Electromagnetic Fields and Waves: Notes, Solved Problems and Interactive Lab

About the worked examples of Section 6.2

Two short calculations with engineering numbers. They use only $γ = α + j β$ (exact and approximate), the skin depth $δ$ and $R_{s}$ , and no new physics. A good way to use them: read the given quantities, decide first whether the medium is low-loss, a good conductor or neither, and only then put the numbers in. Constants: $ε_{0} = 1 0^{- 9} /36 π F/m$ , $μ_{0} = 4 π \times 1 0^{- 7} H/m$ , $c = 3 \times 1 0^{8} m/s$ .

Worked example 6.2.2

Skin effect in copper

cf. skin depth and $R_{s}$

Given. Copper, $σ = 5.8 \times 1 0^{7} S/m$ , a straight copper wire of radius $a = 0.5 mm$ and length $l = 1 m$ , silver, $σ = 6.17 \times 1 0^{7} S/m$ , all with $μ_{r} = 1$ .

Find. (a) $δ$ of copper at $50 Hz$ , $1 MHz$ and $10 GHz$ , (b) $R_{d c}$ of the wire and $R_{a c}$ at $1 MHz$ and $100 MHz$ , (c) $R_{s}$ of copper at $10 GHz$ , and the thickness of a silver plating of five skin depths at $10 GHz$ .

Try it yourself first.

Worked example 6.2.2: Skin effect in copper