所屬科目：中山◆電機◆電磁學
(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).
b. (5%) The characteristic impedance is defined as, find out the characteristics impedance at high frequencies, and please indicate the unit for it. 新告+
a. (5%) Why Curl of Gradient of a potential field is zero, that is, ∇ x ( ∇V) = 0?
c.(5%) Refer to the following figure and prove the law of Cosines,
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.
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.
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, find out the characteristics impedance at high frequencies, and please indicate the unit for it. 新告+
), 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.