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- Thread starter hercules68
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Khashishi

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Gauss's law, is a specific case of Stokes's theorem.

http://en.wikipedia.org/wiki/Stoke's_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.

http://en.wikipedia.org/wiki/Stoke's_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.

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- #3

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Gauss's law is a specific case of Stoke's theorem.

http://en.wikipedia.org/wiki/Stoke's_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.

- #4

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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%27s_law_for_magnetism

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

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

[tex]\int_v \nabla\cdot \vec E dv'=\int_s \vec E\cdot d\vec s'=\frac Q {\epsilon}[/tex]

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:

[tex] \int_s \nabla X\vec B\cdot d\vec s'=\int_c \vec B \cdot d \vec l'= \mu I [/tex]

that relate current loop with field through the loop.

http://en.wikipedia.org/wiki/Gauss%27s_law_for_magnetism

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

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

[tex]\int_v \nabla\cdot \vec E dv'=\int_s \vec E\cdot d\vec s'=\frac Q {\epsilon}[/tex]

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:

[tex] \int_s \nabla X\vec B\cdot d\vec s'=\int_c \vec B \cdot d \vec l'= \mu I [/tex]

that relate current loop with field through the loop.

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- #5

Meir Achuz

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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.

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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:

[tex]\nabla X \vec E=-\frac{\partial \vec B}{\partial t}[/tex]

- #8

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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,

c

now,

c

USING ∇.j=-∂ρ/∂t and the fact that gradient of curl vanishes.

one gets,

∇.E=ρ/ε

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