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

`intvecEvecdl=|(dphi)/(dt)|, S|(dB)/(dt)|`
`or E(2pir)=pia^2|(dB)/(dt)|"for "r gt= a,:.E=a^2/(2r)|(dB)/(dt)|`
`:."induced electric field " prop1/r,"for " r lt= a`
`E(2pir)=pir^2|(dB)/(dt)|`
`orE=r/2|(dB)/(dt)|or Epropr`
At `r=a,E=a/2|(dB)/(dt)|`
Therefore, variation of E with r(distance from centre) will be as follows