Electrostatic force equilibrium

[Prabs3257]

Homework Statement

Three equal charges +q are placed at the three vertices of an equilateral triangle centered at the origin. They are held in equilibrium by a restoring force of magnitude F(r) = kr directed towards the origin, where k is a constant. What is the distance of the three charges from the origin ?

Relevant Equations

Energy conservation

I was thinking that we can equate the electrostatic potential energy and the spring energy (as the force is similar to that of a spring so energy will also be 1/2kx^2 ) but i am not getting the correct ans but by equating the net force on one charge to kr i am getting the correct ans can anybody please explain me why

 

[haruspex]

Homework Statement: Three equal charges +q are placed at the three vertices of an equilateral triangle centered at the origin. They are held in equilibrium by a restoring force of magnitude F(r) = kr directed towards the origin, where k is a constant. What is the distance of the three charges from the origin ?
Homework Equations: Energy conservation

I was thinking that we can equate the electrostatic potential energy and the spring energy (as the force is similar to that of a spring so energy will also be 1/2kx^2 ) but i am not getting the correct ans but by equating the net force on one charge to kr i am getting the correct ans can anybody please explain me why

In this three particle set up, the force on one does not vary as the inverse square of its distance from some fixed point. So the potential energy will not match that for a spring.

Edit: even if you were to model it as three springs connecting them in pairs it still would not work. The electrostatic force goes as the inverse square, while the elastic force goes as the square.

 

[Prabs3257]

In this three particle set up, the force on one does not vary as the inverse square of its distance from some fixed point. So the potential energy will not match that for a spring.
If you were to model it as three springs connecting them in pairs it should work.

If i pair them then they will be in parallel like in the pic below and keff will be 3k but then also i am missing by a factor of 1/2

 

[TSny]

I don't see why one would expect any simple relation between the potential energies associated with the two types of forces when the system is in equilibrium. I think you are going to have to work with forces, not energies.

 

[haruspex]

If i pair them then they will be in parallel like in the pic below and keff will be 3k but then also i am missing by a factor of 1/2

Please see my corrected post #2.