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A useful tool for dealing with high frequency magnetic effects is the complex permeability. While at low frequencies in a linear material the magnetic field and the auxiliary magnetic field are simply proportional to each other through some scalar permeability, at high frequencies these quantities will react to each other with some lag time. [ 36 ]
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 ]
where μ is the magnetic permeability, ε is the (real) electric permittivity and σ is the electrical conductivity of the material the wave is travelling through (corresponding to the imaginary component of the permittivity multiplied by omega). In the equation, j is the imaginary unit, and ω is the angular frequency of the wave.
Low-frequency time domain measurements (10 −6 to 10 +3 Hz) Low-frequency frequency domain measurements (10 −5 to 10 +6 Hz) Reflective coaxial methods (10 +6 to 10 +10 Hz) Transmission coaxial method (10 +8 to 10 +11 Hz) Quasi-optical methods (10 +9 to 10 +10 Hz) Terahertz time-domain spectroscopy (10 +11 to 10 +13 Hz) Fourier-transform ...
μ 0 ≈ 12.566 × 10 −7 H/m is the magnetic constant, also known as the permeability of free space, ε 0 ≈ 8.854 × 10 −12 F/m is the electric constant, also known as the permittivity of free space, c is the speed of light in free space, [9] [10] The reciprocal of Z 0 is sometimes referred to as the admittance of free space and ...
The relative low frequency permittivity of ice is ~96 at −10.8 °C, falling to 3.15 at high frequency, which is independent of temperature. [21] It remains in the range 3.12–3.19 for frequencies between about 1 MHz and the far infrared region. [22]
Its reduction with increasing frequency, as the ratio of skin depth to the wire's radius falls below about 1, is plotted in the accompanying graph, and accounts for the reduction in the telephone cable inductance with increasing frequency in the table below. The internal component of a round wire's inductance vs. the ratio of skin depth to radius.
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: = (+).