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## Homework Statement

Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal insulating rod, extending from the origin to the point D, a third small charged bead is free to slide on the rod at a distance x away from the origin (but shorter than D). Can the equilibrium be stable?

Now I broke it down to

0 = 3d

^{2}- 6xd +2x

^{2}

Solving x = 0.951

The book said that it can be stable if it is positive. But wouldn't a negative charge also worked since

[tex]k\frac{3q*-q_{x}}{x^2} = k\frac{q*-q_{x}}{(d-x)^2}[/tex]

Negative and both sides and hence they cancel?