How to find electrostatic interaction energy?

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To find the electrostatic interaction energy between charged spheres, the general method involves treating them as point charges located at their centers, provided the charge distribution is uniform and the spheres do not overlap. The potential energy can be calculated using the formula E = k(q1q2)/r, where r is the distance between the centers of the spheres. However, complications arise when dealing with conducting spheres, as their charge distribution can change in response to external fields, making the application of this formula non-trivial. It's essential to differentiate between uniformly charged non-conducting spheres and conducting spheres, as the latter cannot maintain a uniform charge distribution under external influences. Understanding these distinctions is crucial for accurately calculating interaction energies in electrostatic systems.
  • #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.
 
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  • #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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