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Engineering Electromagnetics, 8th Edition Solution Manual

Engineering Electromagnetics, 8th Edition Solution Manual provides expert solutions to textbook questions, making complex problems easier to solve.

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CHAPTER 11.1.Given the vectorsM=10ax+ 4ay8azandN= 8ax+ 7ay2az, find:a) a unit vector in the direction ofM+ 2N.M+ 2N= 10ax4ay+ 8az+ 16ax+ 14ay4az= (26,10,4)Thusa=(26,10,4)|(26,10,4)|= (0.92,0.36,0.14)b) the magnitude of 5ax+N3M:(5,0,0) + (8,7,2)(30,12,24) = (43,5,22), and|(43,5,22)|= 48.6.c)|M||2N|(M+N):|(10,4,8)||(16,14,4)|(2,11,10) = (13.4)(21.6)(2,11,10)= (580.5,3193,2902)1.2.VectorAextends from the origin to (1,2,3) and vectorBfrom the origin to (2,3,-2).a) Find the unit vector in the direction of (AB): FirstAB= (ax+ 2ay+ 3az)(2ax+ 3ay2az) = (axay+ 5az)whose magnitude is|AB|= [(axay+ 5az)·(axay+ 5az)]1/2=p1 + 1 + 25 =3p3 = 5.20. The unit vector is thereforeaAB= (axay+ 5az)/5.20b) find the unit vector in the direction of the line extending from the origin to the midpoint of theline joining the ends ofAandB:The midpoint is located atPmp= [1 + (21)/2,2 + (32)/2,3 + (23)/2)] = (1.5,2.5,0.5)The unit vector is thenamp=(1.5ax+ 2.5ay+ 0.5az)p(1.5)2+ (2.5)2+ (0.5)2= (1.5ax+ 2.5ay+ 0.5az)/2.961.3.The vector from the origin to the pointAis given as (6,2,4), and the unit vector directed fromthe origin toward pointBis (2,2,1)/3. If pointsAandBare ten units apart, find the coordinatesof pointB.WithA= (6,2,4) andB=13B(2,2,1), we use the fact that|BA|= 10, or|(623B)ax(223B)ay(4 +13B)az|= 10Expanding, obtain368B+49B2+ 483B+49B2+ 16 +83B+19B2= 100orB28B44 = 0. ThusB=8±p641762= 11.75 (taking positive option) and soB= 23 (11.75)ax23 (11.75)ay+ 13 (11.75)az= 7.83ax7.83ay+ 3.92az1

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Subject
Electrical Engineering & Electronics
Textbook
Engineering Electromagnetics by Wil...

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