No-Nonsense Electrodynamics: A Student Friendly Introduction

310 Pages·1·10.034 MB·English

by  Jakob Schwichtenberg

NATURE ALWAYS CREATES THE BEST OF ALL OPTIONS.
ARISTOTLE
ONE SCIENTIFIC EPOCH ENDED AND ANOTHER BEGAN WITH JAMES
CLERK MAXWELL.
ALBERT EINSTEIN
THE TRUTH ALWAYS TURNS OUT TO BE SIMPLER THAN YOU THOUGHT.
RICHARD FEYNMAN

JA KO B S C H W I C H T E N B E R G
N O - N O N S E N S E
E L E C T R O D Y N A M I C S
NO-NONSENSE BOOKS
Firstprinting,September2020
Copyright©2020JakobSchwichtenberg
Allrightsreserved. Nopartofthispublicationmaybereproduced,storedin,orintroducedinto
aretrievalsystem,ortransmittedinanyformorbyanymeans(electronic,mechanical,photo-
copying,recording,orotherwise)withoutpriorwrittenpermission.
bookedition: 1.6
Dedicated to my parents

Preface
Therearealreadydozensoftextbooksonelectrodynamics. So
whyanotherone?
Firstofall,almostallexistingtextbooksfollowthesame"well-
establishedroute"whichisinspiredbythehistoricaldevelop-
ments. Themainideaistostartbydiscussinglotsofexperimen-
talfactsandonlyafterwardsputthesepuzzlepiecestogether.
ThiswaythereaderisslowlyguidedtowardsMaxwell’sgeneral
1
theoryofelectrodynamics. 1Inthissense,thisisabottom-up
approach.
However,Idon’tthinkthisapproachisthemosteffectiveand
certainlynotthemostentertainingone. Withoutseeingthe
biggerpicture,discussingindividualelectricandmagnetic
phenomenacanbequiteconfusingandmakeselectrodynamics
appearmorecomplicatedthanitreallyis. Moreover,readers
areoftenleftinthedarkregardingwhichstatementsholdin
generalandwhichonlyinspecialsituations. Inaddition,books
whichfollowsuchabottom-upapproachusuallyspendmostof
thetimeatthe"bottom"andonlyneartheveryendgettothe
"top". Thisoftenmeansthatthegeneraltheoryisnotdiscussed
indetailandmanyquestionsremainunanswered.
Incontrast,thisbookfollowsatop-downapproach. Westart
bydiscussingthegeneraltheoryandonlyafterwardsdiscuss
variousspecialcases. Allfundamentalaspectsofelectrody-
namicsaredescribedinthefirstchapterandputintocontext.
Thisallowsthereadertoseethebiggerpicturerightawayand
8
immediatelymakesclearwhichstatementsholdingeneral. In
addition,thereisnoriskthatstudentsgiveupbeforetheygetto
themostimportantstuff.
Secondly,mostotherelectrodynamicstextbookstrytodoalot
atonce. Forexample,it’snotuncommonthatinadditionto
Maxwell’sgeneraltheory,dozensofapplications,edgecases,
advancedtopics,historicaldevelopmentsorevenbiographies
ofthemostimportantcontributorsarediscussed. Ithinkthisis
problematicbecause,asthesayinggoes,ifyoutrytobegoodat
everything,youwillnotbegreatatanything.
Incontrast,thisbookfocusessolelyonthefundamentalaspects
2
2Applicationsareonlydiscussed ofelectrodynamics. Thisnarrowfocusallowsustodiscussall
insofarastheyhelptodeepenour theimportantconceptsseveraltimesfromvariousperspectives.
understandingofthefundamental
Aclearadvantageofthisapproachisthatthereaderhasmul-
conceptsandnotasanendin
themselves.Inaddition,thereare tiplechancestounderstandagivenconceptwhileinanormal
alreadydozensofgreatbooks
textbook,thereaderimmediatelyhasaproblemwhenapassage
whichdiscussapplicationsorother
3
specialtopicsingreatdetail.Some isnotunderstoodperfectly. Asecondadvantageofournarrow
ofthebestonesarerecommended focusisthatitminimizestheriskofunnecessarilyconfusing
inChapter9.
thereader. Likeallotherfundamentaltheories,electrodynamics
3Inanormaltextbookeachtopicis is,atitsheart,quitesimple. However,usingittodescribecom-
onlyintroducedonce.Asaresult, plicatedsystemsisfarfromeasyandthisiswheremostofthe
laterchaptersbecomeharderand 4
difficultiesusuallyarise. Therefore,restrictingourselvestothe
hardertounderstandwithouta
fullunderstandingofallprevious fundamentalsallowsustointroduceelectrodynamicsasgently
chapters.Moreover,it’seasyto 5
aspossible.
becomediscouragedwhenafew
passagesarenotperfectlyclear
sinceyouknowthatyouneedthe Whilethisalonemayalreadyjustifythepublicationofanother
knowledgetounderstandlater
electrodynamicstextbook,thereareafewotherthingswhich
chapters.
makethisbookdifferent:
4Mostofthedifficultiesarereally
(cid:66)
mathematicsproblemsnotphysics Firstofall,itwasn’twrittenbyaprofessor. Sothisbookisby
problemsanyway.Forexample,
nomeansanauthoritativereference. It’smorelikeacasual
solvingadifficultintegralorsolv-
ingagivendifferentialequation. conversationwithamoreexperiencedstudentwhoshares
withyoueverythinghewishedhehadknownearlier. I’m
5Whileadvancedapplications
convincedthatsomeonewhohasjustrecentlylearnedthe
are,ofcourse,important,theyare
notessentialtounderstandthe topiccanexplainitmuchbetterthansomeonewholearned
fundamentalsofelectrodynamics. itdecadesago. Manytextbooksarehardtounderstand,not
Asalreadymentionedabove,there
becausethesubjectisdifficult,butbecausetheauthorcan’t
aregreatbookswhichfocuson
specificapplications.Afteryou’ve rememberwhatit’sliketobeabeginner.
developedasolidunderstandingof
thefundamentals,it’sfareasierto
learnmoreaboutthoseapplications
you’reinterestedin.
9
(cid:66)
Anotheraspectthatmakesthisbookuniqueisthatitcon-
tainslotsofidiosyncratichand-drawnillustrations. Usually,
textbooksincludeveryfewpicturessincedrawingthemis
eitheralotofworkorexpensive. However,drawingfigures
isonlyalotofworkifyouareaperfectionist. Theimagesin
thisbookarenotasprettyasthepicturesinatypicaltext-
booksinceIfirmlybelievethatlotsofimperfectillustrations
aremuchbetterthanafewperfectones. Thegoalofthis
book,afterall,isthatyou’llunderstandelectrodynamicsand
notthatIwinprizesformyprettyillustrations.
(cid:66)
Moreover,myonlygoalwiththisbookwastowritethemost
student-friendlyelectrodynamicstextbookandnot,forex-
ample,tobuildmyreputation. Toomanybooksareunnec-
essarilycomplicatedbecauseifabookishardtounderstand
6
itmakestheauthorappearsmarter. Nothingisassumedto 6ToquoteC.Lanczos:"Manyof
be"obvious"or"easytosee". Moreover,calculationsaredone thescientifictreatisesoftoday
areformulatedinahalf-mystical
step-by-stepandannotatedtohelpyouunderstandfaster.
language,asthoughtoimpress
thereaderwiththeuncomfortable
feelingthatheisinthepermanent
So,withoutanyfurtherado,let’sbegin. Ihopeyouenjoyread- presenceofasuperman."
ingthisbookasmuchasIhaveenjoyedwritingit.
Karlsruhe,October2018 JakobSchwichtenberg
PS:Iupdatethebookregularlybasedonreaderfeedback. Soif
youfindanerror,Iwouldappreciateashortemailto
[email protected].
Acknowledgments: SpecialthankstoMichaelHavrilla,Tom
Harper,LukeDurant,SteveBurk,AlexHuang,JonathanHob-
son,VicenteAboites,XavierConstant,FabianWaetermans,
andPhilConnollyforreportingseveraltypos. Moreover,many
thanksareduetoJacobAyresforhiscarefulproofreadingand
countlessinvaluablesuggestions.
10
Beforewedivein,weneedtotalkabouttwothings. Thefirst
oneisthefollowingcrucialquestion:
Why should you care about Electrodynamics?
Firstofall,electrodynamicscorrectlydescribesthebehaviorof
7
7Thisistrueatleastonamacro- oneofonlyfourknownfundamentalinteractions.
scopiclevel.Electromagnetic
interactionsofelementarypar-
ticlesaredescribedbyquantum (cid:66) Atlarge(cosmological)scales,gravityisthemostimportant
electrodynamics.
ofthefourinteractions.
(cid:66)
Attinyscales,strongandweakinteractionsareresponsible
formostoftheinterestingphenomena. Forexample,pro-
tonsareheldtogetherbythestrongforceandatomsdecay
throughweakinteractions.
(cid:66)
However,inbetweenthesetwoextremesit’selectromagnetic
interactionswhichholdsway.
Inparticular,electrodynamicsnotonlyallowsustounderstand
howelectricityandmagnetismcomeabout,butalsowhatlight
isandhowittravels.
Inaddition,asolidunderstandingofelectrodynamicsisessen-
tialtounderstandthetheoriesdescribingallotherfundamental
interactions. Moreover,theequationsdescribingelectromagnetic
interactionsofmacroscopicobjectsareexactlythesameasthe
equationsgoverningelectromagneticinteractionsofelementary
8
8Theequationsdescribingthe particles. Thismeansthattheknowledgegatheredbystudying
otherfundamentalinteractions electromagneticinteractionsonamacroscopiclevelhelpsusim-
areextremelysimilarandcanbe
mediatelytounderstandwhathappensonamorefundamental
understoodmucheasieroncethe
equationsofelectrodynamicsare level.
understood.
Moreover,electrodynamicsisanidealplaygroundtounder-
standseveralofthemostimportantconceptsunderlyingmod-
ernphysicsinasimplifiedsetup. Inparticular,inthecontextof
electrodynamicswecanunderstand: