ELECTROMAGNETISM II: Aims and Objectives 2016
Thestudentshould:
Part 1: Vacuum solutions (Professor Peter Török)
1.Maxwell'sEquations
1.1ParticlesandFields;
understandtheconceptsofchargeandcurrent;
understandtheconceptofanelectromagnetic(EM)field;
knowthatthechargeandcurrentaresourcesforfields.
1.2Gauss’Law;
knowaboutelectricfieldsandelectricfieldlines;
knowGauss’Lawinintegralform;
beabletoderiveGauss’Lawindifferentialformfromtheintegralform;
knowGauss’Lawformagneticfields,andunderstanditseffectonBfieldstructure.
1.3Ampère’sandFaradayLaw;
knowtheintegralformofAmpère’sLaw;
beabletouseStoke’stheoremtofinddifferentialformofAmpère’sLaw;
knowtheintegralformofFaraday’sLaw;
beabletouseStoke’stheoremtofinddifferentialformofFaraday’sLaw.
1.4DisplacementCurrent;
beabletoderivedifferentialformofcontinuityequationfromconservationofcharge;
knowhowthisimpliesanextratermforAmpère’sLaw;
beabletoderivedisplacementcurrenttermforAmpère’sLaw;
knowexpressionfordisplacementcurrent.
Atthisstage,studentsshouldbeabletoquoteMaxwell’sequationsinbothintegralanddifferentialformandbe
abletoidentifyallterms.
2.ElectromagneticwavesinaVacuum
2.5VacuumSolutions:
beabletorecastMaxwell’sequationsin1D;
use1DMaxwell’sequationstoderivethe(1D)waveequation.
2.6EMwavesin1D:
beabletofindthedispersionrelationof1Dwaveequationfromatrialsolution;
knowthedefinitionsofperiod,frequency,angularfrequency,wavenumber,wavevector,amplitude;
knowthemeaningofphasevelocity;
beabletowriteexpressionsforforwardandbackwardtravellingsolutions.
2.7Energyconservation:
beabletoshowj.EisrelatedtotherateofworkdonebyEMfields;
beabletoderivePoynting’stheoremandshowthatenergyisconservedwhenthePoyntingVectorisincluded;
beabletocalculatetheenergyinaplaneEMwave;
knowthemeaningofpolarisation;
beabletodemonstratethatPoyntingvectorN=c.(energydensity);
beabletocalculateaveragerateofenergyflow,andusethistocalculatetheEfieldforEMwavesofgiven
intensity.
3.Potentials
3.8Electrostaticpotential:
knowtheconceptofelectrostaticpotentialandwhyitisuseful;
beabletoderivePoisson’sequationfromthedefinitionofV;
knowtheexpressionofVforapointsource;
knowhowtousethistofindpotentialforextendedsourcesorcollectionsofcharges.
3.9VectorPotentials:
knowthedefinitionofvectorpotential,A;
knowthelimitationsofdefiningavectorpotentialandtheuseofgauges.
3.10Potential,chargeandcurrent:
beabletowriteBandEintermsofVandA;
beabletorewriteMaxwell’sequationsintermsofpotentialsintheLorenzgauge;
knowthatwithoutsources,equationsforpotentialsreverttowaveequations.
3.11Solvingforpotentials,retardedpotentials:
knowthatthesourceequationscanbesolvedbysplittingintoindividualpointsources,bysuperposition;
showthatsolutiontosourceequationsforapointsourceisasphericalwaveemanatingfromorigin;
knowthesignificanceofretardedtime.
3.12Solvingfortime-harmonicproblems:
beabletoderivethetimeharmonicwaveequationforB,E,VandAwithandwithoutsources;
beabletoderivethesolutionforAandVbysuperposition
beabletoderivesolutionsofBandEforsimplegeometries.
Part 2: EM fields and materials (Dr Michael Coppins)
knowaboutpolarisationchargesandmagnetisationcurrentsandtheirmicroscopicorigin;
knowtherelationshipbetweenEandD,andBandH;
understandthetermsrelativepermittivityandpermeability,andelectricandmagnetic
susceptibility;
understandthetermsparamagnetic,diamagnetic,andferromagnetic;
beabletorewriteMaxwell’sequationswithmaterialeffectsincluded;
understandtheDrudemodelofconductionandbeabletouseittoestimatetheresistivityofa
conductor;
knowOhm’slawintermsofEandj;
understandtheskineffect,andbeabletoderiveanexpressionfortheskindepth;
beabletoderivethewaveequationanddispersionrelationinadielectric;
knowthedefinitionofrefractiveindex;
understandthetermdispersionappliedtoemwaves,andknowsituationsinwhichitoccurs;
beabletoderivetheboundaryconditionsforthefieldsattheinterfacebetweentwoarbitrarymaterials;
knowtheboundaryconditionsintheirmostgeneralformandhowtoapplythemtospecialcases;
beabletocalculatethereflectionandtransmissioncoefficientsatnormalincidence;
beabletoshowthatphasematchingleadstothelawsofreflectionandrefraction(Snell’slaw);
beabletoderivetheFresnellawsforboths-andp-polarisations;
knowthatreflectivityiszeroatBrewster’sAngleandbeabletocalculatethisangle;
beabletoshowthatpropagationfromhightolowrefractiveindexcanleadtototalinternalreflection;
beabletofindtheformofthetransmittedandreflectedfieldsinthecaseoftotalinternalreflection;
understandevanescence;
beabletoderive,andfindthesolutionsto,thewaveequationforconductors;
beabletotakehighandlowfrequencylimitsforemwavepropagationinconductors;
beabletoshowthatforpoorconductors(highfrequency)thesolutioncorrespondstoadampedwave
propagation;
beabletofindthesolutionsforbothEandBatthesurfaceofagoodconductor;
beabletofindtherefractiveindexofametal;
knowtheboundaryconditionsatametalsurface(forgoodandperfectconductors);
beabletocalculatethereflectivityofaconductingsurface;
understandradiationpressure;
beabletoderivethewaveequationinaplasma;
beabletofinddispersionrelationinaplasma;
beabletoderivephaseandgroupvelocityinaplasma;
beabletoshowthatdispersionrelationleadstoacut-off:i.e.alowerlimittofrequency.