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HW2-sol - 56 hp(on ECE604 Homework#2 Out Wednesday Due...

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Unformatted text preview: 56 hp; (on ECE604 Homework #2 Out: Wednesday, January 21, 2009 Due: Wednesday, January 28, 2009 These problems are from Chapter 1 of the text by Ramo, Whinnery, and Van Duzer (3rd edition, 1994). 1) 1.8b 2) 1.10d 3) 1.110 4) 1.11e 5) 1.12b 6) 1.13a 7) 1.13b 8) 1.15b Also find the capacitance. Show that if the two dielectrics have the same dielectric constant (81 = 82 ), the capacitance reduces to what you would expect for a system of spherical conductors separated by a single dielectric. (You should solve for the single dielectric system independently.) 9) 1.180 10) 1.18e ECment 0&3 ohar c P5 AS =Jbsa’sin 9 d9dd> .5 03's..“ d 64’ _~ _‘ 7. ,‘ t A§cn= *e‘z—az'rfir‘ffr ;lr~6f\-(r +a~zmmose> 2:: w i ; 9&9 Q“) = 30 44’ = 39 4R6 Lr’-+0L‘—2raucose) =It = ‘ jodflr‘+03—2ra.c,ose)“i = é§%—[Cr+a)tLr-a)) 36? l-Bb Cons’sdefins mean3n3 o? (r1 +az—2racose) at \W‘ts, we sec that 1’ Sign appfies 'ms'\de s‘meve and —$'%n outside . ~'.§:Mu¢ = (1% 3 §w¢§de ‘7 $1.25.:- me Gauss: law 1 E'hm'de: = - {g}. :7.» mee= constant N50, mm“ = >%‘ %%‘t-’-- = * 2% Qoutszdc= $4? (Using 40.01: fined: §»o 0.5 r —-—>ao) :7. (Log-es— 5‘ch § ‘5 wnfinuous at r = a, , §in€ude r. = 1:0: +%)*+Szji 77777777 \.\od $6.5) “-3 ng‘éw"% ’Efi—ehé; where {a = [0“‘314'5’1t Thus (+¢\z+ ’ QM) = 44:20” $171-$337} W 5— 22 _ 4%” [14" dr+nznux§ggr+y12gx+si)- [(X—ri‘t-t-g’l'zh—éfi} 9“ ” e (”9’ +5’ - C‘“'=§‘*‘3’P é‘: = W; 5:53 SW“ ‘+ 2:. $3.313: ’ 1 51mpu<cieation Swes .—~ G5 ! A a 3" E = 5'35. 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