Gauss' Law for spherical shell vs Coulomb's law, regarding reativity

[Ammah]

Shalom

We are used to hearing that Coulomb's law doesn't settle with the relativity principle that nothing moves faster than the speed of light, in the sence that it embeds 'Action in a Distance'. Meaning that if somthing changes in r1 at time t1, and we write the law for any t before t1+(|r1-r2|/c), (r2 is the where the test charge is) then the law doesn't represent reality, because the 'knowledge' about the change hasn't reached r2 yet.

And it is often said that Gauss' law fixes that because of its local nature. But what I can't figure out is:

(1) how does one settle that with one of the famous implementations of Gauss' law, the one for a spherical shell with a charge in its center. When we use the Divergance law to find the same form of Coulomb's law, resulting from Gauss' Law. How does this implementation not violate the relativity principle, violated by Coulomb's law (nothing travels faster than the speed of light)?

(2) another related question is how does Gauss' law, or Maxwell's laws express that the information about the change in r1 travels at speed c? (other than the wave equation please, and other than being local). I just can't see how Gauss' law shows that principle, which Coulomb's law couldn't.

And I would really love to hear from anyone who might have a better vision and be able to see what I seem to be missing here.

Thank you in advance

[swansont]

Electrostatics problems ignore this because they are static — there is no change occurring. It's implied that the system has existed for a long enough time that the finite c is not an issue.

 

If you have a varying field it's electrodynamics, and you have to include retarded potentials http://en.wikipedia.org/wiki/Retarded_potential

[timo]

Gauss' law does not fix the perceived problem with action at a distance. You probably mixed up something (e.g. Gauss' law with Maxwell equations).

Edited June 25, 2013 by timo

[Ammah]

Gauss' law does not fix the perceived problem with action at a distance. You probably mixed up something (e.g. Gauss' law with Maxwell equations).

I'm under the impression that the differential form of Gauss' law does fix it, just by being local.

you're welcome to correct that impression, if you feel I'm wrong.

 

Electrostatics problems ignore this because they are static — there is no change occurring. It's implied that the system has existed for a long enough time that the finite c is not an issue.

 

If you have a varying field it's electrodynamics, and you have to include retarded potentials http://en.wikipedia.org/wiki/Retarded_potential

thank you.

 

I need you to clarify a bit, if possible. I know Coulomb's law deals with electrostatic, but Gauss' law doesn't. the field and the charge are both dependent on location and time. That is exactly why I don't understand how it is implemented for a spherical shell in a way that results in the same form of a law just like Coulomb's law, while gauss' law isn't supposed to be limited to electrostatic cases.

[timo]

you're welcome to correct that impression, if you feel I'm wrong.

Doing so happened to be the purpose of the post you replied this to. You are free to disregard the statement of a random stranger on the Internet, of course.