Unformatted text preview: 10.12. PROBLEMS 10.29 where k is the wavenumber, c the speed of light, MP the plasma frequency, wc the
electron gyration frequency, and w the wave frequency (all frequencies are positive).
a. If cup and we are given constants, for what values of w is the wave evanescent? b. If u: = 107 s‘l, wp = 8 x 106 s‘l, and we = 6 x 10ﬁ s‘l, ﬁnd the phase velocity of
the wave. c. Find the group velocity of the wave (for the same conditions). Problem 10.17: An electromagnetic wave propagates downward into sea water
(a = 4 U/m, s = 8180). Just below the surface, the power ﬂux (magnitude of
the Poynting vector) is 100 W/m2. If we want the power at a depth of 100 In to be
10‘2 W/Ing, what must the wave frequency be? Problem 10.18: A plane wave with a frequency of 10 GHz propagates in a dielectric
with permittivity given by 5/50 = 4.0 — 34.0 x 10-3 a. Evaluate the phase and attenuation constants, the wavelength, the phase velocity, and the intrinsic impedance of the medium.
b. In what distance will the wave attenuate by 20 dB?
c. In what distance will the electric ﬁeld strength decrease by a factor of 100? Problem 10.19: A plane wave propagates within a dielectric with a permittivity
given by: 1 _ 5’ — 3'5”
1 +j10—10w _ so a. What are 61/60 and 5”/E’ for this dielectric? b. Consider the three frequency regimes of (1) w << 1010 5—1, (2) (.0 >> 1010 s“1,
and (3) w = 1010 5*. Is the low—loss approximation valid in all three regimes? c. Sketch the dispersion relation (w as a function of k) for this dielectric. From the
sketch, estimate the phase and group velocities of the wave. Is there anything peculiar
about the region a: as 1010 5‘1? Explain. 52/80 = 1+ Problem 10.20: A 10 MHz wave propagates in a medium, satisfying the dispersion
.12 = w: + 192.22 Where fo = Lac/211' = 6 MHz. 3. Find the phase and group velocities and show that their product equals the square
of the speed of light. b. Determine the effective dielectric constant. c. Find the amplitude of the magnetic ﬁeld if the electric ﬁeld amplitude is 1 V/m. ...
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- Fall '06