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e. 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, [1] in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not exist. [2]
Here, the electric field outside (r > R) and inside (r < R) of a charged sphere is being calculated (see Wikiversity). In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the ...
Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current. Gauss's law for magnetism states that electric charges have no magnetic analogues, called magnetic monopoles; no north or south magnetic poles exist in isolation. [3]
The second equation corresponds to the two remaining equations, Gauss's law for magnetism (for β = 0) and Faraday's Law (for β = 1, 2, 3). These tensor equations are manifestly covariant , meaning they can be seen to be covariant by the index positions.
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
In physics, specifically electromagnetism, the Biot–Savart law (/ ˈ b iː oʊ s ə ˈ v ɑːr / or / ˈ b j oʊ s ə ˈ v ɑːr /) [1] is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current.
Gauss's law for magnetism, one of Maxwell's equations, is the mathematical statement that magnetic monopoles do not exist. Nevertheless, Pierre Curie pointed out in 1894 [ 9 ] that magnetic monopoles could conceivably exist, despite not having been seen so far.
Gauss's law for magnetism (∇⋅ B = 0) is not included in the above list, but follows directly from equation by taking divergences (because the divergence of the curl is zero). Substituting (A) into (C) yields the familiar differential form of the Maxwell-Ampère law .