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

## Homework Statement

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.

## Homework 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

## 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:

Andrew Mason
Homework Helper

## Homework Statement

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.

## Homework 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

## 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.
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

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.

ideasrule
Homework Helper

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.

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.