# Using gauss's law to calculate the change in electric field across an electron cloud

1. Aug 11, 2011

### 02pedwsa

1. The problem statement, all variables and given/known data

A very short pulse UV laser is used to liberate a number of electrons from the negative plate in the arrangement in (ii) above(describes parallel plate capacitor system, states plate thickness and seperation in vacuum ignore edge effects, charge density and electric field calculated). The electrons drift towards the positive plate under the influence of the electric field over a time scale much longer than the laser pulse length. Suppose that after the centre of the cloud has travelled approximately 10 mm the spatial distribution of the charge is described by a Gaussian distribution with a standard deviation of 0.5 mm. Calculate the change in electric field across the electron cloud if 5×10^9 electrons m-2 were emitted during the laser pulse. Over what distance does the electric field effectively change?

2. Relevant equations
I believe i have to use gauss's law in its differential form V.E=P/e P=charge density e=8.85x10^12
with V.E being the divergence of the electric which i hope i can equate to the 10mm spatial distribution quoted but i really am stuck, ive been attempting it in all different ways and really havent got a clue. If anyone can help please be as specific as possible as i could sit here all year otherwise

3. The attempt at a solution
ive made various attempts but all have thrown out wild looking answers

Cheers sam