Question

ECE 336 Mid 1 (2020 spring) Name: In a non-magnetic medium (6-3), z<0, the E field component of an EMag wave given by: E = 10 cos(0-1-1/32 - x)a,, The wave oblique incidence to air at z 0. Please determine: (a) The polarization state of the oblique incidence (5pt) (b) The phaser form of the incident E field (5 pt) (c) (10pt) (d) The reflected E field (30 pt) (e) The transmitted H field (30 pt) (1) Assuming if we can change the relative dielectric constant (E) of the medium (z<0), can total reflection been achieved for the incident field? If it can, what would be the value range of &? (10pt) (8) Assuming if we can change the relative dielectric constant (E) of the medium (z<0), can total transmission been achieved for the incident field? If it can, what would be the value of &? (10 pt)

Answer 1

I it is pageNor-1 evident Isolation - Ee to cos (wt - 3z-x ay. (a) from the electromagnetic wave, it is en that the peopagation vector is K= √3 aztax. k=√(√3)² + (12 = 2 (k = 2 k=w Jub Eo = w a (6) The propagation vectos tanoi - kx at [01-300 J. c) Thee tore, w=kC 3 X108 m/8ee het [speed of light] = 2 X3x108 Grad/sec W = 6x10 6 Gad/sec la unit vector homal to the interface. is az, the plane containing te az.is y constant, which is the xy-plane, the plane at incidence. d) Easy way to find Er Let Ev=En coslut-kehday.

which is similar to form to the the unit vectos ay is chossen given in, vie ghen El, in view of the Component of E the interface. ab fact that the tervential component must be continuary at the in Koi = kraad-Kroaz. x = kor Sindr, kg = kx Cosos. But Dr= Di & ko=kiz 2 becue both krgki are in the same medium. K8= 3az ax. to find the Ero, we need or, fom Snell's law. - Cruel Sindi. Alizez Sinzo - 16.26°. Tut or - hence necosoi thi color. 3 Where ni=no=377, h = Mour = 377 ερες = 217.66. L-217.600](304) –377.00$(16.26) .-173.49 217.6 Cox (300)-4377CA (16.26) 549. [1=-0.316. Hence Eso = Tz Eio = -0.316 (10) =-3.164

xay vlm, Ex=-3.614 Cos (6x10 Pt-13z-x) ay v/m. es similarly, het the transmilted Ele Et=Eto Cos[wt-stray. Ist = B2=w Jerez = w jurer. - 6x08 3x108 VIX 3 = 3.464. Kra= ki Sinot = 0.969. Ktzaki casot &3.325 10) Ist0.969 ax +3.325593 To=Eto = 292 cordi 2Cojoithicosor 2X217.66 C08 (30) - 20.683 219-66 (os (30)°+377 (0f (16.26) The Same result could be obtained from the relation Tait Tz Hence, Eto = Ti E10 = 0.683x10 = 6.83 ft = 6.83 co${6x1047-0.96ax - 3.222)ay. from Et, it is easily obtained by tt = - KEX Et = aktxet اربيل

HP - 0.96ax +3.2@2_x6-83 cos (Gx1084-0.96Q% 3.46 X 217.16 -3.2a2). K HE = (8.1ax +55.99) C08 (6X108f-6.969X-3.292) ar malm Note! - If you like this solation, please give me Thoms up.