工程电磁场第八版课后答案第01章.pdf

《工程电磁场第八版课后答案第01章.pdf》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、CHAPTER11.1.GiventhevectorsM=10ax+4ay8azandN=8ax+7ay2az,find:a)aunitvectorinthedirectionofM+2N.M+2N=10ax4ay+8az+16ax+14ay4az=(26,10,4)Thus(26,10,4)a==(0.92,0.36,0.14)

2、(26,10,4)

3、b)themagnitudeof5ax+N3M:(5,0,0)+(8,7,2)(30,12,24)=(43,5,22),and

4、(43,5,22)

5、

6、=48.6.c)

7、M

8、

9、2N

10、(M+N):

11、(10,4,8)

12、

13、(16,14,4)

14、(2,11,10)=(13.4)(21.6)(2,11,10)=(580.5,3193,2902)1.2.VectorAextendsfromtheoriginto(1,2,3)andvectorBfromtheoriginto(2,3,-2).a)Findtheunitvectorinthedirectionof(AB):FirstAB=(ax+2ay+3az)(2ax+3ay2az)=(axay+5az

15、)p1/2whosepmagnitudeis

16、AB

17、=[(axay+5az)·(axay+5az)]=1+1+25=33=5.20.TheunitvectoristhereforeaAB=(axay+5az)/5.20b)findtheunitvectorinthedirectionofthelineextendingfromtheorigintothemidpointofthelinejoiningtheendsofAandB:ThemidpointislocatedatPmp=[1+(21)/2,2+(

18、32)/2,3+(23)/2)]=(1.5,2.5,0.5)Theunitvectoristhen(1.5ax+2.5ay+0.5az)amp=p=(1.5ax+2.5ay+0.5az)/2.96(1.5)2+(2.5)2+(0.5)21.3.ThevectorfromtheorigintothepointAisgivenas(6,2,4),andtheunitvectordirectedfromtheorigintowardpointBis(2,2,1)/3.IfpointsAandBaretenunits

19、apart,findthecoordinatesofpointB.WithA=(6,2,4)andB=1B(2,2,1),weusethefactthat

20、BA

21、=10,or3

22、(62B)a(22B)a(4+1B)a

23、=103x3y3zExpanding,obtain368B+4B2+48B+4B2+16+8B+1B2=100939p39orB28B44=0.ThusB=8±64176=11.75(takingpositiveoption)andso2221B=(11.75)ax(11.75)a

24、y+(11.75)az=7.83ax7.83ay+3.92az33311.4.Acircle,centeredattheoriginwitharadiusof2units,liesinthexyplane.Determinetheunitpvectorinrectangularcomponentsthatliesinthexyplane,istangenttothecircleat(3,1,0),andisinthegeneraldirectionofincreasingvaluesofy:Aunitvectorta

25、ngenttothiscircleinthegeneralincreasingydirectionist=a.Itspxandycomponentsaretx=a·ax=sin,andty=a·pay=cos.Atthepoint(3,1),=150,andsot=sin150acos150a=0.5(a+3a).xyxy1.5.AvectorfieldisspecifiedasG=24xya+12(x2+2)a+18z2a.Giventwopoints,P(1,2,1)xyzandQ(2,

26、1,3),find:a)GatP:G(1,2,1)=(48,36,18)b)aunitvectorinthedirectionofGatQ:G(2,1,3)=(48,72,162),so(48,72,162)aG==(0.26,0.39,0.88)

27、(48,72,162)

28、c)aunitvectordire