# Homework Help: Surface charge density(error in my work)

1. Sep 14, 2010

### juggalomike

1. The problem statement, all variables and given/known data
In Figure (a), an electron is shot directly away from a uniformly charged plastic sheet, at a speed of vs = 2.00 106 m/s. The sheet is nonconducting, flat, and very large. Figure (b) gives the electron's vertical velocity component v versus time t until the return to the launch point. (The vertical axis is marked in increments of 5.00 105 m/s.) What is the sheet's surface charge density?

http://www.glowfoto.com/static_image/14-184719L/4743/jpg/09/2010/img4/glowfoto

2. Relevant equations
Vf=Vi+at
a=QE/M (Q = 1.609 x 10^-19, m = 9.109 x 10^-31)
E*ε₀=surface charge density (ε₀ = 8.85 x 10^-12)
3. The attempt at a solution

a=-4*10^6/14*10^-12=2.857E17
E=(2.857E17*9.109*10^-31)/(1.609*10^-19)=1617508.66
Surface charge density=1617508.66*8.85*10^-12=1.43E-5

I have tried the answer as both positive and negative and neither are working. What am i doing wrong?

Last edited by a moderator: Apr 25, 2017
2. Sep 14, 2010

### kuruman

If I am not mistaken, the electric field from an infinite plastic sheet of finite thickness is given by

E = σ/(2ε0)

This is a direct consequence of Gauss's Law. Your E-field is twice that.

3. Sep 14, 2010

### juggalomike

Ah your right, thanks, correct answer was 2.86E-5