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 as `1/r^(2)`

Answer

B

Explanation

`oint (vec E).(vec dl)=(d phi)/(dt)((vec B)(vec A))=(d)/(dt) (BA cos(0^@))=A(dB)/(dt)`
`implies E(2 pi r)=(pi)(a^2)(dB)/(dt) for rgea`
`implies E=(a^2)/(2r)(dB)/(dt)implies E(prop)1/r`.