第14章电流和磁场

Example14 1Magneticfieldofastraightcurrent AsshowninFig14 10thereisflowingasteadycurrentIincircuit FindthemagneticfieldatPproducedbythecurrentinastraightofthecircuitoflengthL thedistancefromthatsegmenttoPisr Or Example14 2Magneticfieldofacircularcurrent ThereisacurrentcarryingcircularcoilradiusRandcurrentI Findthedistributionofmagneticfieldtheaxisofcoil Definethemagneticmomentofacurrentcarryingcoiltobe 2 Atthecenterofthecoil x 0 Eq 14 29 givesthemagneticfieldproducedbyacoilofmagneticmoment onitaxis Thefieldatotherpointcanalsobecalculated TheresultisthatthedistributionofinductionlinesofthemagneticfieldproducedbyamagneticmomentshowninFig 14 13issimilartothatoftheelectricfieldlinesoftheelectricfieldproducedbyanelectricdipoleshowninFig b exceptinthelocationoftheelectricdipoleandthecoil Example14 3Themagneticfieldalongtheaxisofacurrent carryingsolenoid AsshownnFig 14 4thereisastraightsolenoidoflengthL radiusR wouldevenlywithnturnsofcoilperunitlength AcurrentIisflowinginthecoil Findthedistributionofmagneticfieldontheaxisofthesolenoid Or Foraverylongstraightsolenoidforanypointontheaxisinthesolenoid 1 2 0 ThedistributionofB linesofacurrent carryingsolenoidinFig14 16 whichissimilartothatinFig 14 8 c demonstratedwithironchips Themagneticfieldoutsidethesolenoidisveryweakandinsideisessentiallyuniform thelongerthesolenoid themoreremarkablethisfeature Example14 4Thedistributionofthemagneticfieldofaninfinitelylongcylindricalsurfacecurrent Assumetheradiusofthecross sectionofthecylindricalsurfacebeRwithtotalcurrentIflowingonthesurfaceuniformlyalongthelengthofthecylinder Example14 5Thedistributionofthemagneticfieldofacurrent carryingtoroid AtoroidisacircularsolenoidasshowninFig 14 22 a AssumethattheradiusofthecircularringRandthereareNturnsofcoilwoundclosedandevenlyonthering Fig 14 22 b withcurrentIflowinginthecoil inthetoroid Foranypointoutsidethetoroid takethecircleC orC coaxialwiththetoroidastheAmpereloop Asnow 0 weget outsidethetoroid Example14 6AparallelplatecapacitoriscomposedoftwocircularconductingplatesofradiusR 0 2m Findthemagneticfieldbetweentheplatesatpointsr1 0 1mandr2 0 3mfromtheaxisoftheplateswhenthecapacitorisbeingchargedwithcurrent 10 Neglectedgeeffect Theelectricfieldbetweentheplatesis Takethecircleofradiusr1astheAmpereloopC1 thecirculationofB1is And 2 SUMMARY 1 Currentdensity whereistheaveragevelocityofthecurrentcarriers i e thedriftvelocity Current Continuityequationofcurrent 2 Aclassicalmicroscopicviewofcurrentinmetal Thedirectionalmotionoffreeelectronsinmetalisaseriesofacceleratedmotioninsuccessionandeachacceleratedmotionstartsfromzerodirectionalvelocity Conductivity Ohm slaw differentialform Commonform Electromotiveforce theworkdonebynon electrostaticforcewhenchargepassingthrough 3 Magneticinduction DefinitionequationWhereistheforceonthetestchargemovingwithvelocitybythemagneticfield 4 TheBiot Savartlaw themagneticfieldofacurrentelementSuperpositionprincipleTheoremofcontinuityofmagneticfluxMagneticfieldofalongstraightcurrent 0 2 withfieldlinesallcirclesperpendiculartoandcenteredonthecurrentline Magneticfieldinalongstraightcurrentcarryingsolenoid 0 withfieldlinesparalleltoaxis 5 Amperecirc