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- Homework Statement
- Two small beads having positive charges 3q and q are fixed a the opposite ends of a horizontal, insulating rod, extending from the origin to the point x=d. A third small charged is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium?

- Relevant Equations
- E = kq/r^2

Let a = distance between the charge on the left to the third bead.

Since the electric field is equilibrium, we equate the electric field emanating from the left charge to the right charge at the location of the third bead. I want to try to find the ratio of d with a.

E=E

Kq/(d-a)^2 = K*3q/a^2

1/(d-a)^2 = 3/a^2

3(d-a)^2 = a^2

3(d^2 - 2ad +a^2) = a^2

3d^2 - 6ad + 3a^2 = a^2

3d^2 - 6ad + 2a^2 = 0

This is as far as I got. I'm not sure how to proceed.