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Gauss's law for magnetism is one of Maxwell's equations, the four equations that underlie classical electrodynamics. It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not exist. Rather than "magnetic charges", the basic entity for magnetism is the magnetic dipole. Gauss's law for magnetism can be written in two forms, a differential form and an integral form. These forms are equivalent due to the divergence theorem.
Note that the terminology "Gauss's law for magnetism" is widely used, but not universal.The law is also called "Absence of free magnetic poles". (or some variant); one reference even explicitly says the law has "no name".
It is also referred to as the "transversality requirement" because for plane waves it requires that the polarization be transverse to the direction of propagation
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