Stable equilibrium and net force

[physgirl]

"stable equilibrium"

Homework Statement

Is there a difference b/w stable equilibrium and just equilibrium (of charged particles)? My homework problem exactly is:
2 small beads with charge +3q and +q each is fixed at opposite ends of a horizontal insulating rod. If a third charge is placed in between the two charges on the rod, at what position is the third bead in equilibrium? Can it be in stable equilibrium?

The Attempt at a Solution

I was able to calculate stuff for the first question and found the position... but I don't really know what the second question is asking.

 

[tim_lou]

equilibrium means net force is zero. if you move an object slightly off the equilibrium, the object can either go further away from the equilibrium (unstable equilibrium) or get back to the equilibrium (stable equilibrium).

in your second question, you need to consider the sign of the third charge. if it's negative, what is the direction of the forces, and what if it's positive? (at equilibrium)

 

[physgirl]

So if the third charge is negative, it'll feel a net attractive force from either side of the rod/charges and it'll end up moving away from the equilibrium somehwere in the middle... and if it's positive, it'll feel a net repulsive force (once its off equil) so it'll end back up in equilibrium?

 

[radou]

Perhaps not necessary to add, but an example of stable equilibrium is a sphere on a 'U-shaped' surface; move it from the state of equilibrium, and it will eventually return to it's original resting point. Further on, an example of unstable equilibrium is a sphere on the top of a '/\-shaped' surface; move it, and it won't stop falling. The last state of equilibrium is called indifferent - take the example of a sphere resting on a horizontal plane; move it, and it will eventually come to rest again, but at some other point of the plane.

 

[arkool]

what equation did you use to solve the first part of the problem?