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- Thread starter LucasGB
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Gauss's Law from magnetism is as it is because a magnetic monopol has never been observed. Is one is observed, the equations will have to change.

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OK, sort of a semantics issue.There are no proofs in physics. The "proof" you cite is a proof that Coloumb's law and Gauss's Law are equivalent.

I know that. I would like to know, as you put it, if there is a way of rigorously showing whether Ampere's Law and Gauss's Law are equivalent.Gauss's Law from magnetism is as it is because a magnetic monopol has never been observed. Is one is observed, the equations will have to change.

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I see, but that's not a formal proof. The proof for Gauss's Law for electric fields is quite rigorous and general.

- #6

Born2bwire

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As for Gauss' Law for magnetism, that is simply derived from the fact that we currently do not allow for magnetic monopoles. The basic unit for magnetic fields is the dipole.

Maxwell's equations are the basic equations for classical electrodynamics. Coupled with Lorentz force you have the groundwork for it all. So there is no proof for these equations alotted using classical electrodynamics because electrodynamics is derived from them in the first place. They were primarily derived via experimentation. If you go up to quantum electrodynamics, then we can find more basic theories that predict Maxwell's equations.

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PS.: I know you can use the field line arguments, but I think field lines are a rather crude way of proving things.

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jtbell

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If there is charge at a point, then the divergence of the associated field is nonzero at that point; if there is no charge at that point, then the divergence of the field is zero at that point.

If there is non "magnetic charge" anywhere, then the divergence of B is zero everywhere, and so the flux of B through any closed surface must be zero.

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