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Volume 2; 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
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 n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The most elementary force between magnets is the magnetic dipole–dipole interaction. If all magnetic dipoles for each magnet are known then the net force on both magnets can be determined by summing all the interactions between the dipoles of the first magnet and the dipoles of the second magnet.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
A magnet's magnetic moment (also called magnetic dipole moment and usually denoted μ) is a vector that characterizes the magnet's overall magnetic properties. For a bar magnet, the direction of the magnetic moment points from the magnet's south pole to its north pole, [ 15 ] and the magnitude relates to how strong and how far apart these poles ...
For zero net magnetic charge density (ρ m = 0), the original form of Gauss's magnetism law is the result. The modified formula for use with the SI is not standard and depends on the choice of defining equation for the magnetic charge and current; in one variation, magnetic charge has units of webers, in another it has units of ampere-meters.
The third of Maxwell's equations is called the Ampère–Maxwell law. It states that a magnetic field can be generated by an electric current. [13] The direction of the magnetic field is given by Ampère's right-hand grip rule. If the wire is straight, then the magnetic field is curled around it like the gripped fingers in the right-hand rule.
The magnetization field or M-field can be defined according to the following equation: =. Where is the elementary magnetic moment and is the volume element; in other words, the M-field is the distribution of magnetic moments in the region or manifold concerned.
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