05. Comparison to Skin Effect Equation - Nonmagnetic Material

The skin effect equation was derived from Maxwell's equations for the case of a uniform electromagnetic field at low frequency penetrating a semi-infinite conducting slab with a flat face.

The amplitude decay is expressed as Bz(distance into the slab)/Bz(surface) = exp(-distance/skin depth)

The phase change in radians with distance is: Phase(Bz(distance into the slab) - Phase(Bz(surface)) = -distance/skin depth

where the electromagnetic skin depth = sqrt(2/(angular frequency x electrical conductivity x magnetic permeability))

angular frequency is frequency x 2pi

Although this equation is derived from a special case with a flat interface between free space and a semi-infinite slab with a flat face, it is often used as an approximation for other geometries.

TB-FIELD.EXE was used to calculate the change in axial magnetic field Bz as with respect to radial distance into a conducting rod. Results from TB-FIELD.EXE were compared to an estimate using the skin effect equation.

The radius of the rod was 6.35 mm (radius = 1/4" or diameter = 1/2")

Electrical Conductivity was 2.08E6 Siemens/m

Relative Magnetic Permeability = 1

Inner radius of the encircling coil Ri = 7 mm, outer radius of the coil Ro = 8 mm, Coil Length = 20 mm

Input screens for the TB-FIELD.EXE program are shown below:

Within TB-FIELD.EXE, the external tube was given the properties of free space and the inner "tube" was given a very small inner radius (1E-10 m or 1 angstrom). Field calculations were performed at various radial positions within the rod.

Results showing TB-FIELD.EXE calculated Bz amplitude decays as a function of radial distance from the outer surface of the rod is shown in the chart below as compared to the estimation made using the basic skin-effect equation:

A chart of phase change with respect to distance from the surface of the rod is shown below: