Moving a charge to infinity

aoc0708

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

The figure below shows three charges at the corners of a rectangle of length x = 0.35 m and height y = 0.22 m.

http://www.webassign.net/walker/20-23alt.gif (rectangle image)

(a) How much work must be done to move the +2.7 µC charge to infinity?

(b) Suppose, instead, that we move the -6.1 µC charge to infinity. Is the work required in this case greater than, less than, or the same as when we moved the +2.7 µC charge to infinity?

Explain.

(c) Calculate the work needed to move the -6.1 µC charge to infinity?


2. Relevant equations

W= kq₁q₂/r

3. The attempt at a solution

I got the correct answer for (a) like this:

W= (9e9)(2.7e-6)(6.1e-6)/.35 + (9e9)(2.7e-6)(3.3e-6)/.4134, with .4134 as the distance between the -3.3 charge and the 2.7 charge via the pythagorean theorem.
.61749 J, was correct; and I guessed that it would take less work to move the -6.1 µC charge for (b). But I'm not entirely sure why this is the case-- is it simply because the distances between the charges are smaller? And for some reason, when I use the same method on (c) as I did on (a), I'm wrong:

(9e9)(6.1e-6)(2.7e-6)/.35 + (9e9)(6.1e-6)(3.3e-6)/.22 yields 1.247, which is not the correct answer. Why is this?

Thank you!


Thank you!

Matterwave

It looks to me like you need to take into account the sign of the charges. Remember opposite charges attract while same charges repel. The -6.1 uC charge is easier to move to infinity because it sees 1 positive charge attracting it, but also 1 negative charge repelling it.

aoc0708

Ah, I see what you mean. Thank you! The correct answer was -.3999 Joules.