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. decrease as `(1)/(r)`
C. increases as r
D. decreases as `(1)/(r^(2))`

Answer

B

Explanation

Draw 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, induced emf
`e=ointE.dl=|(dphi)/(dt)|=S|(dB)/(dt)|`
`therefore" "E=oint" dl"=pia^(2)|(dB)/(dt)|" "["but" oint" dl"=2pir]`
`therefore" "Exx(2pir)=pia^(2)|(dB)/(dt)|`
`therefore" "E=(a^(2))/(2r)|(dB)/(dt)|`
`rArr" "Eprop(1)/(r)`