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Electromagnetic Skin Depth

Skin depth is a property of the skin effect, the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor, and decreases with greater depths in the conductor. The electric current flows mainly at the skin of the conductor, between the outer surface and a level called the skin depth.

Skin depth increases inversely with decreasing electric conductivity and magnetic permeability. Increasing electric permittivity also leads to a larger skin depth. The effect of frequency is more complicated, but for high frequencies, skin depth is roughly proportional to the reciprocal of the square root of the frequency.

Formula

QuantityVariable["δ", "Depth"] == Sqrt[1/(QuantityVariable["ε", "ElectricPermittivity"]*QuantityVariable["μ", "MagneticPermeability"])]/(Sqrt[2]*Pi*QuantityVariable["ν", "Frequency"]*Sqrt[-1 + Sqrt[1 + QuantityVariable["σ", "ElectricConductivity"]^2/(4*Pi^2*QuantityVariable["ε", "ElectricPermittivity"]^2*QuantityVariable["ν", "Frequency"]^2)]])

symbol description physical quantity
δ electromagnetic skin depth "Depth"
ε permittivity "ElectricPermittivity"
μ magnetic permeability "MagneticPermeability"
ν frequency "Frequency"
σ electric conductivity "ElectricConductivity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Electromagnetic Skin Depth"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Electromagnetic Skin Depth"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Electromagnetic Skin Depth"], {QuantityVariable[ "\[Sigma]","ElectricConductivity"] -> Quantity[1.`*^6, ("Siemens")/("Meters")], QuantityVariable["\[Nu]","Frequency"] -> Quantity[6.1`*^7, "Hertz"]}]
Out[3]=

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