Is There a Gauss' Law for Gravitation?

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There is a Gauss's law for gravitation, expressed as Φ = 4πG * Menclosed, which parallels the electric version. For magnetic fields, Gauss's law exists as part of Maxwell's Equations, stating that the net magnetic flux through a closed surface is zero, indicating the absence of magnetic monopoles. Magnetic field lines can intersect only at points where the field strength is zero, leading to questions about the existence of magnetic monopoles. Current theories, including those referenced in introductory physics textbooks, suggest that magnetic monopoles might exist, but none have been discovered. The inclusion of magnetic charge in Maxwell's equations introduces symmetry but creates inconsistencies with magnetic potential.
aniketp
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hello,
I was wondering if there is an equivalent gauss' law for gravitation like:
\Phi=4\piG*Menclosed
any help would be appreciated. Thank you.
 
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Absolutely. See: "[URL law for gravity[/URL]
 
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thank you. but do magnetic fields have any such law? intuitively, i am inclined to say no,
because magnetic field lines can cross...but i would like a rigorous proof
 
aniketp said:
but do magnetic fields have any such law? intuitively, i am inclined to say no,
because magnetic field lines can cross...but i would like a rigorous proof
Yes, there's a Gauss's law for magnetic fields--it's one of Maxwell's Equations. Since there are no magnetic monopoles, it is rather simple: http://en.wikipedia.org/wiki/Gauss%27_law_for_magnetism" .

Magnetic field lines can cross only where the field is zero.
 
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I'm curious as to why there isn't any magnetic monopoles. The freshman physics textbook I read for my intro physics course says that current theory (I think it was Serway) does predict the existence of magnetic monopoles.
 
No one seems to have found any magnetic monopoles. By including magnetic charge and magnetic current terms in Maxwell's equations you postulate magnetic charge. It brings some (anti-) symmetry to the equations, but this is inconsistence with the magnetic potential.
 
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