# Propagation of static electric field

• Interested2

#### Interested2

At what speed does a change in a static electric field propagate through a medium? I understand that through a vacuum it's the speed of light, but through a medium such as a conductor or insulator how fast will this change propagate? In classical electrodynamics, how do we model
the propagation of this change - as an electromagnetic wave? If so, is there anything that
can slow or absorb the propagation of this electromagnetic wave carrying the information of the change?

For a concrete example, suppose I move a charge on one side of a wall to a new position on the same side of the wall. On the other side of the wall I wish to determine how long it takes for the information about the change in charge position to be a detectable change in the electric field
on the other side of the wall. I imagine that any speed of propagation different than the speed
of light would be determined by the wall medium and the frequency of the electromagnetic wave propagating the change? If the acceleration of the charge during the move is small, does that
mean a low frequency EM wave which would not normally be slowed by the wall at all?

Also, a related question which probably draws in quantum electrodynamics - once the charged
particle is moved and remains in place at its current position for some time, how is it that the
space on the other side of the wall contains the information about the static electric field there?

Changes in the electric field will propagate at the signal velocity, which is the speed of light divided by the index of refraction. See https://en.wikipedia.org/wiki/Wave_propagation_speed

By definition, a static field doesn't propagate. Rather, it is the changes in the field that propagate (as a wave).

Changes in the electric field will propagate at the signal velocity, which is the speed of light divided by the index of refraction. See https://en.wikipedia.org/wiki/Wave_propagation_speed

By definition, a static field doesn't propagate. Rather, it is the changes in the field that propagate (as a wave).

Thanks for your response. Is it possible that the em wave generated by the acceleration of the source charge could be absorbed by the wall (if it's frequency were in the visible range for example) and then the information about the change to the static electric field would never be received on the other side?
Also, since the index of refraction changes with the frequency of an em wave,
do we expect that typically the index of refraction will be approximately 1 for a slowly accelerated source charge so the em wave generated has a long wavelength?

I'm also still interested in understanding what it is about the space on the other side of the wall that's been altered by the presence of the static electric field. In other words, long after the change in the position of the source charge, something lingers on the other side of the wall that's detectable as an electric field. What is it?

"I'm also still interested in understanding what it is about the space on the other side of the wall that's been altered by the presence of the static electric field. In other words, long after the change in the position of the source charge, something lingers on the other side of the wall that's detectable as an electric field. What is it?"

The electric field lines will have shifted ... so for example, you may be able to locate the source charge by the new distribution of the electric field.

If the source moves and doesn't come back to the starting spot, the wave will have some really low frequency components. It is analogous to a step in a DC value. If you take a Fourier transform, then it will include some low frequency parts, which you can't really filter out unless you block the signal altogether.

The electric field is pretty fundamental, so there's no satisfactory answer for what the electric field is other than what it does.

A static field cannot propgate, because in the static case all fields are time independent. So it's a contradiction to say a static field would propagate somehow.

Static fields, by definition, don't propagate. If you have an initially static field, and a change occurs, you no longer have a static field. You now have a regular electrodynamic field and the change propagates out at the speed of light in the material just like all propagating electrodynamic effects. An electromagnetic wave is just one type of propagating effect (it tends to be the most far-reaching effect as waves are self-propelling). Inductive and capacitive effects can also propagate into empty space, but they die off more quickly. Any time you accelerate a charge, you potentially create conductive (near-field), inductive (mid-field), and radiative (far-field) disturbances that spread out through space. Which one dominates depends on how close your observation point is to the source compared the wavelength of it's movement.