superpositions of electrostatic forces

raindrops

1. The problem statement, all variables and given/known data

Three particles P1, P2, and P3 are located at the points (−2.00, −1.00), (0, 2.00), and (3.00, −1.00), respectively. P1 has a charge of 5.00 μC, but the charges of P2 and P3 are unknown. However, the three particles exert no net force on a charged particle that is placed at the origin. You are asked to find the unknown charges. (a) Use the fact that the net horizontal force on the particle at the origin is zero to find the unknown charge on P3. (b) Then use the fact that the net vertical force on the particle at the origin is zero to find the unknown charge on P2.


2. Relevant equations

F_net = (Kq₁q₂)r²

K = 9*10⁹


3. The attempt at a solution

I am at a loss on where to go with this one. I have tried about 10 different things but keep getting stuck with unsolved variables.

I also attached a drawing i did with some numbers for angles and such that i came up with.

Any help would be greatly appreciated!!

Attached Thumbnails

 

rl.bhat

From the given hint you can write
K*Q*Q1*cosθ1/(d1)^2 =k*Q* Q3*cosθ3/(d3)^2. where q is the charge at the center.You have already found θ1 and θ3. So find Q3.
Similarly
kQ*Q2/(d2)^2 =K*Q*Q1*sinθ1/(d1)^2 + k*Q* Q3*sinθ3/(d3)^2. Find Q2.

raindrops

This is one of the methods I used and I kept coming up with 9*10^-6 which is wrong so, I don't know what to do. Maybe my math is wrong.

(K (5*10^-6) Q₀ cos (26.56)) / (2.23)² = (K Q₃ Q₀ cos(18.43)) / (3.16)²