Electric potential energy question

[fluidistic]

I've done an exercise that made me think a bit.
Here's it is : https://www.physicsforums.com/showthread.php?t=333608.

So the electric potential energy of a 1 dimensional crystal (lattice?) formed by alternating ions is about $$\frac{-ke^2 \ln 2}{a}$$. So as it is a negative number, I would have to do some work to separate the charges composing the crystal and the crystal is stable.
While if it would have been a positive number, the crystal wouldn't have been stable and I would have to do work to maintain the charges the place they are.
But what if the infinite sum is worth $$0$$?
I know that I need no work to take one charged particle from infinity to anywhere, so the electric potential energy of the particle would be $$0$$... but what if I have a system of charged particles with a total electric energy equal to $$0$$? Is this hypothetical system stable? What does that mean that its electric potential is null?

 

[eljose79]

Hello!

Thank you for sharing your exercise and thoughts on electric potential energy in a 1 dimensional crystal. It is always great to see people actively engaging with scientific concepts and asking questions to further their understanding.

To answer your question, if the infinite sum of the electric potential energy in a 1 dimensional crystal is equal to zero, it means that the crystal is in a state of equilibrium. This means that there is no net force acting on the charges in the crystal and they are in a stable configuration.

In terms of stability, a system with a total electric energy equal to zero can still be stable. This is because the electric potential energy is just one factor in determining the stability of a system. Other factors, such as thermal energy and entropy, also play a role in determining the stability of a system.

In the case of a hypothetical system with a total electric energy equal to zero, it is possible for the system to be stable if the other factors are in balance. However, this would depend on the specific conditions and properties of the system.

I hope this helps to clarify your question. Keep exploring and asking questions, that's how science progresses!

 

[astrokreng]

First of all, great job on completing the exercise and thinking critically about the concept of electric potential energy in a crystal lattice. Your understanding of the relationship between the electric potential energy and stability of a system is correct.

To answer your question, a system with a total electric potential energy of 0 can be considered stable. This means that the forces between the charges in the system are balanced and there is no net movement of charges. In other words, the system is in equilibrium.

However, it's important to note that a system with a total electric potential energy of 0 does not necessarily mean that there are no forces acting on the charges. It simply means that the net force is 0. So while the system may be stable, individual charges within the system may still experience forces and move within the lattice.

Overall, a system with a total electric potential energy of 0 can be considered a stable equilibrium, but it's important to also consider the forces and movements of individual charges within the system.