Table Of ContentUndergraduate Lecture Notes in Physics
Teruo Matsushita
Electricity
and
Magnetism
New Formulation by Introduction of
Superconductivity
Undergraduate Lecture Notes in Physics
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Teruo Matsushita
Electricity and Magnetism
New Formulation by Introduction
of Superconductivity
123
TeruoMatsushita
DepartmentofComputerScience&
Electronics
KyushuInstituteofTechnology
Iizuka,Fukuoka,Japan
OriginalJapaneseedition,ShinDenjiki-gaku,ByTeruoMatsushita,Copyright(cid:2)c (2004),Publishedby
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ISSN2192-4791 ISSN2192-4805(electronic)
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Preface
Electromagnetism is an important subject in today’s physics. The number of
textbooks on electromagnetism is much larger than those on other subjects. This
is because abstract concepts are frequently used and therefore it is not easy
for students to come to a complete understanding of electromagnetism, although
variousphenomenaareconciselydescribedwithmathematics.Forthisreasonmany
textbooks have been published to assist students to understand electromagnetism
better.Why,then,isanewtextbookonelectromagnetismnecessarynow?
Electromagnetismisaclassicalsubjectthatwasalmostcompletelyformulatedin
thenineteenthcentury.However,concerningitstheoreticaldescription,thereisstill
roomforfurtherprogress.Inaddition,textbooksarerequiredtodescribetheirtopics
adequatelywithinalimitedspace.Therefore,thereisalsoroomforimprovementin
textbooksfromthetechnicalpointofview.
In principle, there is a beautiful formal analogy between static electric and
magnetic phenomena,as will be shown in this textbook. However, the analogy is
not necessarily perfect in existing textbooks because of the lack of an important
concept. Electric materials are classified into conductors and dielectric materials,
but only magnets are studied as magnetic materials. While it is known that
electricphenomenaindielectricmaterialsandmagneticphenomenainmagnetsare
analogoustoeachother,noonehasdiscussedmagneticmaterialsthatcorrespondto
electricconductors.However,wehavetonotesuperconductors.Inasuperconductor
acurrentflowsonitssurfacetoshieldtheinsideagainstanexternalmagneticfield,
sothatthemagneticfluxdensityBiszerointhesuperconductor.Thisisanalogous
to the electric phenomenonof a conductorin an externalelectric field. Thatis, an
electricchargeappearsonitssurfacetoshieldtheinsideagainstanexternalelectric
field,sothattheelectricfieldEiszerointheconductor.Thisisoneoftheremarkable
analogiesinthepresentE–Banalogy.
Thus, the introduction of the superconductor into electromagnetism, which
has not yet been tried systematically, seems to be quite useful for understanding
electromagnetism.That is, the analogy between electricity and magnetism can be
completedbytheintroductionofthesuperconductor.Therecanbevariouswaysof
v
vi Preface
education without such a comprehensive analogy, and this is another reason why
manytextbooksonelectromagnetismhaveappeared.
From another point of view, superconductivity is a general phenomenon that
appearsinmanysingleelementsandmostmetalliccompounds,ifthecasesofpres-
surizationandthinfilms areincluded.The intrinsicpropertyofsuperconductivity,
the breaking of Ohm’s law, may seem to be peculiar. However, superconductivity
isapurelyphysicalphenomenonthatcanbederivedfromminimizingfreeenergy.
In contrast,the empiricalOhm’slaw associated with energydissipationcannotbe
derived theoretically, and electromagnetic theory is incomplete for other current-
carryingmaterialsinthissense.
Usuallystudentslearnaboutstaticmagneticenergyaftertheystudyelectromag-
netic induction. One of the appreciable advantages of using a superconductor is
the direct derivation of magnetic energy as mechanical work done by magnetic
force,similartotheelectricenergyresultingfromtheelectricforce.Thisisbecause
themagneticfluxisconservedinasuperconductingcircuitdisconnectedfromany
electric sources. As a result, the electromagnetic induction can be predicted for a
usualelectriccircuitusingtherelationshipbetweentheenergyandmagneticforce.
In electromagnetism the magnetic moment of a magnet caused by spins and
orbital motions of electrons is described using a virtual magnetizing current.
However, the magnetic moment of a superconductor comes from a real current
flowingin it. Hence,the introductionofthe superconductoris alsobeneficialwith
regardtopersuasionoftheappropriatenessofthevirtualmagnetizingcurrent.
It should be noted that the definition of magnetization is differentfor magnets
andsuperconductors.Thatis,magnetizationcomesdirectlyfromthemagnetization
M inmagnets,whileitcomesfromthemagneticfieldH insuperconductors.This
arises from the difference in the origin of the magnetic moments. According to
the definition used for magnets, superconductors are classified as non-magnetic
materials. On the other hand, the analogous electric phenomena are electrostatic
shielding in conductors and electric polarization in dielectrics. These are similar
electricshieldingmechanismscausedbyelectricchargesandpolarizationcharges,
but the above-mentioned different terms are used. Such comparison between
electricityandmagnetismisalsousefulforeducation.
The final merit of the introduction of superconductors is application of the
analysismethodofelectromagneticphenomenainsuperconductors.Thecontinuity
equation of magnetic flux used for superconductors is useful for estimating the
velocity of magnetic flux lines under a magnetic field varying with time. This
enablesustounifythemagneticfluxlawandthemotionallawforelectromagnetic
induction,whichusuallyhavebeentreatedseparately.
The purpose of this textbook is to show the remarkable analogy between
static electric phenomena, described in Part I, and static magnetic phenomena,
described in Part II. Hence, a comparison between the corresponding chapters in
each part, such as Chap. 2 on conductors and Chap. 7 on superconductors, will
assistinunderstandingelectromagnetism.Dynamicelectromagneticphenomenaare
describedinPartIII.
Preface vii
IwouldliketoexpressmysincereacknowledgmenttoProf.KlausLuedersatthe
BerlinFreeUniversityfortheusefuldiscussionwehad.Inaddition,Iwouldliketo
thank Tomoko Onoue, Etsuko Shirahasi, and Kaori Ono for assistance in making
electronicfilesanddrawingelectronicfigures.
Iizuka,Fukuoka,Japan TeruoMatsushita
Contents
PartI StaticElectricPhenomena
1 ElectrostaticField .......................................................... 3
1.1 ElectricChargeinVacuum .......................................... 3
1.2 Coulomb’sLaw....................................................... 4
1.3 ElectricField ......................................................... 7
1.4 Gauss’Law........................................................... 11
1.5 ElectricPotential..................................................... 16
1.6 ElectricDipole........................................................ 23
Exercises ..................................................................... 29
2 Conductors.................................................................. 33
2.1 ElectricPropertiesofConductors ................................... 33
2.2 SpecialSolutionMethodforElectrostaticField.................... 41
2.3 ElectrostaticInduction............................................... 46
Exercises ..................................................................... 51
3 ConductorSystemsinVacuum............................................ 55
3.1 CoefficientsinConductorSystem................................... 55
3.2 Capacitor.............................................................. 60
3.3 ElectrostaticEnergy.................................................. 65
3.4 ElectrostaticForce.................................................... 70
Exercises ..................................................................... 73
4 DielectricMaterials......................................................... 75
4.1 ElectricPolarization.................................................. 75
4.2 ElectricFluxDensity................................................. 81
4.3 BoundaryConditions................................................. 85
4.4 ElectrostaticEnergyinDielectricMaterials ........................ 92
Exercises ..................................................................... 95
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