB)/(dt)|`
`rArr E(2pi r) =pia^(2)|(dB)/(dt)| " for "r ge a`
Therefore, `E=(a^(2))/(2r) |(dB)/(dt)|`
Therefore, Induced electric field `prop (1)/(r )`
For `r le a`
`E(2pir ) =pi r^(2) |(dB)/(dt)|`
or
`E=(r )/(2) |(dB)/(dt)| or E prop r`
At `r=a, E =(a)/(2) |(dB)/(dt)|`
Therefore, variation of E with r (distance from centre) will be as follows: