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

Case -1 For `r lt R`
Case -2 `r =R`

`E.2pi r =-A(dB)/(dt) , E.2pi R = -pi R^(2)(dB)/(dt)`
`E.2pi r = -pi r^(2)(dB)/(dt) , E = (R )/(2)(dB)/(dt)`
`E = -(r )/(2)(dB)/(dt) = -(r )/(2) alpha , E = -(R alpha)/(2) , E alpha r`
case -3 `r gt R , E.2pi r = -piR^(2)(dB)/(dt)`
`E = -(R^(2))/(2r)(dB)/(dt) , E = -(R^(2))/(2r)alpha, E_("out")alpha(1)/( r)`