EM2_2000_Mid.pdf

# EM2_2000_Mid.pdf - Electromagnetics(II Midterm Exam May 3...

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Unformatted text preview: Electromagnetics (II) Midterm Exam. May 3. 2000 1. In vacuum. a time-varying charge density p(F, r) and a time—varying current density IT? , t) are distributed ever a ﬁnite regien ef velume V'. Under the Lerentz cenditien, what are the scalar petential V(ﬁ ,t1) and vecter petential 30", ,II) at an external point F, en instant 1‘. due te these seuree distributions? Write dawn the integral expressiens ef the results directly and interpret the physical meaning ef time retardatien brieﬂy. (15%) 2. A time-varying electric ﬁeld E(x,y,z,f) = jsin|:2rr[10't+£y-iz]+£:l+i 3 sin|:2rr[10't+£y—lz]+ 55] 443 443 exists in an inﬁniter extended dielectric medium ef permittivityr ans, and permeability #0 . Here all the quantities are in SI units. (a) Shew that the E -f1eld prepagates as a uniferm plane wave. (b) Find the phase velecity ef this uniferrn plane wave. (c) Find the dielectric censtant a, . x (d) Find the unit vecter' indicating the directien ef wave prepagatien. (e) Describe the pelarizatien ef the wave. Medium 1 Medium 2 (f) Find the cerrespeuding H -ﬁeld. (13%) 3. Censider the x-y plane as the interface between twe nencenducting media 1 and 2. as shewn in Fig. 1. A plane wave with the electric ﬁeld vecter expressed as E! (x, s) = jEme'iﬁ'lm‘EHWW is incident upen the E interface with an angle ef incidence 9-. H- Fig. 1 I I (a) Give an expressien fer its magnetic ﬁeld intensity vecter. (2%) (b) Give expressiens fer the electric ﬁeld intensity and the magnetic field intensity vecters ef the reﬂected wave. (4%) (c) Give expressiens fer the electric ﬁeld intensity and the magnetic ﬁeld intensity vecters ef the transmitted wave. (4%) (d) Derive the expressiens fer the reﬂectien and transmissien ceefﬁcients. (10%) (e) If rt, = p: . please discuss if it is pessible that the transmissien ceefﬁcient is unity. (5%) (i) Let #1 = #2 . E. = 25.}, a: = .9n and i9. = 60” , please give an expressien fer the magnitude ef the transmitted electric ﬁeld as a ﬁmctien cf 3. (5%) (g) What is the phase velecitjs,r ef the transmitted wave fer the case in part (1)? (3%) 4. Feur lessless transmissien lines are cennected as shewn in Fig. 2 with a 100 f2 resister terminatien. Find lengths L1, L2 and L3 fer a matched eenditien at AA" peints. (15%) 5. The standing-wave ratie en a lessless 50( Q ) transmissien line terminated in an unknearr lead impedance is 2.0. and the nearest veltage minimum is at a distance 0.125 xi. frem the lead. Determine (a) the reflectien ceefficient F ef the lead (9%) (b) the unltnewn lead impedance Z L (10%) ...
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