Electron Cloud described by a Gaussian distribution

[MrBeano]

Homework Statement

A cloud of electrons are drifting from a negative plate to a positive plate after being liberated by a laser pulse, (separated by a distance z = 10cm with an original potential difference of 15V) at an instant in time the centre of the cloud has traveled 25mm from the negative plate and the spatial distribution of the charge is described by a Gaussian distribution with a standard deviation of 1.0mm.

Calculate the the change in electric field across the electron cloud if the electron cloud consists of 12 X 10⁹ electrons.

Homework Equations

The tutor said that Gauss' law, in one form or another must be used in the solution.

After some further reading I discovered the equation for the cylindrical gaussian surface of;

Flux = \oint E dA

= E \oint da

= E * 2\pirh

Flux also equals q/\epsilon

Therefore

E = s / 2\pi\epsilonr

The Attempt at a Solution

I have not really found a reasonable numerical solution yet, which has led me to believe that the problem lies with my derivation of E or my understanding of what E means in the context of the question.

 

[marcusl]

To make this approach work you need to do two things. 1) The cylindrical form you quoted is inappropriate to the problem, which has spherical symmetry. Use the spherical form instead (hint: it involves the surface area of a sphere.) 2) Express the portion q(r) of total charge that is enclosed within the sphere of radius r by using the given charge distribution.