# Finding an Unknown Charge using Coulomb's Law

## Homework Statement

Three identical point charges, each of magnitude q, are located on the vertices of an isosceles triangle with its altitude oriented vertically. The altitude of the triangle is 4.00cm and the base is 6.00cm long. The resultant electrical force on the charge located at the upper vertex of the triangle has a magnitude of 0.500N. What is q?

## Homework Equations

Coulomb's Law:
F=(1/4*pi*E0)*(|Q1Q2|/r2)
1/4*pi*E0 = 8.99x109

## The Attempt at a Solution

First, I converted all the cm to m.
4.00cm = 0.04m
6.00cm = 0.06m
And then I drew out the charges on the triangle and the distances to help me get a better picture of what the question in talking about.
I thought about plugging in 0.500N for F, but since it's a 'resultant' force, it would mean it's the 2 forces of the 2 charges, not just a single force. So I'm a bit stuck here. The other question that came to mind was, will I need to know whether the charges are negative or positive?

Any help is greatly appreciated. I would love it if I am given hints, instead of just directly telling me how to solve it; because I do want to learn. Thanks!

## The Attempt at a Solution

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I would say that by their use of, 'three identical point charges', that they are saying the charges have the same sign. Thus, I would recommend the following steps towards solving:

step 1: Determine the angle of the bottom sides
step 2: Recognize the symmetry of the charge distribution and use this to your advantage.
step 3: Apply newton 2, and solve.

At your disposal, here is the equation you should get:
0.5 = 2* sin( arctan(4/3) ) * k q2/r2