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

For `rleR`
Using `El=S|(dB)/(dt)|` or `E(2pr)=(pir^2)alpha`

`:. E = (r alpha)/(2)`
`:. E propr` i.e. `E-r` graph is a straight line passing through origin.
At `r=R, E=(Ralpha)/2`
For `rgeR`

Using `El=S|(dB)/(dt)|,`
`E(2pir)=(piR^2)(alpha)`
`:. E=(alphaR^2)/(2r)`
`:. Eprop1/r,` i.e. E-r graph is a rectangular hyperbola.
The E-r graph is as shown in figure

The direction of electric field is shown in above figure.