The magnetic field at all points within the cyllindrical region whose cross section is indicated in the accompanying Figure starts increasing at a constant rate `alpha`. `T//s`. find the magnitud of electric field as a function of `r`, the distance from the geometric centre of the region.

Explanation

`rltR`
`ointvec(E).vec(dt)=(dphi)/(dt)=(d)/(dt)(B.pir^(2))`
`Eointdi=(dB)/(dt).pir^(2)`
`E.2pir=alpha.pir^(2)`
`E=(alphar)/(2)(Ealphar)`
`E` will be tangential to circle at every point and its direction will be as of inducd current i.e. anticlockwise.
(b) `rgtR` : `ointvec(E).vec(dt)=(dphi)/(dt)=(d)/(dt)(B.piR^(2))`
`Eointdi=(dB)/(dt).piR^(2)`
`E.2pir=alpha.piR^(2)`
`E=(alphar)/(2)(Ealpha1//r)`
`r=R` , `E=(alphaR)/(2)`