The proof that equation ∂ 2 E y ∂ x 2 = 1 c 2 ∂ 2 E y ∂ t 2 is satisfied by E y = E 0 sin ( k x − ω t ) .

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Chapter 30, Problem 42P

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The proof that equation ∂2Ey∂x2=1c2∂2Ey∂t2 is satisfied by Ey=E0sin(kx−ωt) .

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a) Show that the propagation constant (y), and the intrinsic impedance (7) of a uniform plane wave propagating in a lossy medium are related by yn = jwu. b) The phasor fields of a uniform plane wave of angular frequency w = 1.6 x 10° (rad/sec) in a nonmagnetic (i.e. µ = Ho), lossy medium are given by Ē(2) =100 e-az,-ißz â, (Volts/m) H(2) = 0.5 e-7/8 e -az -jßz e â, (Amps/m) Determine: i. the intrinsic impedance, ii. the numerical values of a and ß, iii. the phase velocity and the depth of penetration, iv. the time-domain fields, E(z,t), Ħ(z, t), v. the time-average Poynting's vector associated with this wave, vi. the distance at which the power carried by this wave decays to 1% of its value at z = 0.

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