# Does it take energy to create an electric field?

A charged particle (like an electron), creates an electric field surrounding it. But where does the energy to create the electric field come from? Does it come from the electron?

It seems that it must take energy to create the electric field since the electric field is an excited state of the electromagnetic field... The electric field is really just virtual photons

• If you think about it, as the electric field is intrinsic to the electron, you might instead ask: where does the electron come from? I don't follow the logic of your second statement, although I appreciate it's truncated. – user176049 Nov 23 '17 at 16:11
• What do you mean by the electric field is an excited state of the electromagnetic field? – Andrei Geanta Nov 23 '17 at 16:21
• If you consider the case of a capacitor, energy is needed to separate the two plates because they attract each other, and that energy manifests itself in form of electric field energy, which wasn't there initially. In this sense, it does take energy to create electric field which wasn't in a region initially. – Mitchell Nov 23 '17 at 16:29
• @Mitchell, the capacitor is a good example. Energy is needed to establish an electric field between the two plates. And the energy is provided in the charging procedure. When the capacitor is discharged, the energy gets released. – Zhuoran He Nov 23 '17 at 16:34
• There is a limitation in classical electromagnetism, though, because the total energy of a $1/r^2$ field integrated over the whole 3D space is infinity. So we know that below a certain distance scale $r_{\min}$ the concept of a classical Coulomb field should break down. – Zhuoran He Nov 23 '17 at 16:38

In QFT, this energy, which is associated with Coulomb field, works out to a correction to the electron rest mass.

The question of where the energy comes from is the same question as "where did the energy to make the electron come from?" I.E. If you want to make an electron, you need to make its electric field as well.

A charged particle (like an electron), creates an electric field surrounding it.

Creating something presupposes that it was not existing befor the creation. For a free electron this is not the case. The electric field of the electron is an intrinsic - existing independent from external circumstances - property of the electron.

But where does the energy to create the electric field come from? Does it come from the electron?

As said above, there isn’t any creation. A more usefulness question would be, to ask, could one extracted energy from this field.

An electron, in an excited state in some distance from a nucleus emits energy when falling back to the initial state. The emitted energy has to come from the mass or from the field. It is a consensus since over 100 years that the field is unchanging under any circumstance (intrinsic), even in bonded states in the atom. Following this view, one could not extract energy from the electric field of an electron.

It seems that it must take energy to create the electric field since the electric field is an excited state of the electromagnetic field... The electric field is really just virtual photons

You can produce electrons with there electric field (if you want, you can use the word create in this case) from a neutral subatomic particle. The neutron decay produces an electron, a proton - both with electric fields - and an electron-antineutrino.

Some words about the mentioned by you virtual photons. The electric field is considered as something without inner structure. Only for the description of interactions between the fields from two charged particles virtual photons are used.