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I'm trying to develop simple computational tools to study the dynamics of electric particles. I asked a question about my implementation of particle dynamics using differential equations derived from Coulomb's law.

On Computational Science SE, I was told my equations are correct, but on StackOverflow I was told Coloumb's Law doesn't hold for particles in motion.

This material is not covered in my physics class and due to the special case (relative to what I have learned) of particles in motion I am hoping someone can explain what the kind answerer on Stackoverflow might have meant?

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Yes it is applicable because u see as u move then ur distance changes at a constant rate so u can take derivative and also as u may be knowing about relativity so there would be relative transformations ie average difference so it is applicable Because it is not proportional to motion in any way it depends on distance and charge value only So at any small instinct of time u can calculate the force and u sum up all the rate of changes taking place