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If two point charges $q1$ $q2$ of same charge approach from infinity and we want to know work done in some distance between q1 and q2. Can we just integrate Coulombs law? Or is this increasing force between charges some how ”contained” in electric field of q2 and just solve potential difference?

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  • $\begingroup$ For two point charges the negative of the potential energy is the quantity that you are looking for. Since this by definition is the amount of work done by the electric field in moving a charge from infinity to its location $\endgroup$ Commented Apr 12, 2023 at 22:15

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Your question is not so clear. If I got you right, total work done to bring those two charges at some distance from infinity will be same as chane in the electrostatic potential energy of system of those two charges. You can either integrate using $F \cdot \mathrm{d}s$ or calculate ΔP.E. using formula, both will give the same result i.e. $K q_1q_2/r$. You can better learn more about Coulomb's Law here with interactive demo.

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