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The magnetic constant μ 0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources. In particular, it appears in relationship to quantities such as permeability and magnetization density , such as the relationship that defines the magnetic H ...
The permeability of vacuum (also known as permeability of free space) is a physical constant, denoted μ 0. The SI units of μ are volt-seconds per ampere-meter, equivalently henry per meter. Typically μ would be a scalar, but for an anisotropic material, μ could be a second rank tensor. However, inside strong magnetic materials (such as iron ...
In free space, where ε = ε 0 and μ = μ 0 are constant everywhere, Maxwell's equations simplify considerably once the language of differential geometry and differential forms is used. The electric and magnetic fields are now jointly described by a 2-form F in a 4-dimensional spacetime manifold.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
The magnetic field generated by a steady current I (a constant flow of electric charges, in which charge neither accumulates nor is depleted at any point) [note 8] is described by the Biot–Savart law: [21]: 224 = ^, where the integral sums over the wire length where vector dℓ is the vector line element with direction in the same sense as ...
The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by q m (Wb) = μ 0 q m (Am).
As before, it is defined by the equation ε 0 = 1/(μ 0 c 2), and is thus determined by the value of μ 0, the magnetic vacuum permeability which in turn is determined by the experimentally determined dimensionless fine-structure constant α: = = ,
The energy of a localized magnetic charge q m in a magnetic scalar potential is =, and of a magnetic charge density distribution ρ m in space =, where µ 0 is the vacuum permeability. This is analog to the energy Q = q V E {\displaystyle Q=qV_{E}} of an electric charge q in an electric potential V E {\displaystyle V_{E}} .