工程电磁场与电磁波基础参考答案-张惠娟.pdf

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r q eEP 2 21 02 2022 )(2 )( )( 0) 1 ( d d1 )(2 )( , 0) 1 ( d d1 )(2 )( 2 2 2 21 02 22 2 2 2 21 01 11 r r rr q r r rr q pp PP 2 21 02 22 2 21 01 11 )(2 )( , )(2 )( a q b q ar rpa br rpb ePeP 2 21 02 22 2 21 01 11 )(2 )( , )(2 )( b q b q br rpb br rpb ePeP 0)( 2112 ePP p (3) 2 21 2 22 2 21 1 11 )(2 , )(2a q a q ar ra ar ra eEeE 2 21 2 22 2 21 1 11 )(2 , )(2b q b q br rb br rb eEeE DE 111 ED 222 EDEEE 21 2- 28 0 00 , 0 byyaxx axby y axy byax byx byax yx 0, 0, 0,0 0,0 0, 0,0 0,0,0 0 2 2 2 2 2- 30a )0,0(sinsin),( 01 ayax b y a x Uayx )0,0(sinsin),( 02 azax b y a x Uzax 0 U 1 a 2 2- 27 z y x a 1 2 a a 2- 30 0 0x x 0 0 0 0 0 0 0 0 2 1 2 (2 1 1 2 ( 1 1 2 ar ar r r e 2 2 2 2b2 2b b E 1 1 ED D 11 11 0 0 yay y y 0 2 2 2 2 2 2 a y a z a z a y a xU zyx 2 sinhsin 2 sinhsinsin )2sinh( ),( 0 2- 31 (kg qmhq 3 102m02. 0hm) 2 0 2 )2(4h q mg 82 0 109 . 516mghq C 2- 32 (1) (2) 01 02 2 1 q 2 qh2 1 q 1 q 111111 21 21 1 3 4 3 1 qqqqqqq 222222 12 12 2 3 2 3 1 qqqqqqq h qq h qq h q A 1 21 1 21 1 1 9 4 )2/3(4)2/(4 h qqq h qq h qq qEqF qq 1 21 2 1 2 1 21 2 1 21 11 9 2 48)2(4 11 2- 33Rq h R b 2 , q h R q 2222222 0 2 222 0 4 1 )()(4)2()()(4hRh Rh Rh Rhq h q bh q bh qq qEF qq q h 2 1 q1 q2 h h 2 1 q1 + 21 qq 2 1 A q2 = 21 qq h h h q h h b b h - q +q -q A A 4 EqFEqFq qF F F 1 1 Eq 111 4 4 q q1 1 q1 2222 qqq2 222 q q2 2 qq q1 1q ()2/ ) qqqq q 21 2(4 1 2- 38RqbRb qqq1 qq2 q 1 q 2 q 2 qq 1 q 1 q t q1 t q1d bRd 2 q t q1 t q1 q b R q R d qt 1 q t q1 q t q1 2 q 2 q 2- 41a(1)q E(2)(3) 2- 41 1Er Earr9 ESd 0 2 4dd q ErSES ro S ro E 2 0 4r q Ero )( 4 2 0 ar r q ro eE arr q ErSE ri S ri 2 4ddSE q 3 3 3 33 ) 3/4 ( 3 4 3 4 a qr a q rrq )( 44 33 ar a qr a qr E riri eE ar o a max E (a)(b) a0 0 r a ar r 2- 412- d 2 max 4a q Eri 2 0 max 4a q Ero 1 2 ri a rq eEP 3 0 0 4 )( )( 3 02 2 4 )(3 )( 1 a q Pr rr rp P 2 0 0 4 )( )( a q EE ar rirop 3 21 2 2 01 2 e d 2 1 d 2 1 V o V i VEVEW 0 2 1 5 1 8 a q 2- 42ba 0 a b Wln 4 2 0 )( 2 0 bra r E a b r r VEVW b a ln 4 d2) 2 ( 2 d 2 d 2 1 2 0 2 02 DE 2- 43 V b a)(abba a b V F ln )( 2 0 a b r V Er ln a b zV dzr r a b rE VEW zb av ln )( d )(ln 2 )( 2 1 d)( 2 1 2 0 0 22 2 0 2 0 a b V z W F constV ln )( 2 0 d d a a ) ) b E b 2 d 2 )()b( 2- 44mA ( B 0 l 1 l 2 lK Kg/m) Bmg TK )( 01 llKTmg (1) A, BBmg )( 02 llKT 2 l 2 2 2 0 4 1 l Q F )( 4 1 02 2 2 2 0 llK l Q mg (2) (1)(2) 01 12 01 02 2 2 2 0 1 4 1 ll ll mg ll ll mg l Q A B 2- 4401 12 02 4 ll ll mglQ A 1 3- 1aq r sinvr= 3 (4/3) Q a = 3 3sin 4 Q r Jv a = 2 2 3 00 3 3 0 3sin 2 4 3 2 ( cos ) 432 a S Q r IJ dSrdrd a QaQ a = = u vu v 3- 1 3- 2 2222 A/m2210 zyx zxyxzyeeeJ+=1)3=x 32 y2 . 58 . 3 z x e2) 3)x x J (1) x dSdydze= uu v 22 (102 xy J dSy zex ye= u vuu vuu v 2)10 zx x zedydzey zdydz+= uvuu v 35.23 2222 23.82 105(5.23.8 )399(A) z S IJ dSy dyzdzydy= u vu v (2)3x =2.5y =4.5z =J u v 2 281.254581 (A/m ) xyz Jeee=+ u vuu vuu vuv 2222 (281.5)( 45)(81)296.121 A/m )J =+ + u v (3) x J x J 2 399 285(A/m ) 1 1.4 x x I J S = 32 3 3 2 3.8 5.2 x y z r O Q a 2 . 5 2 . 5 x x dy yd d dzezex xd d u uu v u v u u u 10e u u u 2 2 2 y xy y 2 2 2 2 y (1J dS Sd=( 10y y z zdy 2 2 y y d 2 J u v x 3- 32.0 cm2.5 cm 20A 0.01m )02 . 0 025 . 0 ( 107 . 8 22 8 S R 2 02 . 0 01 . 0 S R 20A 5 105 . 1 R R I I (1) AII20(2) (1)(2) 0IAI20 3- 4Iz0z =z S J600 3- 4 0z = 2 sr I Je r = uu vuv 60o 60 0 26 s II IJ dld r = o s J A/m 60o r z I Iz z S S A A20 3 s IJ dl=IJdS= 3- 5() )(= E 0=J 0)(=+=EEEJ EE = EEED+=)( )(= =EEE 3- 6 12 12 U0(1)JE (2) 1Jr=1E1ra 00 ()r r E 0 U 0 ,ha ar, r ( )F= (1) 2 2 1 (sin) sin dd rdd = (sin)0 dd dd = 1 sin d C d = 12 ln(tan) 2 CC=+ 0R V = = 2 2R dd 2 2R2 2R R ) ) z z z d d d 01 1 0 R R J0+ + 0 h 0 7 1 C 2 C 0 = 0 U= 0 10 ln(tan) 2 CU= 90=0= 2 0C = 0 0 ln(tan) 2 ln(tan) 2 U (1)E uv E = uv 0 2 1 ln(tan) 2 ln(tan) 2 U Eee r r = = uvuu vuu v 0 0 ln(tan) sin 2 U e r = uu v 0 0 ln(tan) sin 2 U E r = 3- 12z l (0,d) 1 1 sin n z a n n n Aye a = =(0)x 2 1 0 1 sin()sin() n x l a n nn dy e nnaa = = (0)x R1, dR2) qq 12 ,dR dR 1 12 11 4 q RdR = =2(2 abU ab 2 2 a b ,= D E E , , U = = v v 11 2 21 11 4 q RdR = 12 2112 4 1111 q C RRdRdR = + 12 2112 4 1111 I G RRdRdR = + 2112 11111 4 I R GrRRdRdR =+ 3- 19E( 0 r), 100V/m 2 00 )rr()r(+=S/m 14 0 103 =S/m 20 1050 = .S/m3 6 0 106=rm (1)I (2) (3) 0 ( )r 1 122 00 ( ) ( )3 10/ r Jr E raA m = u ruruu r 2 0 4 s IJ dsr J= u r 6 212 4 (6 10 )3 101357.2A = = 2 2 000 0 22 ( ) ( ) ( )() 4 rr rr E rI J raarr rr = = u ruu ruu r 2 000 2 ( )1( ) ( )( ) J rJ r Er rrrr = u r ur 2 0 000 2 220 0000 22 1 ( ) ( ) () 2( )/ ( ) r E r rrr rr r E rC m rr = = I = 0 rr(rr(r(r( 0 0 ( 6 0000) 3 r r 00 a a= = 3a u uu r u ru 4 4 s J d ds sdr JJ d ds sd 4 4 (6 64=(64 u r u 12 0000 ( )( ) sr a E rE r= uu r ur 102 8.85 10/C m = 1 0 0 ( )( ) r rE r dr = urr 0 2 000 22 00 2 0 2 0 20 0 0000 0 22 00 20 0 0 0000 2 00 0 ( ) () ( )2 ln ( ) 1 ln 2 384000 r rE r dr rrr r r E r r r rr r E rr rr V = + + = + + + 3- 20ac br = 1122 (1) 0 UJra=bc (2)(3) 1I s JdSI= 22 12 22JrJrI+= 12tt EE= 12 EEE= 111 JE= 222 JE= 2 12 2()rEI+= 2 12 2 () I E r = + ()arb rr I B 5 0 102 2 = 4- 8a a rJ x 0 eJ = 0 J ra ea r J B r r 2 00 3 = 4- 9Sl r NI (1)HB (2)(3)(4) 1 = NIdHNIH2=eH l2 NI = e l NI H r r 2 B 0 0 = v 2 l ISN N r 2 2 0 = 3NS l r 2 L 0 = = 4 4- 10abab z M z z MMe= v v M 0 m JM= vv 4- 10 I N N r N 2 0 = L= = = = I I ( ( = l ISI 2 NS l l r0 () 1 0 mnzz KMeMee= = vv vvv 5.9 mnz KMeMeeMe= vv vvvv m IK b= ba ()() 22 00 3 23 2 2222 22 IaMba B zaza = + () 2 3 2 22 02 BMba H za = + B v H v z 0 0 0 1BM = vv 0 BM vv 4- 11H0 12 H1H2 12 BBB= vvv 1 H v 2 H v 0 H v 2 hl vv 0 BM 12 1 H H 4- 11 ( )( )()() 11211222 c H dlHPhHPhHPhHPhI= + = vv H v 0Hl = vv I ( )() 00102 22 c H dlHPhHPhI= = vv 1 P 2 P 120 2HHH+= vvv 0 12 2 BB H+= vv v 12 0 12 2 BH= + vv 2 10 112 2B HH= + v vv 1 20 212 2B HH= + v 4- 12y=0 x eK4=A/m Zyx eeeH332 1 +=A/mH2 4- 130y y yx eeB105 . 0 0 =mT B yx eeB5 . 010+=mT B0 1 xxyyzz Be Be Be B=+ 1212 , nntt BBHH= 0 10 yy BB= y 12 0 0 12 BH 1212 + vv 10 1 1 B HH B B 2020 B B HHHH 2020 B 2020 v v B y 3 3e e e ey y 0 000 0.5 xx r BB = 0 00 0 zz r BB = 2500,10,0 xyz BBB= = 250010 xy Bee= 2 0000xxyyzz Be Be Be B=+ 1212 , nntt BBHH= 0 0.5 yy BB= 0 000 10 5000 xx r BB = 0 00 0 zz r BB = 000 0.002,0.5,0 xyz BBB= 0 0.0020.5 xy Bee=+ 4- 14d 0 J z e a 0z a Juu r B ur 0z a J uu r 100y BaJ x= uu ruu r 2 d x z zz AA a= 2 0 AJ= 1 A 2 A ra 1 00 1 () A rrJ rrr = + ra 2 1 ()0 A r rrr = 3 10012 1 ln 9 AJ rCrC=+ 234 lnACrC=+ 1234 ,C C C C 0r = 1 0C = 3 200 1 9 CJ a= 3 300 1 3 CJ a= 3 400 1 ln 3 CJ aa= 33 110000 11 () 99 zz Aa AJ rJ a a= 33 00 1 () 9 z Jra a= 3 2200 1 ln 3 zz r Aa AJ aa a = BA= 2 1 1100 1 3 A BAaJ r a r = = 32 2200 1 3 z A BAaJ a a rr = = = 4- 181=x0=yz I- IB 1= = 2 2 B B = 0000 1 3 J 00 = zz ln zz r ln a 1 1 AA = 2 2 A2 A = 00 ln 2 z Ir Aa r = 0 r p1x = 1x = + 000 12 (lnln) 2 z Irr Aa rr = 02 1 ln 2 z Ir a r = 2 0 2 12 cos ln() 212 cos z Irr a rr + = + 1 () zz zzr AA BAa Aaa rr = = + 2 0 22 12 (1)sin r Ir B r r + = 2 0 22 12 (1)cosI r B r r = 0 z B = 4- 19 cos 0 KeK z = ( , ,0)P r x y z r r 1 r - 110 a= = 12 n) rr 12 1 1 r1 2 0 0 1 1 ln n 21 I I 1 +rr B = 1m2m a 1m2m r 2 11 22 11 0 mm r rrrrr += 2 22 22 11 0 mm r rrrrr += cos 1m2m 111 sincos m C rDr=+()ra 11 11 1 mm mr Hee rrr = = v vv ()() 1111 sincoscossin r eCDeCD= + vv 22 22 1 mm mr Hee rrr = = v vv ()() 2222 22 11 sincoscossin r eCDeCD rr = + vv ra= 12rr HH= 210cosS HHJ= 12 0DD= 10 1 2 S CJ= 2 20 1 2 S CJa= () 00 1 sincos 22 SS ry JJ Heee= += v vvv ()ra 4- 20r0=15cma=2cm r=1400 N=1000I=0.7A l0=0.1cm( r ) 1212121212 (CDc cos sc c sc 2222mmmm222222 rrrr 2222 ) 2 2222 2 11 )c 222222 sD rrrr ) )D 12 H H CJCJ 1 0 ar 0 2 NI H r = 22 0 2 a N I NS H r = 22722 0 1400*4 *10*0.02 *1000 2.346 22*0.15 a N LH Ir = 2 0 BBB= 0 000 (2)H lHrlNI+= 0000 , r BHBH= 0 BBB= 0 000 (2) r r NI B lrl = + 22 0 000 (2) r r a N I NSB lrl = + 222722 0 000 4*10*1400*0.02 *1000 0.944 (2)1400*0.0012*0.150.001 r r a N Ilrl = + 1 2 2 0000 0.5 m WH Sl= 2 000 0.5(2) mr WH Srl= 00 00 1400*0.001 1.487 22 *0.150.001 mr m Wl Wrl = 4- 21ab 12 I 1 ra 0 0 ( r r l l0 0+ + 0000) 22 0000 (2)2) 0000 a2 222 2)2) 0000 (2)2)+( ( 2 4*1 ) )140 4 rl 00) 140rl 0 0.5 .5 m m Wm= = WW 2 0 2 2 I rHr a = 0 2 () 2 I Hr ra a = arb() 12 r HHI+= 12 12 12 , BB HH= 12 BBB= () 12 12 () I Barb r = + 222 abb 0 0aa 012 111 2 rdr+rdr+rdr= 222 m BBB W = () ab 2012 2 0a 01212 r11111 2 rdr+rdr= 22 a2 II r + + () 22 012 12 b ln 162a II + + 2 2 0.5 M WLI= () 012 2 12 2b ln 8a M W L I =+ + 4- 22a I 2 2 0 2 00 2d a r IJrIrBlB= = 2 0 2 a Ir B = dr 2 dSd 2 0 a Ir = r I ,I , 2 2 a r = I I N ab 0a0a ()()()() 0a 2 ()() ab 0a 0a 0a 2a () 0 8a8a()8a8a8a =+=+ 0 I 0I I 8 dr a r 2 d 0 a 0 2 2 2 0 I a Ir N= 8 0 i I L = 4- 23d a(ad)b 1 C 1 I 2 1 1 3 22 2 2() z I b B bd = + daB 2 S 2 2 0 1 2112 3 22 2 2() I b B Sa bd = + 22 021 3 22 2 12() a b M I bd = + 4- 24 21222122 0 )(2 ln 2RbCRb Ra M + = I r2 0I B = 0 1 I d b 1 C z 1 1 1 11 I I 2 z I b B = = R RII SB 10 R R 0 ln r2 a dr r2 a d 1 = ()() 2 1 22 2 1 22 2 1 2 222 1 bcb2cbc += +=RRRR 4- 25(a)d )( 22 0 addM= )cos(22 00 rd I x I B + = rdrd rd I BdS a + = 0 2 0 0 )cos(2 = + 2 022 2 cos ad ad d )( 22 0 022 0 addI rd rdr I a = = )( 22 0 addM= 4- 26d=5mmD=25mm U=1000V I=1AP P x y z r r 1 r - 1 1 0 4- 18 z I1 d C1 a 4- 23 0 b I - I I= r r r r r rdrd )rc = 2 2 cos 02 d 0 12Dd l 0 ln(2) C D d = 0 ln(2) l U CU D d = P 0 22 2(2)ln(2) l p U E DDD d = P 2 2 00 1 2 2ln(2) ep U E DD d = 2 12 3 33 1000 2 8.854 10 25 10ln(2 25 5) 5.344 10J m = = P 2 2 (2) p I H D = 2 2 00 1 2 2 mp I H D = 2 7 3 43 1 2 410 25 10 4.07 10J m = = 2 2 2 0 0 22ln(2) l e U F DDD d = 2 12 3 4 8.854 101000 2 25 10ln(2 25 5) 1.05 10N m = = 272 4 0 3 4101 0.08 10 2225 10 m I FN m D = 444 1.05 100.08 100.97 10 em FFFN m =+= += mp 2 5) 5 ( 2 2 0000 2 2 2 mpmp000000 2 2 2 2 2 2 2 4 4 4 4 4 4= 4 4- 27aI1I2 Fm 1z2 a I eB 2 10 = 2 22dl I1 a dlII ra dlII z eeeBdlIdF 2222 22102210 = 2 a dlII r eF 2 2210 = 4- 28 y e I B x2 10 = BdlIF= 22 + = baa cII eF x 11 2 210 a bac M + =ln 2 0 a bac IIIMIW + =ln 2 0 2121 a a + = + = = baa c II aa c II W F I 11 2 1 b 1 2a 0 21 0 21 4- 24 d I 4- 26 I U P D = y I x x 10 0I x x x IF F 4- 29UNI m S C = y 123mmmm WWWW=+ 1m W 2m W 3m WU 1m W 2m W 2 2m20 VV 1 dVH dV 2 m W= 22 y 1 2 V0 00 1 0 B dVSdy 22S y 2S = = 5.20 4- 29 x y 0 d b a I 4- 28 00000000 2 m21 C 0 W 2| S y F y = = = 2 1 0S y Fe = v v 1 ly 3 l 1033 () 1 123 3 2H lHyH lNI+= 123 BBBB= 31 103 2 NI B lly = + 1 31 103 2 NIS BS lly = + 22 1 31 103 1 22 2 m N I S WNI lly = = + 22 2 01 0 31 103 2 | 2 2 m yI C N I S W F ySl ly = = = + 2 1 0 yyy Fe Fe S = v vv y y F = = I SI S 22 l2 1 1 103 2 2 |I C I C ySyS |I C I CI C= = F Fe= = v v 5 5- 1wh y n ey(1)(2) m tBeB)sin( x (1) ny hwtee )sin( m S BSB d cos)sin( thwBm td d cos) tcos(hw (2) n e)(t n et Stt n )()(eB)cos()sin(cos)sin(tthwBhtB myxm ee td d )cos( m thwB 5- 2)cos(ti m baI (1)(2)v 2 00 Ii B 2 )cos( t m S SB d ac c Im b t d ) 2 cos( 0 c ac tI b m ln)cos( 2 0 td d c ac tI b msin( 2 0 ln) (2) i a b c 5- 2 in in x en h w B 0 z y 5- 1 in i iI I )( cosB y y cos e td mh B Bm )cos() 0i vtac vtc m b tI d 2 )cos( 0 vtc vtac tI b m ln)cos( 2 0 t d d )cos( )( ln)sin( 2 0 t vtacvtc av vtc vtac t bIm in 5- 3 y zteA/m 10310.2H 95 )10cos(7 0J t D H x y d z H t eH D J x zte10310.2 94 )10cos(7 (A/ 2 m ) 5- 4t A/ 2 J 92 10cos1025. 1m 3 10 S/m5 . 6 r J E)10cos(1025. 1 10 )10cos(1025. 1 95 3 92 t t (V/)m )10cos(1025. 11085. 85 . 6 9512 tED)10cos(1019. 7 916 tC/ 2 m t D Jd)10sin(1019. 7 97 t (A/ 2 m ) 5- 5 rd zkt r eJ)cos( 104 1, 2 rr EH 5- 6 x zV/mte106E 9 )9 .2028.sin(1 . 0 HB yy x zt z E t e106eE B 9 )9 .2028.cos(09. 2 t yy x ztt z E e106eB 9 )9 .2028.sin(1033 . 3 d 10 (T) 10 0 0 0 J x e ) (A/ (m A/ 9 10cos s 1025. 1 25. 1 5 25. 1 5. 1 10co10 95 D 1 . 7 7 1 . 7 7 y zte106 B H 9 )9 .2028.sin(1065. 2 4 0 (A/m) 5- 70zdz ym xktz d EeE)cos(sin V/mk (1)H(2)K (1) t B E z y x y x E z E t ee H 0 t x E z E z y x y d)( 1 0 eeH zx m xkt d z kxkt d z d E ee)cos(sin)sin(cos 0 EH (2)0z y z z eHK 0 0 y m xkt d E e )sin( 0 dz y dz dz eHK y m xkt d E e )sin( 0 5- 8Ey 0)(cos 0)(cos ztczE ztczE E m m y 0z (1) t H E 0 z H t H y x 0 0z )(sin 0 t c z E ct H m x t )(cos)(cos 1 0 0 0 0 t c z Et c z E c H mmzx z K K d z cos(sin n z 0z E si 0 0 y dz d e 0z)(cos 0 0 0 t c z EH mzx 0z0z KHH tt12 )cos(2 0 0 00 tEKHH myzxzx 5- 9JEH )( 2 2 2 tt JE EJ H H 2 2 2 t (1)J t E JH t H E0HE )(EJH t HHH 2 )( HH 2 )()(EJ t J H H 2 2 2 t H )(HE t EE 2 )()(H t tt 1 2 2 2 JE E 5- 101mm4mm1, 2 r z r r kzt r eE)105cos( 40 7 V/m(1)(2) HK100zm d J E ) ) H 2 J J J H H 2 2 (1)E)()( v z tz k tEvz (2) 2357 . 0 103