Question

Problem 3 A slab of pyrex is sandwiched between two slabs of silica glass. An electromagnetic plane-wave propagates through the three media at an angle normal to both interfaces. Assume zero conductivity for each medium, take the relative permittivity of silica glass as 3.8, and take the relative permittivity of pyrex as 4.7. if the electric field component of the incident plane wave within the first slab of silica glass (.e., Medium 1) is E{(z) = 210e - 122 V/m, then determine the following: a) total phasor electric field within each of the three slabs, assuming there is no reflected wave present in the second silica slab (i.e., Medium 3) b) total phasor magnetic field within each of the three slabs c) net average power density within each of the three slabs

Answer 1

Problem 3: Relative permittivity of dilica slab =3.8. 1. Refractive index of I Pyren ↑ silica slab = 13.8 silica 195 Similarly, refractive inden of pyrex slat 147 - 2117 Pi6= 4.7 67 Wowo, E, CB) - â 10 2 2jz the amplitude of the transmitted wave into the 2nd medium is, ut – 2x 53.8 13.8 +447 1.95 +2:17 2 X 1.95 - 3.90 20.957 4.12 :. Ē (2) - à 0195 x 10 = JZZ E a 9.5 21 27 Similarly, too. 2x29.7 1308 2X2:17 2:17 Hias 4.34 7-12 = 1.05 Ē (2) = 2 105 x 295 = Uzz E = 9.98 vez so the total phasor in electric field within each of twee redine is Ē, Ēr and Eg. Magnetic field in the birst medium, * , , * . 2 x + 1 = 5 10 12 13 14 MN, M M ATX 157 x 3X108 to e D2Z X 125 ATX3X16 A ŷ 0.052 252ZI zx à 9.56 257, - - - * *2 471 81 57 x 3 x 108 W = ý 0.055 ē uzz Ky X Ez iz aus e 127 22:17 40x167 y ATIXIO? ?
  
Ħg Kymes frî 9.98 eusz Ja Uzin, 47x157 x 37,08 8.98 x 1.95 Viz 1207 H = h 0.052 édia and Hts are the total khas or magnetic field i :. Ã Ã of the three slabs. c) Average power density in medium I is, <5>=< J. CĒ, xH)> << Lo 27 49 or 05, 13) 20.52 - se tiz > Å similarly, (52) = Ž x 59.5 eXzz & 0.055 è izz > <33) - * *9.98. 2027 x 01052 ej2z> - 0.52 -120.251 so, <5,>, <52> and <53) are the ret average power density of the three medium, 2