Skin Depth & Coated Wire 1

Plated Wire

The use of plated wire in spacecraft (and other places) is not uncommon; nickel or silver overlaying copper being the most common. Of course there’s a document – this is government work. The pertinent document is entitled:
“CABLE, ELECTRICAL, MIL-STD-1553 DATABUS, SPACE QUALITY, GENERAL SPECIFICATION FOR”

Section 3.3.1.3: Conductor and shield plating for nickel-coated wire
The conductor and shield strands shall have a coating of not less than 50 micro-inches of nickel.

50 $\mu in$ = 1.27 $\mu$ m

Section 3.3.1.4: Conductor and shield plating for silver-coated wire
The conductor and shield strands shall have a coating of not less than 80 micro-inches of nickel.

80 $\mu in$ = 2.032 $\mu$ m

And much more beyond. Note that nickel is ferromagnetic with a relative permeability of “100 – 600” … sources not being overly specific.

Coated Copper
Plain AWG#24 has diameter of 0.511mm

Both AWG#22 and #24 are characterized; I’ll assume #24 wire for this discussion (as that was the primary wire I used).

$\textnormal{\small{Copper:}}\quad \rho_{Cu}\;=\;16.78\times 10^{-9}\;\;\mu_r\;=\;1.0$
$\textnormal{\small{Silver:}}\quad \rho_{Ag}\;=\;15.87\times 10^{-9}\;\;\mu_r\;=\;1.0$
$\textnormal{\small{Nickel:}}\quad \rho_{Ni}\;=\;69.3\times 10^{-9}\;\;\mu_r\;=\;100-600$

$\mu_o\;=\;4\,\pi\times 10^{-7}$ *

*this value was recently modified from “exact” to a value with uncertainty of interest only of those seeking ultimate precision. The NIST 2018 CODATA value for μ_o is 1.256 637 062 12 (19) x 10^-6 whereas the numerical value of the “exact” 4π x 10^-7 is (1.256 637 062 121 954 …) x 10^-6 … an insignificant difference herein. I’ll use the former value – easier to manipulate using 4π.

Incremental Inductance

The DC current distribution through a solid copper wire is uniform. Imagine two annular rings of equal area but different diameters such that the cross-sectional areas are equal.

The incremental current in each path is identical since the current density in each ring is identical: $I \;=\; \textnormal{\small{J}}\,\times\,A$

Even so, the incremental current creates an incremental magnetic field which introduces the concept of inductance. The inductances of each path are not identical even though the current densities are; the incremental self-inductance decreases as the current path moves to the center (self inductance is inversely proportional to radius). However, as frequency increases, the current density in the center decreases, lowering the internal magnetic field strength.

Next: Part 2

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