# Gauss's law for electrodynamics

by hercules68
Tags: electrodynamics, gauss
 P: 10 Gauss's law can be proved qualitatively by proving that the field inside a charged closed surface is zero. However Maxwells' equations says that gauss's law holds true even for electrodynamics. how can this be verified experimentally? Thanks in advance !
 P: 743 Gauss's law, is a specific case of Stokes's theorem. http://en.wikipedia.org/wiki/Stoke%27s_theorem edit: I interpreted Gauss's law to mean the divergence theorem, which is a mathematical statement. My mistake; that would probably be called Gauss's theorem.
P: 532
 Quote by Khashishi Gauss's law is a specific case of Stoke's theorem. http://en.wikipedia.org/wiki/Stoke%27s_theorem
Gauss' law is a law of physics that relates electric charges to electric fields.

Stoke's theorem is a purely mathematical statement, like the commutative property of addition.

P: 3,795

## Gauss's law for electrodynamics

I am not good in definitions but I did look into Gauss Law. I really don't see the relation of Stokes and Guass. Even in Guass law for magnetism:

http://en.wikipedia.org/wiki/Gauss%2..._for_magnetism

It only said $\nabla \cdot \vec B = 0\;$ where it states there is no mono magnetic pole.

Guass law is mainly used in Divergence theorem where $\nabla \cdot \vec E=\frac {\rho_v}{\epsilon}$ Where:

$$\int_v \nabla\cdot \vec E dv'=\int_s \vec E\cdot d\vec s'=\frac Q {\epsilon}$$

http://phy214uhart.wikispaces.com/Gauss%27+Law

http://phy214uhart.wikispaces.com/Gauss%27+Law

The only one that remotely relate magnetic field through a surface is:

$$\int_s \nabla X\vec B\cdot d\vec s'=\int_c \vec B \cdot d \vec l'= \mu I$$

that relate current loop with field through the loop.
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P: 1,834
 Quote by hercules68 Gauss's law can be proved qualitatively by proving that the field inside a charged closed surface is zero. However Maxwells' equations says that gauss's law holds true even for electrodynamics. how can this be verified experimentally? Thanks in advance !
1. The charged closed surface must be a conductor.
2. I don't know of any direct experimental test for a time varying E field.
The fact that its inclusion in Maxwell's equations leads to many verifiable results is an indirect proof of its general validity.
 P: 925 I just want to say that gauss law follow immediately from maxwell's fourth eqn when combined with continuity eqn for charge density.(just take the divergence)
 P: 3,795 I can't think of any direct prove on Guass surface with varying charge inside. But I cannot see anything wrong that the total electric field radiate out of a closed surface varying due to vary charge enclosed by the closed surface still obey $\int_s \vec E\cdot d\vec s'$. The difference is with varying charges generating the varying electric field, a magnetic field MUST be generated to accompany the varying electric field according to: $$\nabla X \vec E=-\frac{\partial \vec B}{\partial t}$$
P: 925
 Quote by andrien I just want to say that gauss law follow immediately from maxwell's fourth eqn when combined with continuity eqn for charge density.
Let us see,
c2(∇×B)=j/ε0+∂E/∂t
now,
c2{∇.(∇×B)}=∇.j/ε0+∂(∇.E)/∂t
USING ∇.j=-∂ρ/∂t and the fact that gradient of curl vanishes.
one gets,
∇.E=ρ/ε0

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