# In 2 point charge system, the work done in bringing the first charge to desired configuration shouldn't be zero?

In the derivation of potential energy of two-point charge system, we define the potential energy of the system as the work done in giving both charges to their present configuration, and while doing the derivation, we assume the work done in bringing the first charge to its desired configuration to be zero, but I think it shouldn't be like that. Why is the force = qE acting on the first charge due to the second charge being ignored while calculating the work done in bringing the first charge to the desired configuration?

• If both charges are initially at infinity, and far from each other, there is negligible E-field on charge 1 as it is brought to the desired location.
– Puk
May 28, 2023 at 21:47
• Sir I think I am wrong in the basic definition, the definition that I mentioned is correct?
– user363737
May 28, 2023 at 21:59
• Your definition is fine. The point is while you are bringing in charge 1, there is no force against which you must do work, because charge 2 is so far away as this is happening and its force on charge 1 is negligible.
– Puk
May 28, 2023 at 22:04
• Sir does that mean I have to place first charge at - ∞ and second charge at + ∞, and thank you so much for helping me with so much patience.
– user363737
May 28, 2023 at 22:21
• That's one way to do it. Both charges could also be at $+\infty$ and still be infinitely far apart. Note also that space has 3 dimensions so there is a lot of room "at infinity".
– Puk
May 28, 2023 at 22:47