Electron cloud from uv pulse aimed at negative plate of a capacitor

[nicholasjgroo]

Homework Statement

A very short pulse UV laser is used to liberate a number of electrons from the negative plate in the arrangement in (i) above. 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 traveled approximately 10 mm the spatial distribution of the charge is described by a Gaussian distribution with a standard deviation of 0.5 mm. Write down an expression that relates the electric field to the charge density and calculate the change in electric field across the electron cloud if 5×10^10 electrons m^-2 were emitted during the laser pulse. Over what distance does the electric field effectively change?

Homework Equations

god knows, this guys notes don't make any sense

The Attempt at a Solution

 

[gabbagabbahey]

god knows, this guys notes don't make any sense

I didn't know God took notes.

Anyways, you'll find that the more effort you show the more people here are willing to help you. If your notes are too messy to read, I suggest you start by reading the relevant sections of your textbook instead.

As a hint for the problem at hand: what is a Gaussian distribution? What does that tell you about the general form of the charge density?

 

[nicholasjgroo]

ok, spent the last 2 hours on this and here's what I've got. the equation I've got for electric is the charge density divided by the permitivity of free space

for the change in electric field across the cloud E=q/4(pi)epsilon nought r squared.

and for the last bit i don't have a clue, i know of gaussian distributions but I've never used them.

 

[nicholasjgroo]

i'm thinking the electrons arent uniformly distributed they're like a blob and the distribution of the electrons is modeled by the gaussian distribution but i can't figure out what he means by 'over what distance does the electric field change'