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----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------89----------------------------------------------------------114------------------------------------------------------121012314πεqqrr=F0q=FEi=∑12NiE=E+E++EE00aaaWUq==∫idElbababaUUUd=−=∫iEl0aaU=∫idEl=-gradUEldUEdl=−100aaWqdqU==∫iEl0aa→b()00abababAWWqUUqd=−=−=∫ibaEl101kiiSdε==q∑∫iES0Ld=∫iEl0()E=rR20(q)E=r4rπε≥R0()4qUrRRπε=0()4qRrπε=≥Ur02πεrEλ=220E=σε()032224πεqxE=Rx+()12220044PqqUrRxπεπε==+EFq020q=4rπε0ErqrEFEFqEqrrEABdS+qqf=q2/(4π0d2)fqEE=σ/σ=q/Sf=q2/(0S)fE=q/(0S)qf=qEqd+q-q2002qqfEdqSε==∫30dEdlLL⋅=⋅≠∫∫aElABCDDσExbσ02ε45EEEE1BEESSSSSEEEQLr22π1QE=04Lrε−2r2204Lrr+π21QεE=LdxdqQdxLPrrqεeE20dπ41d′=P∫=EEd1PP∫=LEiEd2PaExP∫∫==LyEαEjjEdsind1Pd2L0qE4πεr=′∫r'rx=−()220022204π12/12/1π4dπ41LrQεLrLrLεQxrLxQεEL/-L/P−=⎥⎦⎤⎢⎣⎡+−−=−=∫x2PEyErεqαELdπ4dsin20∫′=sinαrr22xrr+=′6()2dππL/23/22222-L/001rQxQ1E4ε2εr4rLLxr==++∫LλPrελLrLQrεEl0220π2/41/π21lim=+=∞→b122r/Lr0λ1x212q=FEFλEE1P+E−EP()iiEEExrxrελxrxελ−=⎟⎟⎠⎞⎜⎜⎝⎛−+=+=+−00000π211π22+F−F7π200λλ2εr+−==FEiiEF002π2rελλ−=−=+−+−F=Fq1=1.0×10-6Cq2=2.0×10-6Cd=10cmPqx()1222001144qqxdxπεπε=−12124.1410qxdmqq−==×+ER1S∫⋅=SSdsEΦ2RSS∑∫=⋅1d0εSSE=0qSS8∫∫′⋅−=⋅=SSSESEΦdd1∫∫′⋅−=⋅=SSSESEΦdddSERπRE22πcosπ=⋅⋅−=Φ2()rEeeeEϕθθϕϕθϕsinsincossincos++=rReSϕθθddsind2=ERERERSS2π0π02222πdsindsinddsinsind===⋅=∫∫∫∫ϕϕθθϕθϕθSEΦR()()Rrρkrρ=≤≤=0Rr0kEr192Sπ4drE⋅=⋅∫SE∫∫=⋅Vρεd1d0SE2rrρq′′⋅=dπ4d20d=ErrεqeE20π4dd=()()()()RrrrRr=≤≤=∫∫dRr0d00EEEE1∫∫=⋅Vρεd1d0SE0rR()400202πdπ41π4rεkrrkrεrrEr==∫()rεkrreE024=rR()400202πdπ41π4RkrrkrrrERεε==∫()rrkRreE2044ε=2rrrkVρq′′′==dπ4dd2100rR()rrrεkrrrrrkεreeE0222004dπ4π41=′′⋅′=∫rR()rrRrkRrrrrkreeE20422004d441εππε=′′⋅′=∫R1R2Q1R3Q2Or24drπE⋅=∫SE∑q∑∫=0/dεqSEr∑=⋅02/π4εqrErR10=∑q01=ER1rR2()31323131RRRrQq−−=∑11()()23132031312π4rRRεRrQE−−=R2rR3Q12013π4rεQE=rR3Q1Q220214π4rεQQE+=brR30230234π4∆εσRεQEEE==−=E1R2R21(RR)r11rR212RrR32rR∫⋅=rLEdπ2SE∑q∑=⋅0/π2εqrLErR10=∑q1201=ER1rR2Lλq=∑rελE02π2=rR20=∑q03=E000π2π2∆εσrLεLλrελE===Q1Q2Q3Q13QQQ==1Q3Q2OQ1Q3Q2W′W1'W=−WlEd02∫∞=QWEQ1Q32()0202VQVVQW=−=∞13V0Q1Q3O1Q1()02π4π420312021=+dεQQdεQQQQQ414132−=−=Q1Q3y()π1y3y3/2220QyEEE2εdy=+=+Q2Oy()ddππ223/22200001QyWQQy48εd2εdy∞∞⎡⎤′⎢⎥=−⋅=−−⋅=⎢⎥⎣⎦+∫∫ElQ21QQ412−=Q1Q3OdεQdεQdεQV003010π2π4π4=+=Q2OdεQVQW0202π8=−=′rrελeE0π2=1rr1rr22r14112012lnπ2d21rrελUrr=⋅=∫rE2rerελE0π2=rσσaxi02εσ±15()()()⎪⎪⎩⎪⎪⎨⎧−−=axaxaax000iEεσ()axaxεσVx−−=⋅=∫d00lE()axaεσV−=⋅+⋅=∫∫−dd00a-axlElE()axaεσV−=⋅+⋅=∫∫dd00a-axlElEbR1R2Q1Q21212∫∞⋅=ppVlEdrεQV0π4=RεQV0π4=16R11()()()22021321201211π4π40RrrεQQRrRrεQRrrr+===eEeEE∫∞⋅=rVlEdrR1202101202121013211π4π4π411π40ddd2211RεQRεQRεQQRRεQVRRRRr+=++⎥⎦⎤⎢⎣⎡−+=⋅+⋅+⋅=∫∫∫∞lElElER1rR2202012021201322π4π4π411π4dd22RεQrεQRεQQRrεQVRRr+=++⎥⎦⎤⎢⎣⎡−=⋅+⋅=∫∫∞lElErR2rεQQVr02133π4d+=⋅=∫∞lE2⎟⎟⎠⎞⎜⎜⎝⎛−=⋅=∫210121211π4d21RRεQURRlE2117rR12021011π4π4RεQRεQV+=R1rR2202012π4π4RεQrεQV+=rR2rεQQV0213π4+=2()2011012112π4π42RεQRεQVVURr−=−==Rρ∫∫=⋅VVεd1d0SEEr()lEd⋅=−∫babarVVVb0alrrR02/ππ2ερlrrlE=⋅()02εrρrE=18rR02/ππ2ερlRrlE=⋅()rεRρrE022=rR()()22004d2rRερrεrρrVRr−==∫rR()rRεRρrrεRρrVRrln2d20202==∫R130102mR2010m45012r005m115rελE0π2=120212lnπ2d21RRελURR=⋅=∫lE1812120mC101.2ln/π2−−⋅×==RRUελ2r005m10mV7475π2−⋅==rελE19+-qOOCDDDABODAB2l=OCDBlAqB000011qq104π4π4πqqUOAODllεεε⎡⎤=−=−=⎢⎥⎣⎦0001114π4π4π36πDqqqqU0qADBDlllεεεε−⎡⎤=−=−=⎢⎥⎣⎦()006πODODqWqUUlε=−=()006πDDqWqUUlε∞∞=−=RRRRU1230()q=RrR4rπεEr22112201d4πRRRRqUdrε=⋅=∫∫Elrq012214πRRUqRRε=−()12220214πRRUqErRRrε==−200E=E⊥0q=0Eσε=01'1r=σσε⎛⎞−⎜⎟⎝⎠0_,rqCCUUε+==−C0rSSCddεεε==()()022lnlnrllCRRRRπεεπε==044rRRRRCRRRRπεεπε==−−211niiCC==∑111niiCC==∑201122ewEε==⋅ED2012eeVVWwdVEdε==∫∫V0()SSdq⋅=∑∫DS0rεεε==DEE0Ld=∫iEl)PP0q0(0q0q0q0FqPP0q0FqPq(0q)2R221R204(qrπε)rP20σε()2224Rqσπ=20σε2σ()2224Rqσπ=ABABBAABAABABBABABBABABBABABB23BAB02σεσ0σεSσdSS012Eσε=SS2E1E2E02E2σε=1E2E0σεσσ0CSdε=d()0ABCQUU=−ABUU−CQ()ABEUUd=−UUAB−d()2ABQWUU=−QMNNN24ANBNCNDNNNNAqRdOAπ0qE0,U4εd==Bππ200qqE,U4εd4εd==CE0,U0==Dππ200qqE,U4εd4εR==qq′q′OOqAABCDE25QQSdSdSdE0/d==⋅∫0∑Sσ2σ3σ4εqSE∑=0qσ1SSS0/d0==⋅∫∑SεqSE260,0∆∆3232=+=+=∑σσSσSσq0,022224104030201=−=−−−σσεσεσεσεσRRQUπ002QU4εR=π002QU4εR≠qdppU∞=⋅∫ElU0QRR()()∑∫⋅=⋅=⋅02/π4dεqrErrESErR()01=rERrR()202π4rεqrE=27rR()202π4rεqQrE+=rR123ddddππ1212RR1rrRR0102qQU4εR4εR∞∞=⋅=⋅+⋅+⋅=+∫∫∫∫ElElElElRrR23dddππ22R2rrR00qQU4εr4ε2R∞∞=⋅=⋅+⋅=+∫∫∫ElElElrRdπ3r0qQU4εr∞+=⋅=∫3ElrRππ10102qQU4εR4εR=+RrRππ200qQU4εr4ε2R=+rRπ30qQU4εr+=ππ100201qQUU4εR4εR==+ππ100201qQUU4εR4εR==+28rR01=E10UU=RrR101222024πRURQErεRr=−π101202RU(rR)QUr4εRr−=−rRπ102132202RU(RR)QEr4εRr−=−π1021302RU(RR)QUr4εRr−=−QbOrqqqOqddUπ0q4εR=RRdsU4εππ00qqR4εR==∫∫qqπππ00qqqU4εr4εa4εb+=−+0QROrrRq29Vqq′q′Odπs0qU'4εR′=∫Oπ00qUU4εr=+'U00q′ddππππss0000qqq1U'q04εr4εR4εr4εR′′=+=+=∫∫qrRqq∫−=′=′d2-13cm0.61=rcm0.122=r3C108−×r11q2r2q20210144rπεqrπεq=12821106−×=+qqCq81102−×=Cq82104−×=1430LπεQdrrπεQWL022020441=