ECE311HW13solns - f=2510‘4x(3581)2’x108x5x60x103(47)3...

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Unformatted text preview: f=2510‘4x(3581)2’x108x5x60x103 / / ./ (47:)3 x0. 26x10‘3 I u" ff l/ 4' fi/fl x 7111684m/in631nm if"). "I i/f 4 ‘. . 3 , . }..581x10 x6(‘)z‘>‘<10.=15,01W/m2 Ear»: ,va its mm Prob. 13.1 1 Using vector transformation, A” = A” sine coscb , A9; = A” c059 c054) , A S =——Am sin¢ 506m . . . A: = ———(s1n6 cos ¢ar +Icos6?cos ¢a6 — Sln ¢a¢) r VxAs =Hs: IOOcosflsin¢ e"””a __5%(1__ jflr)sin¢e"””ag [u pr 2'sin6 ,ur ——59—cos600s ¢(1 + j,6r)e"’”’a¢ yrz At far field,‘ only 1 term remains. Henee r H,= J50 ———,8e'j”’(sin¢a6 —cos6?cos¢a¢) ,ur ES — — ———-——————(sin ¢a¢ +cosflcos¢a3) 3 i t l .g ;i H = Re [Hsejw‘] = fgflsinmt— flr)(sin ¢a9 —cosflcos ¢a¢) A/m E = Re [Esejw‘] = 52:6 sin(a)t— ,Br)(sin ¢a¢ +cos€cos ¢a9) V/m 394 10(1__ __ll__22|)ejflzcoseaz / m if y . Io /[ (1— Lzzlnoswzcosmdzu j (1——2—lil)sin(flzcos0)dz 4717‘ _% _/ Z 22 21 j(1-——)cos(fizcose)dz :41” I e-‘JB' p ] :22an cos2 9 [[1 cos( /cos(9) E3 = “jwflAs"“—’ E0: = jg)!“ Sin 6A2: = jflfl Sill 6A2; 1.111 e—jpr sin9[1— cos(BZcosE))] nrl ' Boos? 9 E9: , S (EQOSGY ' I If 5% ((1, cospécose): 1— —‘-2—2!——. Hence J'nI 81w E9s= Ble'jfl’ sinG, H¢ w = E9: /77 Pave = [E63l2 a 1:011sz (is a VG 1 2r7sm26r2 sin6d6d¢ 2 (b) 0.5 = 201:2—(92— ——> 1: 0.05;» Prob. 13.6 This may be regarded as a Hertzian dipole. 8 =3:3X10 =3.53m0r353cm \ 58?: .emnfiu an Ekzmwfl- 58303qu \ ”Em ; gm N ”838 Em AOHOSQMMHGOAG NLKNEEQ “mm 3ka I...“ 32m $2.? 6 who». uE o 93 Bama. u oasis a mm 2mm w m mm mod ......l|. \I\ I1!“ \ul .l quT |I\ .\.l.|\ \...| Ill. 111‘ ll .l\.|\“ I a a: I wq fq H :5 f X a .8 m m ofi mmoo+\\.l\l.\\\\. \llu .09 $82. 983 # gov ofl Sméfalm ”woos _ \-u ecu“ H >78 mvwmlmalm+Mlalm+ml 3 # w ¢ ¢ ¢ 0 m m Qmoo+.\\\\\\\1\ mnmoow Qmmood 2an = J240n x 12.73 x 10'6 = 0.098 V/m Prob.13.18 _ / I2 11132 i: I 2211B (dl)2 321c2 :(/2§— I21E :01 2211B (dlz) 25in 29 Prob.;1*é.19 _:’J UU _4nr2 Pav____e _ 81: sine cosd) =’jP .as {P .dS IV ave' / ave I E : But JP .=dS 1 £22 sine 0034) $1119 d0d¢ _ ' ' ' ave % ___,___.,..., 0 0 _/ f1 .1" G, = 8sin9 09315 D = G $48 d,max ; = ( § 5 _ ‘3 i. l s i 3. g § Prob. 13.20 . w E )_ El jnlae [004 Zeose cos 2 21trsin6 From Prob. 13.10, E65 = 408 _ D: G, = ,max (0) U ave = fig I]. COS] 9 Sin2 9231119” (76216“ Um = (2.1514, g-‘T‘U‘mx =33. 0200s2 67sin2 ”5 ‘:U _______2_ Gd ,max ave = 3:“0‘2~~~-‘ 12 sifize 2 . I: ' = o _ 26 d — 0 77.” r2 r s1n0dl9d¢- 240” (2n) J (1 cos ) ( cos ) 2 , m 2 2 _ _1_0 (cos 0—c0s6) 1;» _1_ 120 "120 90 I§=9ogve=90x50x10‘M ———> 1 ~2121A "~\\ \\ \_ WWWMW EM.” 3mm ' m . ‘ ( _, .. _ “*“memwmm 1% w: yawn”, “'5‘”: mm "Ex Prob. 13.28 This is similar to Fig. 13.10 except that the elements are z-directed. ~11». ' war: E =Es1 +Es2 =j17fl____1__0 d1 ——————[sin61 e (161+sin6?2 Lam] 47L- ’1 7'2 /" (b)Nu11s qccu’fahen 9036: c059) = 0 ———) 1c 0030 = in /2,ir31c /2,... 0r , . '9- =600,1200 h bag—":— (c) Maxima and minima occur when H ...
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