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When we calculate the expression for electric potential due to a charge at a point we assume it to be equal to the( work done by an external force in bringing test charge from infinity to the point/ the test charge ). We assume that the external force is acting on the test charge in such a manner that it is equal and opposite to the conservative force that is acting on the charge. BUT WHY IS THIS NECESSARY? why won't we be able to make the calculation if the test charge accelerates?? I have have heard that this is to make sure that the kinetic energy does not change in the process, but why don't we want it to change ?

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  • $\begingroup$ Accelerating charges produce electromagnetic radiation $\endgroup$
    – ChemEng
    Mar 26, 2022 at 17:35

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BUT WHY IS THIS NECESSARY?

First of all potential energy is defined only for systems (combination of two or more interacting particles).

Keeping this fact in mind,

Note that we only want to calculate the potential energy of the system (charge system) i.e. its pure potential energy (total work it can do wrt it's PE)

If an accelerating test charge is brought form infinity to the desired point then the system will also have Kinetic Energy, thus overall ability to do work of the system formed will be different (somewhat increased) from what we want. We want to calculate only potential energy of the system and potential energy depends only upon configuration of the system.

Therefore we assume such a condition that at each and every point equilibrium is maintained (between external and internal con. force), thus no Kinetic energy (charge is moved very very slowly).

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