Finding magnitude and x-coordinate of the third charge

[jheld]

Homework Statement

Two point charges q and 4q are at x=0 and x=L, respectively, and free to move. A third charge is placed so that the entire three-charge system is in static equilibrium.

What is the magnitude of the third charge?
answer in multiple(s) of q

What is the x-coordinate of the third charge?
answer in multiple of L

Homework Equations

F = Kq_0q_1/r^2
K = 8.99 * 10^9 N m^2/C^2

The Attempt at a Solution

I have already completed this problem, months ago. But, I am going through all of the homework and making sure that I can perform them well. The problem is, algebraically I am unable to come up with the correct answer. I keep getting myself stuck trying to find what I need to find.

 

[nickjer]

Calculate the forces on each charge assuming a 3rd charge of unknown magnitude exists at 'x'. Each charge will feel 2 forces exerted on it, so the sum of the forces needs to be 0.

I recommend drawing a picture with the force vectors.

 

[jheld]

Well I understand that. The problem is finding 'x'. If 1st on 2nd charge distance is L - x. I just get confused with all of the algebra, and thus can't solve either problem.

 

[nickjer]

First solve for the 2 forces on the first charge 'q'. You can calculate the force on it from the 2nd charge '4q' easily. Be sure to get the direction of this force. Now you will want a 3rd charge to apply an equal force but in the opposite direction. So you will have to unknowns: Q = charge of 3rd charge, and x = distance of 3rd charge.

Now you have 1 equation and 2 unknowns.

So you do the same for the 2nd charge, and you will have 2 equations and 2 unknowns. That is enough to solve those 2 unknown values.