Electromagnetic Waves Mtatermet 1-) (20 Prints) a) Write the Maxwell Equarlons

Electromagnetic Waves

Mtatermet

1-) (20 Prints)

a) Write the Maxwell Equarlons .

b) write the name and unit of all termes (EH...) im Maxwell EQuariens .

c) write the Maxwell Equation in phaser fava (time dependence nf EM wave | assumed to be giwty

d) write the t) Poynminmg vector it) coneplex Poynting vector awd then describe the relation

between tnéme.

2-) (15 Poimts) Assume that E (x,t) 1s the solution ot wave eauation. And tne emitral comalivons ave

OE i,

E(x,0) = f(x) ana or (x,0) = 0. rnder these tnitiai conditions, E(x, t) becomes E(x,t) =

(f(x —ct) + f(x +ct))/2 of f(x) te a function Given in fictuire below. plot the E(x, ¢) at t=usee

E(x,t ) at t= 2sec

3-) (45 Points)An. CLEctrOMmMag WetLe WAVE LS represented by the Superposition of two plane WAVES of

equal frequencis (Wy = Wz = Ww) which are propagating within a free space(é = Ep, fd = Mg) see

figures celow. The electric fielol of the first and second wave is aven by E, = Ege—!*1"8, and

E, = Eye tka. respectivel lt.

y ‘ ky

iy - z

i

x - . 1”

Zz _¢ LF

i ee ky

! f

|

Da) Complete the frcwre with the maanerte fields Hy and Ho. Determine the macnnitunes (absolute

value) nt H, Awd H,

b) What are the maanrtuae S ef k, and K> Lu terms of Ww. Wirite down the ki. r QnUnA k,.7 YS

functions ef C15

c)} Calculate the electric and maanetic field of tne total wave as functions of at1=. Simplify the

result using tne oiven nents.

d) What is dlrection of propaaation of the total wave?

e) Deseribve the pelarization of tne total wave.

JX gpA7JX $X op 4x

Hints: Cosx = ——, Sinx = —*—

4-) (20 Peints)To shield a room frown radio interference, the room must be enclosed im & Layer oF

copper five skim-depths thick. If the frequency to be sivelded against tn 10 RHz te 1 GHz, what

should be the thiclemess of the copper (in millimeters)? For copper, € = Eo, = Hg AnD O = 5.R X

10 S/m.

Electromagnetic waves

Midterm Exam 2

4- (10) a- write the Maxwell Equations tir differential forme

6- write the name ana unit cf all terms (EH...) tn Maxwell Equations

c- write the SWR (voltage standing wave ratic)

2- (10 Points) Consider the uniform electromagnetic plane wave with frequency f = MHz Ln

a lossless dielectric mexiuva(e = &Eg, Ut = Hy). if the electric field can be written tn the

following form E = E,e7?@* +2V3 z)@> (Ey: constant)

a) Tretermine the wavenumber k, propagation direction, nN and dielectric sowstant Ey.

b) Find the corresper.aing phasor expression of magnetic field H?

3- (25 Points) The electric fleld trtensicyy of uniform plane wave propagate in the +2

direction in seawater is E = 100 cos(10’mt)é, v/ne at z = 0. The constitutive

parameters for the seawater &, = 72, = 1,0 = 4S/m

a- Determine the attenuation constant, pase constant, complex characteristic

impedance, phase velocity, wavelengtn and the skein depth,

b- Determine the amplitude of electric flela intensity at z = 0.8

c- Determine the instantaneous expression of magnetic fleld ?

4) (30 Points)A parallel polarized plane wave (H; [Jey ), with incident angle @; is incident on a

free space-PEC medium (y = 0) as shown in Figure below. . Assume that the frequency of the wave

ls B0CMHZz and tne avaplitude cf the incident magnetic field is 1.

a) write the instantangous expressions of incident magnetic fiela Hi; awd electric fiela E; Lv.

free space.

b) Determine the pnasor expressions of total electric and maanetic fields.

c) Write the bropaaatiow. Atrectlon of total wave,

d) what is the time-averaged power bin free-space?

4- (25 Poimts) Consider a plane wave tnci2zent on a planar boundary atx = 0 froma

Avelectric medium as shown in the Figure. The riont-hana cireula rly polarized incident

tLectvic field is

E; = Eo[2é, sin(wt—(k,x + kyy)) + (V3é, — é,) cos(wt — (k,x + kyy))|

Wrert Eg is a real constant. Reflected wave is

E, = Eo[TPe'P 22, sin(wt — (—k,x + kyy)) + rPar(_/3é,, — é,) cos(wt — (—k,x + kyy))]

a- What is the incident anale, 0;?

b- For ky = 1, determine the frequency awd the wavelenath

c- Iw the case cf & = 3£p, find the polarization of the reflected wave.