# Homework Help: Electron repulsion work problem.

1. Oct 23, 2012

### B3NR4Y

The problem: If two electrons are held at fixed points (5,0) and (-5,0), respectively, find the work done in moving a third electron from the origin to (3,0)

All equations:
Force of repulsion between two electrons:

\frac{1}{d^{2}}.

W = \int_{a}^{b} \, f(x) dx

"D" is the distance between the electrons

Attempt at a solution:
The distance between the electron at (-5,0) and the third electron is, 5+x where x is the position of the electron at any point on its journey to (3,0). The distance between the electron at (5,0) and the third electron is (5-x). I found the work by adding the two work equations like this:

\begin{split}
W&= \int_{0}^{3} \frac{1}{(5+x)^{2}} dx + \int_{0}^{3} \frac{1}{(5-x)^{2}} dx \\
& = -[-\frac{1}{5-x} |^{3}_{0}] + [-\frac{1}{5+x} |^{3}_{0}\\
&=\frac{3k}{8} ergs
\end{split}

Book says the answer is

\frac{9k}{40}\, ergs

2. Oct 23, 2012

### Dick

3. Oct 23, 2012

### B3NR4Y

So probably just an error in the book?

Good :3

4. Oct 23, 2012

### Dick

Yeah, I think so.

5. Oct 24, 2012

### Dick

Hope it's not to late to change my mind. There is a problem. The forces you are integrating don't point in the same direction. You need a minus sign on one of your forces. The book answer is correct. Sorry about that!

6. Oct 24, 2012

### B3NR4Y

No worries! Thank you. Makes sense, the answer is correct now. I feel honored you answered me.

7. Oct 24, 2012

### Dick

Glad you feel honored by a not very accurate response :). Hope that won't deter you from posting again.

8. Oct 24, 2012

### B3NR4Y

It most definitely will not. I'm 15 and self-teaching, so I will post here often. Thank you again.