Sunday 12 May 2019

electrostatics - Coulomb's law and Gauss' Law


Which of these laws is more fundamental or forms the basis of electrostatics? I started off with Coulomb's law and then I studied Gauss' law. I was wondering which one is more universal?


My professor derived Gauss' law using Coulomb's law but didn't do it the other way, so is Coulomb's law more fundamental? And can Gauss' law be used to prove the other?



Answer




Because Gauss's law applies for both moving and stationary charges, while Coloumb's law applies only for stationary charges, Gauss's law can be considered more fundemental. This is why Gauss's law is one of the four Maxwell equations. The derivation of Gauss's law from Coloumb's law only works for stationary charges; for moving charges the derivation is invalid yet Gauss's law still holds. However, Gauss's law along with the information from Maxwell's third equation that the $curl E = 0$ for stationary charges (since then $B$ will be constant), can be used to derive Coloumb's equation. In short, Gauss's law can be considered more fundemental because it applies to both stationary and moving charges, while Coloumb's law applies only to stationary charges.


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