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.

Options

A. is zero
B. decreases as r increases
C. increase as `r` increases
D. none of the above

Answer

B

Explanation

Constant a concentric circle of radius `r`. The induced electric field `(E)` at any point on the circle is equal to that at `P`. For this circle

`ointvecE.vec(dl)=|(dvarphi)/(dt)|=A|(dB)/(dt)|`
or `Exx(2pir)=pia^(2)|(dB)/(dt)|`
`impliesE=(a^(2))/(2r)|(dB)/(dt)|impliesEprop(1)/(r)`