# I What propagates changes of Coulomb force?

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1. Dec 3, 2016

### sweet springs

Hi.

Say a positive charge is at (x,y,z)=(0,0,0) at t<0 then (1,0,0) at t>0.
Electric field at (x,y,z)=(l,0,0) is (a,0,0) at t<l/c then (b,0,0) at t>l/c thus a<b.

With time delay of l/c, what propagates from (x,y,z)=(0,0,0) to (l,0,0) ?
I do not think it is electromagnetic wave because it is not transverse but longtitudinal.

Electromagnetic wave by accerelation necessary for charge position change has nothing to do with my question, I guess.

Not charge position but charge velocity change causes similar propagation question.

Best

2. Dec 3, 2016

### Delta²

It is a kind of longtitudinal E-wave BUT it does not carry energy (the poynting vector for this wave is zero, because the resulting magnetic field doesn't cooperate with this longtitudinal wave).

Last edited: Dec 3, 2016
3. Dec 4, 2016

### Staff: Mentor

The specifics of this question are not answerable because it presupposes an unphysical movement.

However, with appropriate tweaking you could get a closely related question which would be physical. The answer to the closely related question would be the Lienard Wiechert potentials:

https://en.m.wikipedia.org/wiki/Liénard–Wiechert_potential

4. Dec 4, 2016

### sweet springs

Thanks Dale. The linked document of your recommendation says, "The force on a particle at a given location r and time t depends in a complicated way on the position of the source particles at an earlier time tr due to the finite speed, c, at which electromagnetic information travels."

My question should be translated to : What substance carries this "electromagnetic information" ?
EM wave carries information as radio or television do. Are there similar substance following a wave equation of speed c that carry electro magnetetic information used in Liénard–Wiechert potential?
Best

5. Dec 4, 2016

### Staff: Mentor

Why should a substance be required? The aether is superfluous.

The Lienard Wiechert potential is a solution to Maxwells equations, just like any other classical EM field.

6. Dec 4, 2016

### sweet springs

Dear Dale.
Your answer to my question "what propagates electromagnetic information e,g, displacement of distant source charges with speed of c and how does it?" was "the LW potential that satisfies Maxwell equation". I still cannot leave from idea that something other than EM waves keeps radiated from the source charges with speed of light telling the information of the charge position. Is the LW potential reduced to microscopic relation explicitly containing c? Is the LW potential is unchanged if EM media is inserted between ? I keep thinking about it by myself and ask again if it makes sense. Thank you so much for now.

7. Dec 4, 2016

### Staff: Mentor

Please review the forum rules about personal speculation before pursuing this line of discussion here.

You can read the derivation of the LW potential right there on the Wiki page, and in any halfway decent textbook. Including the online ones from MIT and UT.