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104年 - 104 國立中山大學_碩士班招生考試_電機系(戊組)、電波聯合：電磁學#110200
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題組內容
Problem 4
c.(5%) Refer to the following figure and prove the law of Cosines,
其他申論題
b.(5%) What is the dielectric constant for a metal, for example, Copper?
#471716
c.(5%) The relative permeability for Steel is 100, and is frequency dependent. What is the relative permeability for Copper?
#471717
a. (5%) Why Curl of Gradient of a potential field is zero, that is, ∇ x ( ∇V) = 0?
#471718
b.(5%) Why Divergence of Curl of a vector field is zero, that is, ∇. ( ∇ X A) =0?
#471719
Problem 5 (20%) A plane wave is normally incident on a dielcctric slab of relative permitivity &, and thickness d. where), and λ0 is the free-space wavelength of the incident wave, as shown in Figure (e). If free-space exists on both sides of the slab, find the reflection cocfficient of the wave reflected from the front of the slab.
#471721
Problem 6 (10%) A lossless transmission Iine is terminated with a 100 Ω load. If the standing wave ratio (SWR) on the line is 1.5, find the two possible values for the characteristic impedance of the line.
#471722
Problem 7 (20%) An average power of 1 (kW) at 10 (GHz) is to be delivered to an antenna at the TElo mode by an air-filled metallic rectangular waveguide 1 (m) long and having sides a = 2.25 (cm) and b = 1 (cm). Assume that all the conductors are perfect electric conductors. Find the maximum values of the electric and magnetic field intensities within the waveguide.
#471723
六、求？(20 分)
#471724
(5%) A point charge Q exists at (0, d, 0) in space, as shown in Figure (a). Using Theory of image, a point charge of -Q exists at (0, -d, 0) symmetrically, as indicated in Figure (b). The dielectric constant of the space is εo. Write the electric intensities (Ex|y=0, Ey|y=0, and Ez|y=0) for a point on the ZX-plane in terms of (d and R), or (d and r), as indicated in Figure (b).
#471725
(5%) What is the surface charge distribution on the ZX-plane? Sketch the distribution.
#471726
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