How to find electrostatic interaction energy?

[gracy]

Did you notice the bold letters?

 

[jbriggs444]

I noticed them but discounted them because they were meaningless and substituted "electrostatic potential energy" in their place.

 

[jbriggs444]

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.

 

[gracy]

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

 

[jbriggs444]

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?

 

[gracy]

he took uniformly charged shell

 

[jbriggs444]

he took uniformly charged shell

Which means that it has nothing to do with the question you asked in post #29.

 

[gracy]

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 ?

 

[jbriggs444]

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?