Solving for Net Force on Third Particle: What's Missing?

[Warlax]

particle 1 of charge q1 = +1.2 µC and particle 2 of charge q2 = -2.5 µC, are held at separation L = 14 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3?

I tried expressing the net electrostatic force on the third particle both on the x-axis and on the y-axis. The net force on both axis is =0. I introduced angles alpha and beta to express the angle between the x-axis and a line from particle 1 or particle 2 to particle 3, respectively. I can find the net electrostatic force using this and the Pythagorean theorem - but the expression has too many unknowns to be solved for x and y of the 3rd particle.

What am I missing here? How should I go about solving this?

Thanks.

 

[rl.bhat]

Net force will be zero only on x-axis.
The neutral point will be out side the line joining the two charges nearer to the smaller charge.

 

[Warlax]

Net force will be zero only on x-axis.
The neutral point will be out side the line joining the two charges nearer to the smaller charge.

Thanks for your reply,

Why would the force only be zero on the x-axis?
q1 and q2 are of opposite charge so one is pulling on q3 and another is pushing against it... wouldn't that make q3 have a zero net force on the y-axis as well.

In addition, how do I approach this problem? I need to find the x,y coordinates of q3.

 

[rl.bhat]

Thanks for your reply,

Why would the force only be zero on the x-axis?
q1 and q2 are of opposite charge so one is pulling on q3 and another is pushing against it... wouldn't that make q3 have a zero net force on the y-axis as well.

In addition, how do I approach this problem? I need to find the x,y coordinates of q3.

If +q₃ is placed on y-axis, force between q1and q3 will be away from q1 and force between q2 and q3 will be towards q2. The resultant of these forces cannot be zero. because they are not in a line.

 

[Warlax]

If +q₃ is placed on y-axis, force between q1and q3 will be away from q1 and force between q2 and q3 will be towards q2. The resultant of these forces cannot be zero. because they are not in a line.

Oh, I see... so this reduces the problem to something more like:
What if q3 is on the x axis, either to the right or to the left of both q1 qnd q2?

Am I correct?