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

The problems of this section use the relations of the uniform plane wave, with the phasor convention $e^{j ω t}$ :

E = E_{0} e^{- j k \cdot r}, k = k a_{k}, a_{k} \cdot E_{0} = 0, k = ω μ ε = \frac{2 π}{λ}, η = \frac{μ}{ε}, H = \frac{1}{η} a_{k} \times E, E = - η a_{k} \times H = η H \times a_{k}, P_{a v} = \frac{1}{2} Re {E \times H^{*}} = \frac{∣ E _{0} ∣ ^{2}}{2 η} a_{k}, E_{R, L} = \frac{1}{2} (E_{1} \pm j E_{2} e^{j δ}), f^{'} \approx f (1 + \frac{v}{c} cos θ),

the ellipse formulas, Eq. (6.1.58), the handedness test of Section 6.1.6 (with the amplitude $E_{r} + j E_{i}$ , the wave is right-handed if $(E_{r} \times (- E_{i})) \cdot a_{k} > 0$ ) and the IEEE convention for the hand. Constants: $c = 3 \times 1 0^{8} m/s$ , $ε_{0} = 1 0^{- 9} / (36 π) = 8.842 \times 1 0^{- 12} F/m$ , $μ_{0} = 4 π \times 1 0^{- 7} H/m$ and $η_{0} = 120 π = 376.99 Ω$ .

6.1.9 Problems and solutions

In this part

Problems · 11

Home exercises · 8

Further exercises · 17

Worked examples · 5