NationMaster - Encyclopedia: Skin depth

When an electromagnetic wave interacts with a conductive material, mobile charges within the material are made to oscillate back and forth with the same frequency as the impinging fields. The movement of these charges, usually electrons, constitutes an alternating electric current, the magnitude of which is greatest at the conductor's surface. The decline in current density versus depth is known as the skin effect and the skin depth is a measure of the distance over which the current falls to 1/e of its original value. A gradual change in phase accompanies the change in magnitude, so that, at a given time and at appropriate depths, the current can be flowing in the opposite direction to that at the surface. Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ... In science and engineering, conductors, such as a electrical connector, are materials that readily conduct electric current through electrical conduction. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Oscillation is the variation, typically in time, of some measure as seen, for example, in a swinging pendulum. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... e- redirects here. ... City lights viewed in a motion blurred exposure. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. ... e is the unique number such that the value of the derivative (slope of a tangent line) of f (x)=ex (blue curve) at the point x=0 is exactly 1. ... This article is about a portion of a periodic process. ...

The skin depth is a property of the material that varies with the frequency of the applied wave. It can be calculated from the relative permittivity and conductivity of the material and frequency of the wave. First, find the material's complex permittivity, $varepsilon_c$ The relative dielectric constant of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. ... Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ...

where:

$varepsilon$ = permittivity of the material of propagation

ω

= angular frequency of the wave

σ

= electrical conductivity of the material of propagation

Thus, the propagation constant, $k$ , will also be a complex number, and can be separated into real and imaginary parts. Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... It has been suggested that this article or section be merged into Angular velocity. ... Electrical conductivity or specific conductivity is a measure of a materials ability to conduct an electric current. ... For an electromagnetic field mode varying sinusoidally with time at a given frequency, the propagation constant is the logarithmic rate of change, with respect to distance in a given direction, of the complex amplitude of any field component. ... In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = âˆ’1. ...

= $jomega sqrt {mu varepsilon left( {1 - frac{{jsigma }}{{omega varepsilon }}} right)} qquadqquad(2)$

The constants can also be expressed as

$alpha = {omega}sqrt{{{muvarepsilon}over2}left(sqrt{1 + left({{sigma}over{omega epsilon}}right)^2} - 1right)}qquadqquad (3)$

$beta = {omega}sqrt{{{muvarepsilon}over2}left(sqrt{1 + left({{sigma}over{omega epsilon}}right)^2} + 1right)}qquadqquad (4)$

where:

μ

= permeability of the material

α

= attenuation constant of the propagating wave

The solution of the equation above is if it represent a uniform wave propagating in the +z-direction In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. ... In telecommunication, the term attenuation constant has the following meanings: 1. ...

The first term in the solution decreases as z increases and is for this reason an attenuation term where $α$ is an attenuation constant with the unit Np/m (Neper). If $α = 1$ then a unit wave amplitude decreases to a magnitude of $e - 1$ Np/m.

It can be seen that the imaginary part of the complex permittivity increases with frequency, implying that the attenuation constant also increases with frequency. Therefore, a high frequency wave will only flow through a very small region of the conductor (much smaller than in the case of a lower frequency current), and will therefore encounter more electrical resistance (due to the decreased surface area).

A good conductor is per definition if why we can neglect 1 in equation (2) and it turns to

$k_c = sqrt j , sqrt {mu omega sigma } = frac{{1 + j}}{{sqrt 2 }}sqrt {mu 2pi fsigma } = (1 + j)sqrt {pi fmu sigma }qquadqquad(6)$

The skin depth is defined as the distance $δ$ through which the amplitude of a traveling plane wave decreases by a factor $e - 1$ and is therefore

$delta = frac{1}{alpha} qquadqquad(7)$

and for a good conductor is it defined as

$delta = frac{1}{sqrt {pi fmu sigma }} qquadqquad(8)$

The term "skin depth" traditionally assumes ω real. This is not necessarily the case; the imaginary part of ω characterizes' the waves attenuation in time. This would make the above definitions for α and β complex, and so they would need to be redefined so that $I m {k c} = β$ .

The same equations also apply to a lossy dielectric. Defining A dielectric, or electrical insulator, is a substance that is highly resistant to electric current. ...

replace $varepsilon$ with $varepsilon'$ , and ${sigmaover{omegavarepsilon}}$ with $varepsilon''over{varepsilon'}$

Examples

Skin depths for some metals

The electrical resistivity of a material is equal to 1/σ and its relative permeability is defined as $μ / μ 0$ , where $μ 0$ is the magnetic permeability of free space. It follows that Equation (8) can be rewritten as Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ...

$delta = frac{1}{sqrt{pi mu_o}} ,sqrt{frac{rho}{mu_r f}} approx 503,sqrt{frac{rho}{mu_r f}}qquadqquad(9)$

where

μ 0 =

4π×10^-7 H/m

μ r =

the relative permeability of the medium

ρ =

the resistivity of the medium in Ωm

f =

the frequency of the wave in Hz

If the resistivity of aluminium is taken as 2.8×10^-8 Ωm and its relative permeability is 1, then the skin depth at a frequency of 50 Hz is given by

$delta = 503 ,sqrt{frac{2.82 cdot 10^{-8}}{1 cdot 50}}= 11.9$ mm

Iron has a higher resistivity, 1.0×10^-7 Ωm, and this will increase the skin depth. However, its relative permeability is typically 90, which will have the opposite effect. At 50 Hz the skin depth in iron is given by

$delta = 503 ,sqrt{frac{1.0 cdot 10^{-7}}{90 cdot 50}}= 2.4$ mm

Hence, the higher magnetic permeability of iron more than compensates for the lower resistivity of aluminium and the skin depth in iron is therefore 5 times smaller. This will be true whatever the frequency, assuming the material properties are not themselves frequency-dependent.

References

Ramo, Whinnery, Van Duzer (1994). Fields and Waves in Communications Electronics. John Wiley and Sons.

Category: Electromagnetism

Results from FactBites:

Surgical instrument having self-regulated electrical skin-depth heating of its cutting edge and method of using the ... (2464 words)
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	The depth of this skin effect is the depth at which the current is reduced to about 37% of its surface value and is determined by the electrical resistivity and magnetic permeability of the material conducting the current and by the frequency of the alternating current.
	Since the resistance of the current-conducting path is inversely proportional to cross-sectional area (path width times skin depth), this effect causes an increase in the resistance of the current path in cooled regions and an increase in the Joule heating thereof.

Some Skin Effect Notes (977 words)
	The skin effect is the description given to the phenomenon where electromagnetic fields (and therefore the current) decay rapidly with depth inside a good conductor.
	The skin depth in copper is about.005 centimeters for the 160 meter band,.002 centimeters for the 20 meter band,.001 centimeters for the 6 meter band, and.0003 centimers for the 70 centimeter band.
	For the usual case where the surface of the conductor is flat on the length scale of the skin depth, and the conductor is much thicker than the skin depth, the solution is straightforward.

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