1. ## Force Problem

Two electrons repel each other with a force that varies inversely as the
square of the distance between them. If one electron is fixed at the point
(2, 4), find the work done in moving a second electron from (-2, 4) to
(1, 4).

I said, F = k/d^2 = k/4^2, since the horizontal distance between the electrons is 4 units.

Then, I figured that the incremental Work, delta W = F(x)(delta x) =
(k/d^2)(3) since the second electron is moved 3 units to the right.

Therefore, W = Integral (from -2 to 1) of 3k/16 dx is what I determined the integral to be, which gives 3k/16[x] evaluated from -2 to 1 which gives 9k/16. However, this is wrong, the answer is 3k/4. Help??

2. Originally Posted by kaiser0792
Two electrons repel each other with a force that varies inversely as the
square of the distance between them. If one electron is fixed at the point
(2, 4), find the work done in moving a second electron from (-2, 4) to
(1, 4).

I said, F = k/d^2 = k/4^2, since the horizontal distance between the electrons is 4 units.

Then, I figured that the incremental Work, delta W = F(x)(delta x) =
(k/d^2)(3) since the second electron is moved 3 units to the right.

Therefore, W = Integral (from -2 to 1) of 3k/16 dx is what I determined the integral to be, which gives 3k/16[x] evaluated from -2 to 1 which gives 9k/16. However, this is wrong, the answer is 3k/4. Help??
If x stands for the x-coodinate of the second electron,

$F = \frac{k}{d^2} = \frac{k}{(2-x)^2}$

$W=\int_{-2}^1\frac{k}{(2-x)^2}\,dx$

3. ## Thanks ione

That does the trick. I'm bad to try and put in too much initial info.
For example, they specified that the second electron was located at
(-2,4), so I assumed that d^2 should be [2 - (-2)]^2 instead of (2-x)^2.

How can I adjust my thinking to avoid that pitfall?

Also, how are you writing answers using math symbols. I tried to cut & paste equations from MATH EQUATION that comes with WORD, but it wouldn't paste the math symbols........

4. Originally Posted by kaiser0792

Also, how are you writing answers using math symbols.
Just click on the math symbols and the code used to generate it will pop up in a window. I'm new at this too so I have to click on other people's math expressions so I can see the code that they used.