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

Options

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

Answer

B

Explanation

`int vec(E).vec(d)l = |(d phi)/(dt)|, = S|(dB)/(dt)|`
or `E(2pi r) = pi a^(2)|(dB)/(dt)|` for `r ge a , :. E = (a^(2))/(2r)|(dB)/(dt)|`
`:.` induced electric field `prop (1)/(r )` for `r le a`
`E(2pi r) = 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