Moving Charges to Infinity: Work Required and Comparison

[aoc0708]

Homework Statement

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?

Homework Equations

W= kq₁q₂/r

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.