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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]
Rather than "magnetic charges", the basic entity for magnetism is 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.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
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.
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 .
The second of Maxwell's equations is known as Gauss's law for magnetism and, similarly to the first Gauss's law, it describes flux, but instead of electric flux, it describes magnetic flux. According to Gauss's law for magnetism, the flow of magnetic field through a closed surface is always zero.
A Treatise on Electricity and Magnetism at Internet Archive. 1st edition 1873 Volume 1, Volume 2; 2nd edition 1881 Volume 1, Volume 2; 3rd edition 1892 (ed. J. J. Thomson) Volume 1, Volume 2; 3rd edition 1892 (Dover reprint 1954) Volume 1, Volume 2; Original Maxwell Equations – Maxwell's 20 Equations in 20 Unknowns – PDF
Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism .