Gauss's law for magnetism
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This article is about Gauss's law concerning the magnetic field. For analogous
laws concerning different fields, see Gauss's law and Gauss's law for gravity.
For Gauss's theorem, a mathematical theorem relevant to all of these laws,
see Divergence theorem.
In physics, Gauss's law for magnetism is one of the four Maxwell's
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
[1]
vector field. It is equivalent to the statement that magnetic monopoles do not
exist. Rather than "magnetic charges", the basic entity for magnetism is
[2]
the magnetic dipole. (If monopoles were ever found, the law would have to be
modified, as elaborated below.)
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.
The name "Gauss's law for magnetism" is not universally used. The law is
[1]
also called "Absence of free magnetic poles"; one reference even explicitly [2]
says the law has "no name". It is also referred to as the "transversality
[3]
requirement" because for plane waves it requires that the polarization be
[4]
transverse to the direction of propagation.
Differential form[edit]
The differential form for Gauss's law for magnetism is:
where ∇ · denotes divergence, and B is the magnetic field.
Integral form[edit]
Definition of a closed surface.
Left: Some examples of closed surfaces include the surface of a sphere, surface of a torus, and surface of a cube. The magnetic
Jump to navigationJump to search
This article is about Gauss's law concerning the magnetic field. For analogous
laws concerning different fields, see Gauss's law and Gauss's law for gravity.
For Gauss's theorem, a mathematical theorem relevant to all of these laws,
see Divergence theorem.
In physics, Gauss's law for magnetism is one of the four Maxwell's
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
[1]
vector field. It is equivalent to the statement that magnetic monopoles do not
exist. Rather than "magnetic charges", the basic entity for magnetism is
[2]
the magnetic dipole. (If monopoles were ever found, the law would have to be
modified, as elaborated below.)
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.
The name "Gauss's law for magnetism" is not universally used. The law is
[1]
also called "Absence of free magnetic poles"; one reference even explicitly [2]
says the law has "no name". It is also referred to as the "transversality
[3]
requirement" because for plane waves it requires that the polarization be
[4]
transverse to the direction of propagation.
Differential form[edit]
The differential form for Gauss's law for magnetism is:
where ∇ · denotes divergence, and B is the magnetic field.
Integral form[edit]
Definition of a closed surface.
Left: Some examples of closed surfaces include the surface of a sphere, surface of a torus, and surface of a cube. The magnetic
