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Relative permeability, , for phase is then defined from =, as = / where is the permeability of the porous medium in single-phase flow, i.e., the absolute ...
For example, 4% electrical steel has an initial relative permeability (at or near 0 T) of 2,000 and a maximum of 38,000 at T = 1 [5] [6] and different range of values at different percent of Si and manufacturing process, and, indeed, the relative permeability of any material at a sufficiently high field strength trends toward 1 (at magnetic ...
A practical unit for permeability is the darcy (d), or more commonly the millidarcy (md) (1 d ≈ 10 −12 m 2). The name honors the French Engineer Henry Darcy who first described the flow of water through sand filters for potable water supply. Permeability values for most materials commonly range typically from a fraction to several thousand ...
where μ 0 is the vacuum permeability (see table of physical constants), and (1 + χ v) is the relative permeability of the material. Thus the volume magnetic susceptibility χ v and the magnetic permeability μ are related by the following formula: = (+).
The refractive index of electromagnetic radiation equals =, where ε r is the material's relative permittivity, and μ r is its relative permeability. [ 47 ] : 229 The refractive index is used for optics in Fresnel equations and Snell's law ; while the relative permittivity and permeability are used in Maxwell's equations and electronics.
Here is effective relative complex permeability of the mixture, is relative complex permeability of the background medium containing small spherical inclusions of relative permeability with volume fraction of . This formula was derived in dipole approximation.
All this requires different relative permeability curves for the x and z directions. Geological heterogeneities in the reservoirs like laminas or crossbedded permeability structures in the rock, also cause directional relative permeabilities. This tells us that relative permeability should, in the most general case, be represented by a tensor.
is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇ 2 is the Laplace operator. In a vacuum, v ph = c 0 = 299 792 458 m/s, a fundamental physical constant. [1] The electromagnetic wave equation derives from Maxwell's equations.