Net electrostatic force : four particles form a square

[feistytigger]

I apologize in advance - I am completely clueless about this one. I thought I had it figured out, but it turns out that I think I don't know where to even start.
Four particles form a square. The charges are q1 = q4 = Q and q2 = q3 = q. What is Q/q if the net electrostatic force on particles 1 and 3 is zero?

See, I thought it would work out to be 1 since I thought q and Q must be the same for the force to be zero. Apparently I am mistaken. So... show me start to finish pretty please?

 

[daniel_i_l]

Your right that Q and q have to have oppisite sighns for the forces to cancel out. But you have to show some work first and eaven the we almost never don't give full answers.
Hint: Just draw out the force components and show when the total on each axis is zero.

 

[feistytigger]

But I thought this was one of those that you don't really do work - it's logic. Say Q is 2. q has to be -2. Q/q=-1? But that's not right either...

I tried figuring it out this way:
The distance from particle 1 to 4 is sqrt(2a^2), so the force there is k(2Q/(sqrt(2a^2)^2) which simplifies to k(Q/a).
The combined forces of 2 and 3 will pull 1 in at a 45 degree angle to 2 or 3, which is the same direction 4 is pushing away at.
So, for 1: F=k(Q*q/a^2), except we have to take the 45 degrees into account, so F=k(2*Q*q*cos(45)/a^2).
Set them equal, and we have:
k(Q/a)=k(2*Q*q*cos(45)/a^2)
Q=2*Q*q*cos(45)/a
q=a/2cos(45)

Then for particle 3:
F=k(2q/(sqrt(2a^2)^2)=k(q/a)
F=k(2*Q*q*cos(45)/a^2)
k(q/a)=k(2*Q*q*cos(45)/a^2)
Q=a/2cos(45)

Q=a/2cos(45)=q, so Q/q is 1. ?

 

[daniel_i_l]

The distance from particle 1 to 4 is sqrt(2a^2), so the force there is
k(2Q/(sqrt(2a^2)^2)

It should be:
k(Q^2/(sqrt(2a^2)^2).