By Orfanidis S.J.

ISBN-10: 0130938556

ISBN-13: 9780130938558

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**Sample text**

Positive holes for p-type, or negative electrons for n-type. What is the numerical value of b for electrons in copper if B is 1 gauss? [Ans. ] g. 11 This problem deals with various properties of the Kramers-Kronig dispersion relations for the electric susceptibility, given by Eq. 8). a. 8) can be written in the folded form of Eq. 9). dω =0 ω 2 − ω2 Hint : You may use the following indeﬁnite integral: (ω20 0 dx 1 = , − x2 )2 +γ2 x2 γω20 (ω20 − ω2 )2 +γ2 ω2 ∞ 2 π 0 x2 dx 1 = γ (ω20 − x2 )2 +γ2 x2 Indeed, show that these integrals may be reduced to the following ones, which can be found in standard tables of integrals: 2 π ∞ 0 dy 1 − 2y2 cos θ + y4 = 2 π ∞ 0 y2 dy 1 − 2y2 cos θ + y4 = 1 2(1 − cos θ) where sin(θ/2)= γ/(2ω0 ).

12) 40 2. Uniform Plane Waves This solution has the following properties: (a) The ﬁeld vectors E and H are perpendicular to each other, E · H = 0, while they are transverse to the z-direction, (b) The three vectors {E, H, ˆ z} form a right-handed vector system as shown in the ﬁgure, in the sense that E × H points in the direction of ˆ z is independent z, (c) The ratio of E to H × ˆ of z, t and equals the characteristic impedance η of the propagation medium; indeed: H(z, t)= The term E+ (z, t)= F(z − ct) represents a wave propagating with speed c in the positive z-direction, while E− (z, t)= G(z+ct) represents a wave traveling in the negative z-direction.

89 Ω. 2) will be: 60 2. 8 × 107 Siemens/m. 19 cm. This result assumes that σ ω d, σ/ d , or f f0 , where f0 = σ/(2π d ). 28). For have f0 = 888 MHz.

### Electromagnetic Waves and Antennas by Orfanidis S.J.

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