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It is said that atoms with the same number of electrons as protons are electrically neutral, so they have no net charge or net electric field.
A particle with charge cannot exist at the same position and time as another; an electron cannot be positioned at the location of a proton, at any single point in time, without displacing the proton.
Assuming the above is correct, how can a single electron cancel out the entire electric field of a proton? I don't think there is any position a single electron can take, that would result in the entire electric field of the proton being cancelled out - it seems like it will always be only partially cancelled out.
For simplicity, let's look at a single hydrogen atom that we consider to be electrically neutral. It has one proton and one electron, so at any single point in time, there will be a partial net electric field (because the electron will never be in a position where its field can completely cancel out the proton's field), and the electric field from the electron will only cancel out part of the field from the proton. So at this single point in time, there will be a net electric field from the proton. So how can this atom be considered to be electrically neutral, with no net charge or field?
Here is a graphical representation of two sources of electric fields interacting:
As you can see from the image, only part of the (equal but opposite) electric fields produced by both sources are affected by each other. To have the field from one source cancel out the other, completely, we would need to position the sources in the same location, at the same time, which is not possible.
I know that I'm wrong, so please correct me.