Gauss's law in electrodynamics

[bigerst]

most(or all) proofs i have seen of gauss's law is based on coulumb's law. however coulumb's law is based off of electrostatics which certainly does not hold in electrodynamics. however gauss's law is used extensively in electrodynamics. is gauss's law derived otherwise or is it just a law like an axiom?

thanks

bigerst

 

[andrien]

Gauss law is,
∇.E=ρ/ε₀ .now in most general form
E=-∇ψ-∂A/∂t, if you put it into above you get,
-∇²ψ-∂/∂t(∇.A)=ρ/ε₀...(1)
now using lorentz gauge(more preferable) we have ∇.A=-1/c² ∂ψ/∂t
if you will put it into (1) you will get the the general form of potential equations.this proof starts with gauss law but the converse can also be done in order to arrive at gauss law.here it does not refer to any coulomb law,and so it is more general.

 

[Meir Achuz]

Although EM started with Coulomb historically, the complete classical theory is based
on the four Maxwell equations. Applying the divergence theorem to Maxwell's div D equation gives Gauss's law. Coulomb is the electrostatic case.

 

[bigerst]

alright thanks :)

 

[sardar]

Gauss's law in electrodynamics is a fundamental principle that describes the relationship between electric charges and the electric field they create. It states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of the medium.

The proof of Gauss's law in electrodynamics is indeed based on Coulomb's law, which describes the force between two point charges in a vacuum. However, this does not mean that Gauss's law is only applicable in electrostatics. In fact, Gauss's law is a general law that applies to all types of electromagnetic fields, including time-varying fields.

The reason why Gauss's law is used extensively in electrodynamics is because it is a very useful tool for solving problems involving electric fields. It allows us to calculate the electric field at a point without having to consider the individual contributions of all the charges that may be present in the field. This is particularly useful in cases where there are a large number of charges or a continuous charge distribution.

Gauss's law is not derived from first principles in electrodynamics, but rather it is considered a fundamental law or principle. It is based on experimental observations and has been verified through numerous experiments. Therefore, it can be considered as an axiom in the sense that it is accepted as a fundamental truth without needing to be proven.

In summary, Gauss's law is a fundamental principle in electrodynamics that allows us to relate the electric field to the distribution of charges. While its proof is based on Coulomb's law, it is applicable in all types of electromagnetic fields and is a valuable tool in solving problems in electrodynamics.