(Simple Electromagnetics) A charge placed between 2 charges

[runninthrutha6]

Homework Statement

A charge (q) is placed in-between two other equal charges named Q.
Q-----q-----Q
a) If both Q's are positive, is charge q in equilibrium? If yes, is it a stable or unstable equilibrium?
b) What about if one Q is negative while the other is positive?

The Attempt at a Solution

a) I think the charge q will be in equilibrium, considering the attraction or repulsion forces will cancel out. However, I have no clue how to know if it is unstable or stable.

b) q will not be in equilibrium, the forces will be in the same direction and thus not cancel out, giving q an acceleration.

 

[haruspex]

I'm not sure about the answer to a. It depends whether tjis is to be treated as purely a one dimensional problem or whether other dimensions should be taken into account.
What is the criterion for an equilibrium to be stable?

 

[runninthrutha6]

I'm not sure about the answer to a. It depends whether tjis is to be treated as purely a one dimensional problem or whether other dimensions should be taken into account.
What is the criterion for an equilibrium to be stable?

It is one-dimensional, and nothing to overthink I believe. It's a first-year intro course so nothing too complicated.

The issue is the criterion wasn't provided, so I'm trying to determine this on my own.

 

[haruspex]

It is one-dimensional, and nothing to overthink I believe. It's a first-year intro course so nothing too complicated.

The issue is the criterion wasn't provided, so I'm trying to determine this on my own.

A stable equilibrium is one in which the system will tend to return towards the equilibrium position if slightly perturbed from it.
If the middle charge is pushed a little to one side, will it move back, keep going, or stay where it is put?
Those three possibilities correspond to stable, unstable, semistable.