Proof of Gauss's Law: Connecting Flux and Closed Surfaces

[dextercioby]

I wonder, if columb's law didn't exist, could gauss derive gauss' law?

We don't know that.If Einstein had not existed,would we have gotten today the theory of relativity...??

My teacher derived gauss' law by using columb's law.

For ELECTROSTATIC FIELDS he can do that...Though i'd do it the other way around...

I feel strange that columb's law is wrong when the speed is comparable to c,

Because DYNAMICAL FIELDS (i.e.varying in space and time) have nothing to do with Coulomb's law...

but why gauss' law which is derived from columb's law is valid?

It is,BECAUSE GAUSS'S LAW IS MUCH MORE GENERAL...

I know things like lorentz contraction but logically, if premise is wrong, how can a conclusion drawn can be true?

And what would be the premise...??

Daniel.

 

[Kelvin]

I mean: we start with columb's law and derive gauss' law. if columb's law is wrong in some cases, then anything derived from it should be wrong in those cases. but the fact is gauss' law is always true but columb's law is not. that's strange

 

[dextercioby]

I mean: we start with columb's law and derive gauss' law. if columb's law is wrong in some cases, then anything derived from it should be wrong in those cases. but the fact is gauss' law is always true but columb's law is not. that's strange

I see what you mean...Well,each of them has a range,a domain of applicability.The one of Gauss's law is simply LARGER,as it includes the domain of Coulomb's law...Nobody ever said that Coulomb's law would be wrong...It is VERY CORRECT,but only in it's domain of applicability,which is STATIC FIELDS.In this case,electrostatic...

It's as simple as that...Maybe for me...

Daniel.

 

[Doc Al]

I mean: we start with columb's law and derive gauss' law. if columb's law is wrong in some cases, then anything derived from it should be wrong in those cases. but the fact is gauss' law is always true but columb's law is not. that's strange

If the only justification for Gauss's law were Coulomb's law, then there would be a gap in explaining how it could apply where Coulomb's law does not. But that's not true.

Also, beware the fallacy of "denying the antecedent":

if p, then q.
not-p;
therefore not-q.​

 

[Haelfix]

Incidentally Gauss's law is not always true, nor is the rest of Maxwell's equations or the Dirac equation. One of the great successes (or downfalls in some peoples minds) of QFT is that it outputs its domain of validity. The theory is simply inconsistent past that point.

For instance, QED and Gravity are clearly wrong as field theories at very high energies, but for different reasons. (Landau pole and renormalization flow respectively)