# Dielectric sheet - Find speed with which electron crosses sheet?

• Jun 29th 2009, 02:15 PM
fardeen_gen
Dielectric sheet - Find speed with which electron crosses sheet?
An infinite dielectric sheet having charge density $\sigma$ has a hole of radius $R$ in it. An electron is released on the axis of the hole at a distance $\sqrt{3}R$ from the centre. Find the speed with which it crosses the plane of the sheet.

Spoiler:
$v = \sqrt{\frac{\sigma eR}{m\epsilon_0}}$

How to do it?
• Jan 26th 2010, 01:05 PM
Rebesques
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.