- #1

Rudipoo

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Hi, can you derive Gauss's Law without using Coulomb's Law? If so, how?

Thanks

Thanks

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- Thread starter Rudipoo
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- #1

Rudipoo

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Hi, can you derive Gauss's Law without using Coulomb's Law? If so, how?

Thanks

Thanks

- #2

Troels

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Hi, can you derive Gauss's Law without using Coulomb's Law? If so, how?

Thanks

That depends on what you mean by Gauss Law: There is the Gauss law in matematics, also known as the Divergence Theorem, and then there's is Gauss law in electrodymanics, which is a special case of the Divergence theorem applied to the vectorfunction [tex]\mathbf{\vec F}=kr^{-2}\mathbf{\hat r}[/tex] (which essentally is Coulomb's Law)

The former can be derived mathematically, but that you should be able to find in virtually any undergraduate math textbook.

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- #4

Marco_84

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Well the first principal is that we are trying to solve laplace eqn assuming isotrpy of the universe. so you finf that in a 3-dimensional world, the correct potential is V=-k/r.

Try everybody to solve (with distribution theory it is easier) D(f)=delta. Where D is the laplacian and delta is Dirac one. Physically its like to imagine a point charge/mass genarating the field...

you can figure out also the dipendence of the potential versus the space dimension, for example if i remeber righ, if we were leaving in flat land the electric potential would have been v=Cost*log(r)... somethinh like that.

I think you may apply the same result to the gravitation potantial sinc the mathematical nature is the same.... y

- #5

Meir Achuz

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Maxwell's equation[tex]\nabla\cdot\{\vec D}=4\pi\rho[/tex] can be taken as a starting point for electrostatics, rather than Coulomb's law. Then Gauss's law follows from putting this into the divergence theorem.Hi, can you derive Gauss's Law without using Coulomb's Law? If so, how?

Thanks

- #6

Rudipoo

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Thanks very much.

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