Coulomb's Law Question grade 12

AI Thread Summary
The discussion revolves around calculating the magnitude of a third negative charge, q₃, in a system with two other negative charges, q₁ and q₂, arranged at the corners of a square. The forces acting on q₁ are given, with a specific direction of +20.0° relative to the +x axis. The user has applied Coulomb's Law to express the forces exerted by q₁ and q₂ on q₃ as functions of q₃. However, they are uncertain about the next steps to solve for q₃. Assistance is requested to proceed with the calculations.
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Homework Statement



Three point charges, q₁= -5.00 μC, q₂= -4.00 μC, and q₃ which is negative are arranged as shown on three corner of side a=0.500 m. The direction of the forces on q₁ is at +20.0° with respect to the + x axis. Calculate the magnitude of q₃. The diagram looks something like this:
---------(-) q2
| (square) |
| (square) |
| (square) |
(+)------(-) q3
q1

Homework Equations



F = kq1q2
------
r^2

The Attempt at a Solution


I used the above formula and I put q3 as a variable. I found the two forces, the first one which is what q1 exerts on q3 and the second which is what q2 exerts on q3:

F(1 on 3) = 1.69 X 10^5 x (q3)
F (2 on 3) = 1.44 x 10^5 x (q3)

But then I'm stuck...
 
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