工程电磁场第八版课后答案第02章.pdf

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1、CHAPTER22.1.Threepointchargesarepositionedinthex-yplaneasfollows:5nCaty=5cm,-10nCaty=5cm,15nCatx=5cm.Findtherequiredx-ycoordinatesofa20-nCfourthchargethatwillproduceazeroelectricfieldattheorigin.Withthechargesthusconfigured,theelectricfieldattheoriginwillbethesuperpositionofthei

2、ndividualchargefields:✓◆11551013E0=4⇡✏(5)2ax(5)2ay(5)2ay=4⇡✏5[axay]nC/m00Thefield,E20,associatedwiththe20-nCcharge(evaluatedattheorigin)mustexactlycancelthisfield,sowewrite:✓◆✓◆13201E20=[axay]=2p[axay]4⇡✏054⇡✏0⇢2qpFromthis,weidentifythedistancefromtheorigin:⇢=100/(32)=4.8

3、5.Thexandpycoordinatesofthe20-nCchargewillbothbeequalinmagnitudeto4.85/2=3.43.Thecoodinatesofthe20-nCchargearethen(3.43,3.43).2.2.Pointchargesof1nCand-2nCarelocatedat(0,0,0)and(1,1,1),respectively,infreespace.Determinethevectorforceactingoneachcharge.First,theelectricfieldinten

4、sityassociatedwiththe1nCcharge,evalutatedatthe-2nCchargelocationis:✓◆11E12=p(ax+ay+az)nC/m4⇡✏0(3)3pinwhichthedistancebetweenchargesis3m.Theforceonthe-2nCchargeisthen21F12=q2E12=p(ax+ay+az)=(ax+ay+az)nN123⇡✏010.4⇡✏0Theforceonthe1nCchargeattheoriginisjusttheoppositeofthisresult

5、,or+1F21=(ax+ay+az)nN10.4⇡✏0122.3.Pointchargesof50nCeacharelocatedatA(1,0,0),B(1,0,0),C(0,1,0),andD(0,1,0)infreespace.FindthetotalforceonthechargeatA.Theforcewillbe:(50⇥109)2RRRCADABAF=++4⇡✏0

6、RCA

7、3

8、RDA

9、3

10、RBA

11、3pwhereRCA=axay,RDA=ax+ay,andRBA=2ax.Themagnitudesare

12、RCA

13、=

14、RDA

15、

16、=2,and

17、RBA

18、=2.Substitutingtheseleadsto(50⇥109)2112F=p+p+ax=21.5axµN4⇡✏022228wheredistancesareinmeters.2.4.EightidenticalpointchargesofQCeacharelocatedatthecornersofacubeofsidelengtha,withonechargeattheorigin,andwiththethreenearestchargesat(a,0,0),(0,a,0),and(0,0,a).Findanexp

19、ressionforthetotalvectorforceonthechargeatP(a,a,a),assumingfreespace:ThetotalelectricfieldatP(a,a,a)thatproducesaforceonthechargetherewillbethesumofthefieldsfromtheothersevencharges.Thisiswrittenbelow,wherethechargelocationsassociatedwitheachtermareindicated:2367q6ax+ay+azay+azax

20、+azax+ay7Enet(a,a,a)=26p+p+p+p+

21、{z}ax+ay+

22、{z}az74⇡✏0a4