Potential energy between two oppositely charged ions in a crystal

Click For Summary

Discussion Overview

The discussion revolves around the potential energy between two oppositely charged ions in a crystal, focusing on the concepts of equilibrium and forces acting on the ions. Participants explore the relationship between potential energy and force, as well as the conditions for equilibrium in this context.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • GeoffreyThelm expresses confusion about how equilibrium can exist between two attracting ions.
  • One participant questions whether both terms in the potential energy function are attractive.
  • Another participant suggests that the equilibrium point may be where the attractive forces from each ion balance out.
  • A later reply clarifies that equilibrium occurs where the sum of forces is zero, indicating that the potential must have an extremum, ideally a minimum.
  • There is a suggestion to plot the potential to better understand its behavior.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints regarding the nature of the forces and the conditions for equilibrium, and it remains unresolved whether both terms in the potential are indeed attractive.

Contextual Notes

Participants have not fully defined the terms in the potential energy function or clarified the assumptions regarding the forces involved. There is also an implicit assumption that the potential should behave similarly to electric potential.

geoffreythelm
Messages
11
Reaction score
0
Hi, I am having trouble with the following:

attachment.php?attachmentid=20081&stc=1&d=1250100045.jpg


All I have really done is differentiate the function to give an expression for F(r), but I am a bit clueless about the rest. How can there be equilibrium if the two ions are attracted to each other?

Cheers,
GeoffreyThelm
 

Attachments

  • U.jpg
    U.jpg
    39 KB · Views: 1,593
Physics news on Phys.org
Your potential has two terms, are they both attractive?
 
I see.. So one (the first term?) is due to the attractive force from one ion, and vice versa for the other? So c is going to end up being something which looks like electric potential should. So is the point of equilibrium the point between the ions where the first term= the second term?
 
The point of equilibrium is where the sum of the forces is zero. When you have a potential, it is where dU/dx = 0, i.e. where the potential has an extremum (maximum or minimum). In this case it had better be a minimum. Consider plotting this potential to see what it looks like.
 

Similar threads

High School Ion Trap and Time-Varying Potentials
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Confused about work done on charge
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Understanding dissipation of energy in a resistor through the Drude model
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Electric Potential -- Is my understanding correct?
  • · Replies 6 ·
Replies
6
Views
1K
Graduate Understanding Electrical Potential Energy of a charge distribution
  • · Replies 5 ·
Replies
5
Views
2K
High School Definition of ground potential in infinite sheet charge distributions
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Derivation of the Potential Energy of an Electric Charge System
  • · Replies 2 ·
Replies
2
Views
4K
Graduate The total potential energy of two charges Wikipedia mistake?
  • · Replies 28 ·
Replies
28
Views
4K
Undergrad Can Two Identical Charged Conductors Have a Potential Difference?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Electric Potential midway between a pair of equal opposite charges
  • · Replies 11 ·
Replies
11
Views
10K