Revisit the Old Question of The Energy of The Electric Field

Suppose there is charge Q on a metallic sphere of radius R and the electric field generated by the charge at the distance r is given by Q/(4*pi*e0*r). Now the question is "where is the energy located due to this charge?". The conventional wisdom generally conveyed in the text books is that the energy is in the entire space of the electric field created by the charge Q.

This misconception has created a huge misunderstanding in the physics of electricity and magnetism. In fact, unless there is a separate electric charge nearby or in the entire space around this source charge Q, there is no EM energy in the space(outside of the conductor) due to this charge Q. Instead, the energy is within the charge Q inside the metallic sphere itself repelling each other as the electrons or the ions exert the force against each other as individual entities.

In the case of the concentric spherical capacitor, the electric field in between the two shells comes only from the charges in the inner sphere. However the energy stored in this concentric configuration comes from the attractive force between this electric field and the charges in the outer sphere. So there is no increase in the strength of the electric field between the shells due to the charges in the outer sphere. It is only the additional electrostatic energy in the entire configuration that springs up.

After all, it requires two spatially separated charges in space to create an electrostatic potential energy. So, if two electrons are spatially separated in space, they will create the electrostatic potential energy.

Now the serious question is if the two electrons can be considered to be in the three dimensional space if they are within the voluminous metal(how small it may be), which is the fundamental question that has never been asked seriously in physics.

Suppose there is a thin straight copper wire of length L.

Now, let's put two electrons in this copper wire. Where will these two electrons be located once they are put inside the conducting wire?

Remember the interior of the metallic conductors are free zone for the electric charges within the physical boundary according to our well established Solid State Physics. There is no restriction of the movement of the charges inside the metal. So, it is natural to expect that the two electrons will tend to be separated as far away from each other as much as possible. So the answer to the question regarding the location of the two electrons will be "far at the end of the wire".

One electron in one end of the wire and the other on the other end of the wire. The electric field created by these two electrons is very complex and the analytic solution will be next to impossible and so is the case with the cylindrical configuration. This is the reason the concentric spherical capacitor becomes such an ideal example to prove the case of the capacitor anomaly.

Now the next question is "Is there any electrostatic potential energy between these two electrons?" Yes there should be.

So the energy of the electric charge Q located inside the metallic sphere is not in the space outside of the metal. The energy is inside the metal in the form of the electrostatic repulsive force.

This sounds like an obvious and mundane statement. But the implication of this statement is in the fact that we can not dismiss the self energy inside the charged capacitors which has been out of the physical reality in our conventional theory of electricity and magnetism for the last 160 years of the human civilization.