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Given an ensemble of charges, how to derive the electrostatic potential at any point due to the ensemble?

For example, consider six point charges, each approaching the origin along the three co-ordinate axes. What would be potential say $V(a_o)$ if they are all at some distance $a_o$ from the origin?Similarly, what be the potential at the center of the cube when there are eight-point charges at each of its vertices?

How do you approach such problems in electrostatics?

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  • $\begingroup$ compute each one and add $\endgroup$ – Wolphram jonny Feb 20 at 16:26
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Electrostatic potential is a scalar quantity. If you want to find the potential at the centre of any surface. Find the potential at that point due to each and every charge and add them all together. The potential at that point becomes zero if opposite charges are involved.

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  • $\begingroup$ But how do I account for the collective outcome, say repulsion between any two charges. $\endgroup$ – EverydayFoolish Feb 21 at 6:46
  • $\begingroup$ We are only talking about electrostatics - assuming that the charges are fixed at that moment in time. Since we are only concerned of finding the net potential at a point (there may or may not be a charge at that point), we only have to find the individual contribution of potential. We need not take into consideration the nearby attractions or repulsions or anything else. I hope it is clear ... $\endgroup$ – KV18 Feb 21 at 9:19

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