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Question: Three charged particles lie on the x axis (fig. 1). Particles 1 and 2 are fixed. Particle 3 is free to move, but the electrostatic force on it from particles 1 and 2 is zero. [tex]\mathbf{L}_{23} = \mathbf{L}_{12}[/tex], what is the ratio of [tex]\mbox{$\frac{q_1}{q_2}}[/tex]?

Fig. 1

-----O------------O----------------O-------------x (positive x axis)

[tex]\mathbf{L}_{12}[/tex] is the distance between Particles 1 and 2.

[tex]\mathbf{L}_{23}[/tex] is the distance between Particles 2 and 3

This is from a section dealing exclusively with Coulombs law, so in this case I believe I am obligated to use it. I'm thinking of relating the forces on particle 1 to particles 2 and three in:

[tex] \frac{1}{4 \pi \epsilon_{0}} \frac{|q_{1}||q_{2}|}{(L_{12})^2} = \frac{1}{4 \pi \epsilon_{0}} \frac{|q_{1}||q_{2}|}{(L_{23})^2} [/tex]

I'm not sure this will work, but I'm not sure how to accomplish this task. Any ideas?