Page 422 - Engineering Electromagnetics, 8th Edition

404 ENGINEERING ELECTROMAGNETICS

in some high-power optical experiments, in which tight focusing of light
may be necessary. Estimate the lightwave power in watts that can be
focused into a cylindrical beam of 10µm radius before breakdown occurs.
Assume uniform plane wave behavior (although this assumption will
produce an answer that is higher than the actual number by as much as a
factor of 2, depending on the actual beam shape).
11.21 The cylindrical shell, 1 cm<ρ < 1.2 cm, is composed of a conducting
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material for which σ = 10 S/m. The external and internal regions are
nonconducting. Let H φ = 2000 A/m at ρ = 1.2 cm. Find (a) H
everywhere; (b) E everywhere; (c) S everywhere.
11.22 The inner and outer dimensions of a coaxial copper transmission line are
2 and 7 mm, respectively. Both conductors have thicknesses much greater
than δ. The dielectric is lossless and the operating frequency is 400 MHz.
Calculate the resistance per meter length of the (a) inner conductor;
(b) outer conductor; (c) transmission line.
11.23 A hollow tubular conductor is constructed from a type of brass having a
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conductivity of 1.2 × 10 S/m. The inner and outer radii are 9 and 10 mm,
respectively. Calculate the resistance per meter length at a frequency of
(a) dc; (b)20 MHz; (c)2 GHz.
11.24 (a) Most microwave ovens operate at 2.45 GHz. Assume that σ = 1.2 ×
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10 S/m and µ r = 500 for the stainless steel interior, and find the depth of
penetration. (b) Let E s = 50 0 V/m at the surface of the conductor, and
◦
plot a curve of the amplitude of E s versus the angle of E s as the field
propagates into the stainless steel.
11.25 A good conductor is planar in form, and it carries a uniform plane wave that
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has a wavelength of 0.3 mm and a velocity of 3 × 10 m/s. Assuming the
conductor is nonmagnetic, determine the frequency and the conductivity.
11.26 The dimensions of a certain coaxial transmission line are a = 0.8mmand
b = 4 mm. The outer conductor thickness is 0.6 mm, and all conductors
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have σ = 1.6 × 10 S/m. (a) Find R, the resistance per unit length at an
operating frequency of 2.4 GHz. (b) Use information from Sections 6.3 and
8.10 to find C and L, the capacitance and inductance per unit length,
respectively. The coax is air-filled. (c) Find α and β if
√
α + jβ = jωC(R + jωL).
11.27 The planar surface z = 0isa brass-Teflon interface. Use data available in
Appendix C to evaluate the following ratios for a uniform plane wave
having ω = 4 × 10 10 rad/s: (a) α Tef /α brass ;(b) λ Tef /λ brass ;(c) v Tef /ν brass .
11.28 A uniform plane wave in free space has electric field vector given by E s =
10e − jβx a z + 15e − jβx a y V/m. (a) Describe the wave polarization.
(b) Find H s .(c) Determine the average power density in the wave
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in W/m .