# Electric charges

1. Jul 16, 2006

### jairusgarcia

can someone help me on this? thanks in advance:

A positive charge +2q lies on the x-axis at x=-a and a charge -q at x=+a. Find a point where the electric force on the third charge Q would be zero.

should i continue on using Coulomb's Law, and just use arbitrary variables or is there another waY? thanks :tongue: :surprised

2. Jul 16, 2006

### arildno

Use Coulomb's law in conjunction with Newton's 2d law of motion.
Let "X" stand for the unknown position of the particle with charge Q.

3. Jul 16, 2006

### jairusgarcia

what do you mean?

i have been trying to solve it using x as an unknown distance, and i end up having this equation

2(x-a)^2 = (a-x)^2

help!

do you know an easy solution to this?

4. Jul 16, 2006

### arildno

This is incorrect!
You should end up with:
$$2(x-a)^{2}=(x+a)^{2}$$
To solve this for x, remember the quadratic formula.

5. Jul 16, 2006

### nrqed

It's always better to do this type of problems in 3 steps.

Imagine that the charrge Q is positive, say (it turns out that the final answer would be the same if Q was negative as you can verify later).

First step: just look at the *directions* of the forces due to your two charges in all three regions (to the left of +2q, between the two charges and to the right of the -q). You are obviously looking for a region in which the two forces must be opposite. Here you will find that there are two regions possible

second step: now consider the magnitudes of the two forces. Not only the two forces must be in opposite directions, they must have the same magnitude. In which region is this possible? You will find that only one of the two regions of the first step satifies this.

third step; now pick an arbitrary point in the correct region, at a distance "d" (your unknown) from on ethe two charges. express the distance to the other charge in terms of d (it could be something like 2a-d or d-2a or a-d, depending on the region you are working in), set the two magnitudes of the forces on Q equal (Q will ancel out) and solve for d.

Patrick

6. Jul 16, 2006

### jairusgarcia

thanks for the tips... i appreciate it nrqed and arildno. il try your suggestions. :D

7. Jul 16, 2006

### jairusgarcia

the two given forces or each force with respect to Q?

8. Jul 16, 2006

### nrqed

I don't know what you mean by the "given forces".
The problem is to find where to place Q so that the net force on it will be zero, right? So you need to look at the two forces *on Q*. Those are the only two dorces you are interested in in this problem.
(th eonly other forces you could calculate would be the force of the -2q on the q or vice versa but these are irrelevant to the problem)

9. Jul 16, 2006

### jairusgarcia

well, i still dont get it, but il try. thanks

10. Jul 16, 2006

### nrqed

What part don't you get?
Is the question clear to you? Are you confused about the 3 steps I gave? You need to find the point where a charge Q would feel no net force, which means that the force produced by the -2q (on Q) would cancel the force of the +q (on Q). You need two conditiosn for that: the two forces must have opposite directions and they must have the same magnitude.

11. Jul 16, 2006

### jairusgarcia

ok. ^_^ gotta rush, i need to pass this early this morning, and its already 2am here. hehe thanks for the help!