Ammah

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. 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.

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