1、qqABEABABeFkFEldEKABeFkFkELKl dENNSNS二二.实验分析实验分析l特征：特征：穿过回路所围面积内的穿过回路所围面积内的发生了变化发生了变化l感应电动势：感应电动势：由于回路中磁通量的变由于回路中磁通量的变化而产生的电动势化而产生的电动势Ndtdin00dtd0iin00dtd0i0dtd0iiii0dtd0iRIii21ttiidtIq211dR)(121RdtdR12.LKil dESSdBSLKSdBdtdl dESSdtB)(21Ndtddtd=Nn21dtdidtdN)()()(21dtddtddtdNiiINiINdtdidtdiMIMnIBr0NNB
2、SnISNr0dtdidtdInSNr0V75.0iRIii275.021ttiidtIqtIiC76.0A38.0MIabcd1l2lxvIabcd1l2ldrrSdBddrlrI102SSdB2210lxxrdrIlxlxIl210ln2dtdidtdxlxxlIl)(22210)(22210lxxvlIlIabcd1l2lxlxIl210ln2B 00aaBn2cosBStBacos2ntBa2cos2dtdNintnNBa2sin220302ntnNBai212sinntnNBai2max2slRsNa4)(21RNqi)180cos0cos(0202BaBaRNRNBa222Basn
3、tnNBai2sin22abcd外FvBSBBSBlxldtdi)(BlxdtddtdxBlBlviabcd外FvBliBlviBvef)(BvabffKEeBve)(BvEKLKil dEabKl dEabl dBv)(BlvvBabkE 0iiLil dBv)(vfvBab vV vvVBVeFBveBveffBvve)(f fFBVqfLVFP洛)()(vvff vfvf vBvevBve)()(BvvevevB0v vVf fFvfvf 外 ff外vfv f vf外f0 vfvfP洛mFmFlBIFimabviIF iiiIPlBvIi外PvFP外外lBvIimFabviI外Fdtdi
4、 LildBv)(OAl dl dl l dl dBvdi)(vBdllBdlLoiidLolBdl221BLvOA2021BLUUAOAAOOA ABdSddBL221dtdi221LBOA3lBvIABalvxdxxdIABalvxdxxdBvdi)(BvdxvdxxI20laaixdxIv20alaIvln20IABalvxdxdlcos0cos2laaidxxIvalaIvcoslncos20-涡旋电场涡旋电场NLKil dEdtdiSSdBdtdSSdtBSdtBl dELSKSdtBl dELSK R0rLKdtdl dE)(2SBdtdrEKdtdBr20BdtdBRrEK22d
5、tdBrREK221 R0RkErdtdBrEK2MA1R2RR0R)(SBdtdi解解:dtdBR2MA1R2RR0R21RRIi212i2iR0MA1R2RR11IRUUMA2211iiRRRdtdBRRRRR22112)(2dtdBRRRRRUUMA22112)(2teItI0)(IlvabcdhytItB2)()(0Ilvabcdhy SSdBt)(lhhxdyytI2)(0hlhxtIln2)(0dttdi)()(ln20dtdxIxdtdIhlhhlhtveItln)1(200hlhxtItln2)()(0动感iSlydBvSdtB)(lhhlhhdyytIvxdyytIdtd2)
6、(2)(00IlvabcdhhlhtveItln)1(200hlhveIhlhtveIttln2ln20000BdtBdDOCDOCOCDl dEl dEl dEl dE金属杯金属杯金属块金属块 SN1B2B1I2I12121I12121IMdtd212dtdIM121dtd121dtdIM2121221MMM2121211221IIMM121212dIddIdM1l2l12111InB111IlNSBN122111221lIRNN12121IM1221lRNN221Vnn222InB222IlNSBln221122221SlInn2221VInn1l2l1221212IM221VnnMMM2
7、112dtdIMi1dtdIlRNN11221r1CR2C/Sr cm1.1Rr RINB2220r1CR2CBSN112RSINN222102.021041005010447H1028.662.dtdIM21V1014.34212IMRSNN2210LIdtdLdtdILI-反电动势反电动势dtdILL-电磁惯性电磁惯性nIB0NBSlRIN220ILlRN220Vn20IlN0lI2R1RIrIB20SSdB21RRBldr2120RRrdrIl120ln2RRIlI2R1RIlABCDIlL120ln2RRLK21RRIdtdIL0000020IttLIdIdtRIIdt2002210L
8、IdtRItLK21R002tdtRI00tIdt2021LI200202100LIdtRIIdtttIdtAdL00ILIdIA-等于电流增大时等于电流增大时 反抗反抗 L所作的功所作的功LIdI2021LILK21R221LIWmnIBVnL22221VInWmVB221VWwmmBH21221 B221HVmmdVwWVBHdV21HBEDw21VVdVHBEDwdVW)(2122 RIrH0Rr2021Hwm422208RrIdVwdWmmrldrRrI2842220drrRlI34204RrlWWmm1620IvmmdVwWRdrrRlI0342041620lII2R1RI16201
9、IWmrIB200221Bwm22208rIvmmdVwlW12212812220RRrldrrIl1220ln4RRI21mmmWWW122020ln416RRII12RII 例例 如图同轴电缆如图同轴电缆,中间充以磁介质中间充以磁介质,芯线与圆筒上的芯线与圆筒上的电流大小相等、方向相反电流大小相等、方向相反.已知已知 ,求单位求单位长度同轴电缆的磁能和自感长度同轴电缆的磁能和自感.设金属芯线内的磁场可略设金属芯线内的磁场可略.,21IRR解解 由安培环路定律可求由安培环路定律可求 H rIHRrR2,210,1HRr0,2HRr2m21Hw2)2(21rI则则21RrR2R1R12RIIm
10、w2)2(21rI2228rI21RrRVrIVwWVVd8d222mm2R1Rrdr 单位长度壳层体积单位长度壳层体积1d2drrVrrIWRRd4212m122ln4RRI2m21LIW12ln2RRL001cLmKdtdl dELedtdldH?RIIRII2S1SLLIl dB0Ll dB0DRII2S1SDSDSqdtdqdtdDI dtdDdtdIDDSdtDStD 证：证：SdtdqSdjSqSdDSSdDdtddtdqSSdtDSSSdtDSdj0)(SSdtDj21)()(SSSdtDjSdtDjtDj-永远是连续的永远是连续的LDIIl dHSSSdtDSdjLDSISIl
11、 dH曲面，取曲面取，21DII HRII2S1SL位移电位移电流和传导电流一样激发磁场流和传导电流一样激发磁场)SdSdtDI HtPtEtDjd0E RE RdtdIDDdtdDSdtdER0212122101085.8)1.0(14.3A28.02.RLrl dHrHr2dtdDSSdEdtd020rdtdErLrrHB0dtdEr200dtdERBR20012127101.01085.810421T7106.5dtdErBr200SqSdD0Ll dE00SSdBLIl dHSqSdD0.1Lmdtdl dE.2SSdB0.3LDIIl dH.4VdVSSdtBSdtDSdjSSVSdvSdDLSSdtBl dE0SSdBSSLSdtDSdjl dHSVdVASdA)(LSSdAl dA)(DtBE0 BtDjHSSdB0SSdDVdVLldESSdtBLl dHSdtDSdjSSEjHBEDrr,00/m1610141012101010810610410210010210410/m1610141012101010810610410210010210410
