# Forces on symmetrical electrostatic charges

## Homework Statement

3 point charges L(-b, b) M(b, b) & N(0, 0) have charges Q, -3Q & Q.
I need to find the force on the charge at the origin.

## Homework Equations

Coulomb's Law important, here. F = 1/4∏0 q^2/r^2 r(hat)
z-component no existent (from coordinates given)
x- & y-components to be found

Now, I'm finding it difficult to see thew wood from the trees with this relatively simple thing. I'm trying to find the x- & y- bits of force between the charges 1 & 2 to the charge at the origin for each charge.

## The Attempt at a Solution

Now, F = 1/4∏ε0 ((Q(2b*-cos45)*Q)/(2cos45)) - (-3Q(2b*cos45)/(2cos45)
Then factor out the Q^2/r^2 terms.
I would like it in the form F=1/4∏ε0 (Q^2/r^2) (!!ex - !!ey) but am finding the (!!ex - !!ey) bit difficult to get due to the trig bits I think.
Advice needed, please.

I'm sure this is wrong, but is the main stumbling block.
If I can get this then magnitude of force & direction of unit vector will be easy.

## Answers and Replies

gneill
Mentor
For this problem it would probably be simpler to go right to the geometry rather than deal with a purely vector algebra approach. From the charge locations, what can you say about the type of triangle they form? Do you know anything about angles and sides for such triangles?

The other thing I will point out is that the Coulomb force law applies between two charges, Q1 and Q2 (not Q2 unless both charges happen to be equal). So the magnitude of the force is:
$$F = k \frac{Q_1 Q_2}{r^2} ~~~~~~~\text{where}~~~~k = \frac{1}{4 \pi \epsilon_o}$$