# An electron is shot directly away from a uniformly charged plastic sheet Find σ.

1. Oct 9, 2009

### nejibanana

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

In figure (a) below, an electron is shot directly away from a uniformly charged plastic sheet, at speed vs = 2.13 × 10^5 m/s. The sheet is nonconducting, flat, and very large. Figure (b) below gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density?

There is also a graph that shows Velocity at various times. It is 0 at 7 ps.

2. Relevant equations

V = Vo + at

a = QE/m (Q = 1.609 x 10^-19, m = 9.109 x 10^-31)

E = σ/ε₀ (ε₀ = 8.85 x 10^-12) -> σ = Eε₀

3. The attempt at a solution

So I found acceleration with the first formula, then found E with the second, and found σ with the third. My answer was correct to the second decimal point, but when I did my friends' problems, the answer required me to subtract .4 from both of them to get the correct answer. I'm not sure if I did something wrong or if the homework website was wrong. If its any help, my solution was about 1.5. One of my friends problem had initial velocity of 2.03 x 10^5, all other numbers used were the same (give the same graph), and I calculated 1.4, but the correct answer was a little under 1.

Thanks for any help.

Last edited: Oct 9, 2009
2. Oct 10, 2009

### Andrew Mason

Re: An electron is shot directly away from a uniformly charged plastic sheet...Find σ

Why not show us what you have done. Also, what units are you working in? An answer of 1.5 means nothing without units.

Get acceleration from $\Delta v = a\Delta t$ which it looks like you have done. What did you use for $\Delta t$? The answer I get is:

a = 5.8e16 m/sec^-2

The force on the electron is F=ma where m is the mass of the electron. Since this is the coulomb force, qE, you have it correct that:

E = ma/q where q is the electron's charge.

I get: E = 9.11e-31 x 5.8e16/1.60e-19 = 3.3e5 N/coulomb

So $\sigma = E\epsilon_0$ = 3.3e5 x 8.85e-12 = 2.92e-6 coulomb/m^2

AM

3. Oct 10, 2009

### nejibanana

Re: An electron is shot directly away from a uniformly charged plastic sheet...Find σ

For change in time I used 7 picoseconds. Velocity changes from 2.13e5 to 0 in 7 ps. And I forget to edit it last night, but it wants the answers in microColoumbs/m^2.

So i got 2.13e5/ 7e-12 = a, which resulted in a = 3.04e16.

then I found E, so E = (9.109e-31) * (3.04e16) / (1.609e-19) . E = 172102.9.

Then σ = Eε₀. so σ = (172102.9) * ( 8.85 e-12) = 1.523e-6 C/m^2, converted to microColoumbs/m^2 is 1.523. Which was correct. 1.5313 is the answer given for my problem on the website.

For my friends I did, a = 2.03e5 / 7e-12 = 2.9e16

then E = (9.109e-31) * (2.9e16) / (1.609e-19). E = 164177.1287

then σ = (164177.1287) * (8.85 e -12) = 1.453e-6 C/m^2 = 1.453 microColoumbs/m^2. But according to the website the correct answer for his is 0.92875.

So I'm not sure what is causing the discrepancy between the problems of my 2 friends, since my problem worked out fine.

Thanks again.

4. Oct 11, 2009

### ideasrule

Re: An electron is shot directly away from a uniformly charged plastic sheet...Find σ

That can't possibly be correct. 2.03 is just 5% lower than 2.13, so you'd expect the final answer to be 5% lower than 1.5. 0.929 is way off.