# Is the work done in separating electron from neutral atom stored in its electric field?

This particular thought crossed my mind while deriving the expression for energy density of electric field in parallel plate capacitor.

Energy density= $$\frac12 \epsilon E^2$$

It appears to me that initially when the plates were touching, the interface atoms were neutral.When we slowly pull the plates apart, electrons get separated from the interface atoms creating negative charge on one plate and positive on the other.

The work done in separating the plates is stored as the energy of the field of the capacitor.If we take one plate to infinity,we get electric field due to a single charged plane surface and the work done in taking the plate to infinity is stored as the energy of this field.

Anyways my questions are :-

1. Consider a single atom in place of the capacitor.Let us apply a force on the electron to separate it from the nucleus.Let us take this electron to infinity slowly.We are left with a positive nucleus.Will the work done in taking the electron to infinity be stored as the electric field of the positive nucleus?

2. In case any of my assumptions or arguments is incorrect,please provide proper rectification.

When your original "single atom" system changes to an "electron and ionised atom" system the electric potential energy of the system increases.

• Sir thank you for answering . As it appears to me ,the only external force appearing on the system is the force provided by agent to take electron to infinity.Would it be reasonable to claim that the increase in energy of the system is all because of the work done by agent.Secondly I am under the belief that this increase in energy is stored completely as energy of the field.Is my belief correct? Jul 24, 2020 at 18:32
• The external work done in separating the charges results in the potential energy of the system increasing. The energy is stored in the field. Jul 24, 2020 at 18:43

When you separate the electron from the nucleus, you are doing positive work on the electron + nucleus system, which is stored as electrical potential energy. Indeed, the electrical potential energy of an ionized atom (i.e. with the electron removed) is higher than that of the unionized atom.