Page 157 - Engineering Electromagnetics, 8th Edition

CHAPTER 5 Conductors and Dielectrics 139

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which this solid cone is constructed has a conductivity of 2 × 10 S/m, use
some good approximations to determine the resistance between the two
circular faces.
5.9 (a) Using data tabulated in Appendix C, calculate the required diameter for a
2-m-long nichrome wire that will dissipate an average power of 450 W when
120 V rms at 60 Hz is applied to it. (b) Calculate the rms current density in
the wire.
5.10 A large brass washer has a 2-cm inside diameter, a 5-cm outside diameter,
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and is 0.5 cm thick. Its conductivity is σ = 1.5 × 10 S/m. The washer is cut
in half along a diameter, and a voltage is applied between the two rectangular
faces of one part. The resultant electric field in the interior of the half-washer
is E = (0.5/ρ) a φ V/m in cylindrical coordinates, where the z axis is the axis
of the washer. (a) What potential difference exists between the two
rectangular faces? (b) What total current is flowing? (c) What is the
resistance between the two faces?
5.11 Two perfectly conducting cylindrical surfaces of length
are located at
ρ = 3 and ρ = 5 cm. The total current passing radially outward through the
medium between the cylinders is3Adc.(a) Find the voltage and resistance
between the cylinders, and E in the region between the cylinders, if a
conducting material having σ = 0.05 S/m is present for 3 <ρ < 5 cm.
(b) Show that integrating the power dissipated per unit volume over the
volume gives the total dissipated power.
5.12 Two identical conducting plates, each having area A, are located at z = 0 and
z = d. The region between plates is filled with a material having z-dependent
conductivity, σ(z) = σ 0 e −z/d , where σ 0 is a constant. Voltage V 0 is applied to
the plate at z = d; the plate at z = 0isat zero potential. Find, in terms of the
given parameters, (a) the resistance of the material; (b) the total current
flowing between plates; (c) the electric field intensity E within the material.
5.13 A hollow cylindrical tube with a rectangular cross section has external
dimensions of 0.5 in. by 1 in. and a wall thickness of 0.05 in. Assume that the
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material is brass, for which σ = 1.5 × 10 S/m. A current of 200 A dc is
flowing down the tube. (a) What voltage drop is present acrossa1m length
of the tube? (b) Find the voltage drop if the interior of the tube is filled with
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a conducting material for which σ = 1.5 × 10 S/m.
5.14 A rectangular conducting plate lies in the xy plane, occupying the region
0 < x < a, 0 < y < b. An identical conducting plate is positioned directly
above and parallel to the first, at z = d. The region between plates is filled
with material having conductivity σ(x) = σ 0 e −x/a , where σ 0 is a constant.
Voltage V 0 is applied to the plate at z = d; the plate at z = 0isat zero
potential. Find, in terms of the given parameters, (a) the electric field
intensity E within the material; (b) the total current flowing between plates;
(c) the resistance of the material.