Dielectric sheet - Find speed with which electron crosses sheet?

An infinite dielectric sheet having charge density has a hole of radius in it. An electron is released on the axis of the hole at a distance from the centre. Find the speed with which it crosses the plane of the sheet.

Answer:

Spoiler:

How to do it?

Conservation of energy...

As the electron is released (i.e. has zero velocity) it obtains a charge energy, which is fully turned to kinetic energy the very moment that it crosses the center of the hole. Equate the two energies.