# Static Electric Field

1. Aug 5, 2011

### azaharak

I've asked a similar question before in some way or another, I'm still troubled by it.

Technically there is no such thing as a static electric field: Take for instance a parallel plate capacitor

Argument #1: Electrons are always moving inside the conductor, they have a finite thermal energy, also skin depth penetration and electron electron interaction can also introduce motion, their movements can be averaged out in some quasi steady state at the macroscopic level to generate a "static field".

The movements of these electrons can also generate radiation of varying frequency dependent on their accelerations.

Argument #2: The electric field in QFT is mediated by virtual photons, real photons provide quanta of E/M radiation.

Here is where my question lies.

Can we say a "static electric" field is a superposition (fourier if you will) of different frequency photons that add up to a "static field"?

If so.....

Question 1:

A sufficient static field can "classically" ionize an electron from an atom. If the static field is a superposition of many frequencies, (and since ionization can only occur once you reached ionization frequency QM), is it the higher frequency terms in the superposition that form the static field the "culprits" that are actually doing the ionization?

If so.... then you should be able to ionize an atom with a low intensity static electric field, increasing the intensity would only increase the probability of higher order contributions ( you require more individual photons of many frequencies to reach the larger amplitude static field).

But then ionization should be irrelevant of how strong your classical static E field is, (a problem), just more likely with a larger field.

Question 2:
Would a static electron (not moving) emit an electric field at all? Or is the electric only mediated because it gives off radiation due to its thermal motion or other acceleration, for a static charge should not emit E/M radiation, only E "technically", and if its moving it will emit E and M.

Thank you very much to everyone.

2. Aug 5, 2011

### LostConjugate

If your super position is working destructively how can you ionize an atom. The total amplitude is 0.

3. Aug 6, 2011

### Bill_K

Ok, well you probably won't believe me either then.
The field that results from thermal motion is called black-body radiation. It's true that this will always be present, but is easily distinguished and treated separately from the static field being produced by the conductors. The fact that we can't achieve absolute zero and thereby totally eliminate the black body radiation doesn't mean there's anything wrong with the static field concept.
There's two important differences between real and virtual photons. One, a virtual photon does not have to obey the energy-momentum relation E = pc, or equivalently ω = ck. In particular a virtual photon can have ω = 0 even though k ≠ 0, and all the photons in a static field are of this sort. (The other difference concerns their polarization: they don't have to be transverse.)
This is called Stark ionization. It can happen when the electrostatic potential near an atom is lowered to the energy level of one of the bound electrons. The field that does this is static (zero frequency) and correspondingly the energy of the electron does not change.
Certainly.

4. Oct 8, 2011

### azaharak

When you reach absolute zero in a conductor, the electronics still have kinetic energy. Remember that the fermi level corresponds to the electrons in the highest energy. The fact that a conductor will conduct at absolute zero also implies that they are still moving.

so.... if these electrons are still in motion, how could they produce a static electric field ever?

Shouldn't any electric field ever emitted be in the form of radiation with a frequency?

Or is the problem trying to combine quantum and classical pictures. Is the electron just appearing randomly within the lattice and at that moment giving off the static E field?

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Or is it the actual field at a point is due to the coulomb electric field (which is static), plus the field due to radiation (the charges motion). When the fields are added together from all the electrons the radiative part averages out to zero, leaving the static field?