Where does the energy disappear to?

[IPhO' 2008]

When we have electron and proton . Both electron and proton have electric field and electric field has energy.Inside the atom, there are electrons and protons but atom has no electric field.
Why the energy of the electric field disappear?

 

[Dale]

The energy of the fields becomes the binding energy of the atom i.e. during the binding work can be done on something else.

 

[IPhO' 2008]

Thank you so much.

 

[IPhO' 2008]

I have 1 question.
An energy of the electric field has a positive sign (+) . But the binding energy has a negative sign (-).Why?

 

[Dale]

Remember when you first learned about gravitational potential energy that you learned that you could set your h=0 reference point anywhere you wanted, and when you first learned about voltage that you could set your V=0 reference point (ground) anywhere you wanted. This is because only differences in energy have any physical significance and so energies are always implicitly or explicitly with reference to some specified reference state which is arbitrarily given a value of 0 energy. In the case of binding energy the reference state is the unbound constituents, i.e. infinite separation between the various components. The fact that it is negative reflects the fact that e.g. work can be done in bringing an electron and a proton from far away to form a hydrogen atom.