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

The problems of this section use the TEM results Eq. (7.5.5) to Eq. (7.5.13) and the TE $_{11}$ estimate Eq. (7.5.17), collected here for a line with radii $a < b$ and filling $ε_{r}$ , $μ_{0}$ :

E_{ρ} = \frac{V _{0}}{ρ ln ( b / a )}, H_{ϕ} = \frac{E _{ρ}}{η}, Z_{0} = \frac{η}{2 π} ln \frac{b}{a} = \frac{60}{ε _{r}} ln \frac{b}{a}, L^{'} = \frac{μ}{2 π} ln \frac{b}{a}, C^{'} = \frac{2 π ε}{ln ( b / a )}, P = \frac{∣ V _{0} ∣ ^{2}}{2 Z _{0}}, α_{c} = \frac{R _{s}}{2 η} \frac{1/ a + 1/ b}{ln ( b / a )}, α_{d} = \frac{k tan δ}{2}, f_{c, TE_{11}} \approx \frac{v}{π ( a + b )}, f_{c, TM_{01}} \approx \frac{v}{2 ( b - a )} .

$R_{s} = π f μ_{0} / σ_{c}$ and $1$ Np $= 8.686$ dB. 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, $η_{0} = 120 π = 377 Ω$ , copper $σ_{c} = 5.8 \times 1 0^{7}$ S/m.

7.5.8 Problems and solutions

In this part

Problems · 3

Home exercises · 1

Further exercises · 5

Worked examples · 1