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-I: For `r lt R`
`E.2pi r= -A (dB)/(dt)`
`E.2pi r = - pi r^(2) (dB)/(dt)`
`E= - (r )/(2) (dB)/(dt)= -(r )/(2) alpha`
`E alpha r`
Case-2: r= R
`E.2 pi R= - pi R^(2) (dB)/(dt)`
`E= - (R )/(2) (dB)/(dt)`
`E= - (R alpha)/(2)`
Case-3: `r gt R`
`E.2pi r= - pi R^(2) (dB)/(dt)`
`E= - (R^(2))/(2r) (dB)/(dt)`
`E= -(R^(2))/(2r) alpha`
`E_("out") alpha (1)/(r )`