How to find electrostatic interaction energy?

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Discussion Overview

The discussion revolves around methods for calculating electrostatic interaction energy between charged objects, specifically focusing on uniformly charged conducting and non-conducting spheres, as well as the interaction between a charge and a uniformly charged spherical shell. Participants explore general approaches to finding electrostatic energy in various configurations without a specific problem in mind.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest using Jefimenko's equations as a potential approach for calculating electrostatic interaction energy.
  • There is a discussion about the formula for the force between charges and how to derive interaction energy from it, with some participants providing the equation E=kq1q2/r.
  • One participant questions the compatibility of the terms "uniformly charged" and "conducting," arguing that a conducting sphere cannot remain uniformly charged.
  • Another participant clarifies that they meant the surface charge distribution is uniform on a conducting sphere.
  • Participants discuss the implications of charge movement in conducting spheres and how it can lead to non-intuitive results, such as similarly charged spheres attracting each other under certain conditions.
  • There is a debate about how to treat the charge distribution when calculating interaction energy, with some suggesting treating the total charge as concentrated at the center of the spheres.
  • Concerns are raised about the assumptions that can be made regarding the charge distribution, especially in the context of conducting spheres in external fields.
  • Some participants express uncertainty about the applicability of certain formulas in different scenarios, particularly when dealing with conducting versus non-conducting spheres.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for calculating electrostatic interaction energy, as there are multiple competing views regarding the treatment of charge distributions and the conditions under which certain formulas apply.

Contextual Notes

Limitations include the dependence on whether the spheres are conducting or non-conducting, the uniformity of charge distribution, and the potential complications arising from external fields affecting conducting spheres.

  • #31
Did you notice the bold letters?
 
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  • #32
I noticed them but discounted them because they were meaningless and substituted "electrostatic potential energy" in their place.
 
  • #33
If you re-read this thread, you may notice that in post #8, gneill said (paraphrasing), "with conducting spheres, it's complicated and not intuitive". That is an extremely strong hint that you cannot blindly apply the formula ##PE = k\frac{q_1 q_2}{r}## to the case of two charged conducting spheres.

What you could do would be to use the formula ##PE = k\frac{q_1 q_2}{r}## and integrate it over a distribution of charges on the two charged spheres, searching for the distribution that gives the lowest possible result. But that is more easily said than done.

Edit: There is a tricky piece in that process. We had assumed that you are concerned only with the potential energy of the two charged objects in relation to each other and not with the potential energy of each objects's charge distribution with itself. But the minimization process described above must take into account each object's own self potential energy. That means that the result depends on exactly what question you want answered.

Edit: Unless I am mistaken, it gets even worse in the case of more than two bodies because one might be faced with the possibility of multiple local minima. A naive optimization approach based on incremental relaxation may not lead to the global minimum.
 
Last edited:
  • #34

how he took interaction energy between charge q and a charged sphere
 
  • #35
gracy said:

how he took interaction energy between charge q and a charged sphere

Without looking at that video -- did he assume a conducting sphere? Or, instead, a sphere with a spherically symmetric charge distribution?
 
  • #36
he took uniformly charged shell
 
  • #37
gracy said:
he took uniformly charged shell
Which means that it has nothing to do with the question you asked in post #29.
 
  • #38
you mean we can use that formula for system of uniformly charged shell +charge q but not for system of uniformly charged sphere +charge q ?
 
  • #39
The distinction is between "uniformly charged" and "conducting". They are contradictory conditions if there is an external field.

Have you read responses #4, #6, #8 and #20?
 

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