Electricity & Magnetism for JEE

744 Pages·2017·36.339 MB·English

by  Er. Anurag Mishra

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SHRI BALAJI PUBLICATIONS
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(cid:127) Firstedition :2010
](cid:127) Third edition :April2012
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Preface
Myinteraction with students, sincerely preparing for IIT-JEE motivated me to
writethisbookonelectricity&magnetism.
Electricity and Magnetism is also as importantas Mechanicsbecause in allthe
competitive examinations, this part is given same or even more weightage than
mechanics. Like Mechanics I & II this book "Electricity and Magnetism is also-
A- --V
designedto cleartheconceptsthroughnumericalapproach.
This book will help the students in building analytical and quantitative skills,
addressingkeymisconceptionsanddevelopingconfidenceinproblemsolving.
I sincerely wish that this book will fulfill all the aspirations of the readers.
Althoughutmostfullcarehasbeentakento makethebookfree from errorbutsome
errors inadvertently may creep in. Author and Publisher shall be highly obliged if
suggestions regarding improvement and errors are pointed out by readers. I am
indebted Neeraj Ji for providing me an opportunity to write a book of this
magnitude.
I am indebted to my father Sh. Bhavesh Mishra, my mother Smt. Priyamvada
Mishra, mywifeManjari, mysister Parul,mylittle kidsVrishankand Ira forgiving
their valuable time which Iutilized during the writing ofthis book and people of
Moradabad,who supportedmethroughoutmycareer.
Iam also thankful to Mr. T. Kondala Rao, Mr. AbhishekSinha (Ranchi), Mr.
SunilManohar, Mr. S.P.Sharma, Mr. SudhirSharmaand Mr. RNarendra Reddy
fortheir valuablesuggestionsinimprovingthebook.
In the last, 1 also pay my sincere thanks to all the esteemedrmembers of
ShriBalajiPublicationsinbringingoutthis bookinthepresentform.- (cid:127) (cid:127) "
AnuragMishra
9AD^
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Followingaresomedoubtswhichariseinthemindofalmostallthestudents
butmayface thembytakingsomecare.
1. /can notsolve numericalbecausemyconceptsarenotclear.Infact numerical
solvingitselfisanexercisetolearnconcepts.
2. / can not study because I am in depression, Ifell into it because I was not
studying] Depressionisescapemechanismofpeopleafraidoffacingfailures.
Failureisintegralpartoflearning.
3. / understandeverythingin classbutcan notsolve on myown.WRITINGwork
is vital. It is a multiple activity initiallyideacomes in mindthenwe putinto
languageto expressit,wearefocUssed inhandeye coordination,eyes create
visual impression on brain which is recorded there. WRITINGWORKS ARE
EMBOSSEDONBRAINLIKECARVINGSOFAJANTACAVES.
4. Inexamsmybraingoesblank, butIcan crackthem athome. Homeattemptis
yoursecond attempt! you are contemplatingaboutitwhile home back. You
do not behave differently in exam you replicate your instincts. Once a fast
bowlerwas bowling'no balls-. Hiscoach placed astump on crease, in fear of
injury he got it right. CONCEPTUALIZATION, WRITING EQUATION,
SOLVING,THENPROBLEMGETSTO CONCLUSION!
5. / am an averagestudent. It is a rationalization used by peopleafraid ofhard
work. In their reference frame Newton's first law applies "if 1 have a
misconception 1will continue with it unless pushed by an external agent
1 •
even 1 will surround him in my web of misconception yielding zero
resultant." AVERAGE IS NOT DUE TO CAPACITY LACUANE BUT DUE TO
LACKOFDETERMINATIONTOSHEDINERTNESS.
6. Afamous cliche"Ido nothaveluckin myfavour" PRINCIPLE OFCAUSALITY:
CAUSE OF AN EVENT OCCURS IN TIME BEFORE OCCURRENCE OF THAT
EVENT i.e., cause occurs first then event occurs. SHINING OF LUCK IS NOT
AN INSTANTANEOUS EVENT IT IS PRECEDED BY REL. ITLESS HARj^;.
, WORK.Sowaseedofaspirationin mind,wateritwithpassion,dedication-it
willbearfruit,luckcangiveyousweeterfruit.
1. Do not take studyasaburden actuallyits askilllikesingingand dancing.It
hastobehonedbyproperdevotionand dedication.
2. Without strong sense ofachievement you can't excel. Before entering the
competitive field strong counselling by parents is must. Majority do not
know what for they are here. No strategic planning, they behave like a tail
enderbattinginfrontofSteyn'sbouncers.
3. Science is not a subject based on well laid down procedures or based on
learning some facts, it involves very intuitive and exploratory approach.
Unless theirisdesireandpassionto learnyou can notdiscovernewideas. It
requirespatienceandhardwork,whosefruitsmaybetangiblelateron.
4. Somestudentsrealizeverylatethattheyarestudyingforacquiringskillsand
honingthem.Theirisafeelingthattheycanrideatthebackofinstructorand
achieveexcellence.Studycomesas torturous exerciseenforcedon themand
theirissomemechanismthatcantakethisburdenofthem.
5. Scienceis not about gaining good marks, up to Xth by reading key points
good marks are achieved but beyond that only those survive who have
genuineinterestinlearningandexploring.Selfstudyhabitismust.
6. IFYOUWANTTOGAIN LEAD STARTEARLY. Majorityofsuccessful students
try to finish major portion elementary part of syllabus before they enter
Coaching Institute. Dueto this their maturitylevel as compared to others is
more they get ample time to adjust with the fast pace. They are less
traumatizedbythescientific matterhanded over. Forthosewho enterfresh
must be counselled to not get bullied by early starters but work harder
initiallywithinfirsttwo monthsinitialedge isneutralized.
i
7. Oncea studentlags behind due to some forced or unforced errors his mind
begins to playrationalizationremarkslikeIamanaverage student,mymind
^ 1 isnotsharp enough,1 havelowIQetc.Thesewordsaremechanisms usedto
i'" avoidhardwork.Thesewordsarerelativetermsapersonwhohasearlystart
maybeintelligentrelativetoyou.
Intelligence means cumulative result of hard work of previous years, that
hard work has eventually led to a development of instinct to crack things
easily.
V
I. GLGCTROSTATICS
ElectricCharge(1);WhatisCharge(2); ChargingbyRubbing(5); InsulatorsandConductors(5);Charging
byContact(6);ChargingbyInduction(6); Polarization(8);PropertiesofCharge(8);Coulomb'slaw(11);The
Electric Field (19); PointCharge Distribution (20); PrincipleofSuperposition (21); ElectricField lines (22);
ContinuouschargeDistribution(27), ImportantGraphs(29); Flux(47); ElectricFlux(47);AreaVectors(48);
Solid Angle (52); Developing Gauss's Law from Coulomb's Law (53); Statement ofGauss's Law (55);
-Coulomb'sLawfrom Gauss'sLaw(58); ElectricPotential EnergyandElectricPotential(74);Accelerationof
ChargedParticlestheInfluenceofElectricForces(82);EquipotentiaisandElectricFieldLines(84);TheVanDeGraaffGenerator(86);
Potential EnergyofaDipoleinaUniform Field(102); ElectricFieldandPotentialduetoADipole(104);TheEnergyofaPointCharge
Distribution(113); EnergyofElectricField(114); EnergyforaContinuousDistributionofCharge(116); PropertiesofConductor(119);
Charge Distribution on a Conducting Sheet (126); Earthing ofa Conductor (128); Field between Oppositely Charged Parallel
ConductingPlates(136);
Level-1: OnlyOneAlternatlveisCorrect(145):Answers(163):Solution(164).
Level-2: MorethanOneAlternativeis/areCorrect(172);Answers(183);Solutions(184);
Level-3: ComprehensionBasedProblems(191); MatchingTypeProblems(198);Assertion-ReasonTypeProblems(202);Answers
(204);Solutions(205). 'V
B. GLGCTRIC CURRGNT
ElectricCurrent(211); ElectricCurrentDensity(212); CurrentDensityandDriftSpeed(214); Expressionfor
Resistance (216); Electromotive,Force andIts Sources (218); EMF andInternal Resistance ofa Battery
(221); ElectricEnergyandPower,(222);Series,andParallelCombinationofBulbs(225); OneDimensional
Conduction (231); Two Dimensional .Conduction (232); Kirchhoffs Laws, for"Circuit Analysis (234);
KirchhofTs Rules (235); Combination ofCells (236); Net Work Analysis (238); Nodal Analysis (244);
EquivalentResistance(245); FoldingSymmetry.(260);AmmeterandVoltmeter(264); WheatStone bridge
(267);ThePostOfficeBox(273).
Level-1: OnlyOneAlternativeisCorrect (285);Answers(296);Solutions(297).' '
Level-2: MorethanOneAlternativeis/areCorrect(305);Answers(309);Solutions(310);
Level-3: ComprehensionBasedProblems(314);MatchingTypeProblems(317); Assertion-ReasonTypeProblems(321);Answers
(322);Solutions(323). - " (cid:127)
3. CAPACITORS
SourcesofEMF(326); Capacitors(327);ASphericalCapacitor(328);ACylindricalCapacitor(329); Energy
Storagein aCapacitor(329); Combination ofCapacitors (331); CapacitorsandDielectrics(332); Gauss's
Law andtheElectric Field Vectors (334); ChargeSharing between Conductors (335);Analysis ofSimple
Capacitive Circuits (352); Nodal Analysis for Capacitive Circuits (356); An Introduction toTransients in
Circuits(370);ADischargingCapacitor(372);EquivaienttheTlmeConstant(373);TimeConstant(380)
Level-1: OnlyOnealternativeiscorrect(305);Answers(393);Solutions(394).'
Level-2: MorethanOneAlternativeis/areCorrect (401);Answers(409);Solutions(410).
Level-3: ComprehensionBasedProblems(417); MatchingTypeProblems(424);Assertion-ReasonTypeProblems(427);Answers
(428);Solutions(429).
4. THE MAGNETIC FIELD
Magnetsand Magnetic Poles(436);The MagneticField(438); Forceand Fieldforv1B(439);The Force
Exerted byMovingChargein aMagneticField(439);TheCyclotron(441); BubbleChamber(441); Moving
Charges in Non-uniform Magnetic Fields (442); The Lorentz Force (447); Force on a Current Carrying
Conductor(455); Can Magnetic Force PerformWork (457);Torqueon aCurrentLoop in aMagnetic Field
(460); MagneticMomentofaCircularCoil(461);Galvanometer(469);TheBiot-SavartLaw(470);Direction
of Magnetic Field due to Current Carrying Wire (471); Magnetic Field of Moving Point Charges (471);
MagneticForceandConservationofMomentum(471);MagneticFieldLines(473);MagneticFieldduetoRegularPolygonatitsCentre
(478); ForcebetweenCurrentCarrying ParallelWires(482);Ampere'sLaw(489); MagneticFieldduetoan InfinitelyLongCylindrical
Wire (492): Solenoid (493); Classical Magnetism (500); Tangent Galvanometer (504); Deflection Magnetometer (505); Magnetic
Materials -Ferromagnetism (510); Electromagnets and Solenoids (511); Magnetic Fields in Magnetic Materials, Hysteresis (511);
ParamagnetismandDiamagnetism(512);
Level-1: OnlyOneAlternativeIsCorrect(524);Answers(544);Solution(545);
Level-2: MorethanOneAlternativeis/areCorrect(552);Answers(557);Solution(558);
Level-3: Comprehension Based Problems (562); Matching Type Problems (567); Assertion and Reason Type Problems (571);
Answers(572);Solution(573).
5. eLeCTROMAGNeTIC INDUCTION & AC. CIRCUITS
MagneticFlux(578); Induced EMF(580);Motional EMF(584);TheNatureofEMF(585);Generators(594);
Induced EMF, and Electric Fields (607); Eddy Current (613); Inductance (614); Series and Parallel
CombinationofInductors(616);Self-Inductanceandthe Modified KirchhoffsLoopRule(616);ASeriesLR
Circuit(618); EnergyStored in an Inductor(623); Mutual Inductance(629);AParallel LCCircuit(639);AC
Circuit(650):ACapacitorin anACCircuit(651);An InductorInanACCircuit(652); PhaserDiagram(653);
AnalysisofSeriesInACCircuits(655);SeriesACRLCircuit(656);SeriesACCRCircuit(657); PowerinAC
Circuits(657); Resonance inSeriesLCRCircuit(658); Choke Coil (660);SymbolicNotation ofPhasors(663); Relation betweenthe
PhasorsIandV(664);KirchhoffsRulesforACCircuits(665);
Level-1: OnlyOneAlternativeisCorrect(671);Answers(698);Solution(699);
Level-2: MorethanOneAlternativeis/areCorrect(713):Answers{717);Solution(718);
Level-3: Comprehension Based Problems (720); Matching Type Problems (727); Assertion and Reason Type Problems (731);
Answers(732);Solution(733).
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ELECTRIC CHARGE Finally, we come to see how electricity and
In ancient time the Greeks noticed that amber, a magnetism are two' manifestations of the same
yellow-brown material (fossilized pine tree re.in) when basic phenomenon, electromagnetism.
rubbed with cloth or fur, it attracts small bits ofstraw, hair, Some ofthe basic characteristics ofelectrostatics are :
etc. Thewordelectricderives fromthe Greekwordforamber 1. Physical quantity responsible for static electricity is
ielectron). By the mid-seventeenth century it Iwas electric charge.-
establishedthatasubstance,activatedbyrubbing,possessed 2. There are two types of charges, one called positive
some sort of "amber stuff' or electricity. A piece of hard and the other called negative.
rubber, a glass rod or a plastic comb or ruler after being 3. Like charges repel, whereas unlike charges attract.
vigorously rubbed with a towel can pickup small pieces of
4. The net amount of charge produced in any
paper. From our knowledge of the laws of mechanics we process is zero. Whenever a certain amount of charge is
conclude that there exists another force, electricforce. The produced on one body in a process, an equal amount ofthe
physicalattribute responsibleforsuchelectricinteraction is opposite type of charge is produced on another body. The
electromagnetic charge (electric and magnetic positive and negativecharges are tobe treatedalgebraically.
phenomena both are manifestations of charge). In this
When a plastic ruler is rubbed with a paper towel, the
chapter we will study phenomena due to charges that are
plastic acquires a negative charge 'and the towel an equal
stationary, called electrostatics, or static electricity.
amount of positive charge; the sum of these two charges is
In this chapter, we focus on the physics of zero. Ifone objector one region ofspace acquires a positive
electrostatics, the study of the interactions charge, then an equal amount of negative charge will be
between electric charges that are at rest (or at established in the neighbouring areas or objects.
most moving very slowly).
There are two types of charges, positive and negative.
Though the electric and magnetic forces are
This fact can be easily verified by a simple experiment.
distinct, they are intimately related. That is why When glassisrubbedwithsilk,the glassbecomes positively
we speak of electromagnetism as a unified chargedand the silknegativelycharged [Fig.1.1 (a)]. Since
subject. the glass and silk have opposite charges, they attract one
Electromagnetism is one of the parts of another. Two glass rods rubbed in this manner repel one
physics in which we distinguish between another, since each rod has positive charge on it [Fig.
electrostatics and magnetostatics and study the 1.1(b)]. Similarlytwo silk clothsso rubbed repel each other
two subjects separately. Then we study the because both cloths have negative charge [Fig. 1.1(c)].
remarkable connection between electricity and
magnetismthatbecomes clearin movingsystems.
ELECTRICITY&MAGNETISM
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Fig. 1.2 (d)
Anelectrified glassrod attractsan
electrified rubberoramberrod
Two different kinds of electrification properties are
needed toexplain alloftheseobservations.
All electrical phenomena can be described by assuming
only two different kinds ofelectrification properties. Dufay
called the two types ofelectrification properties vitreous
(c)
electricity (thatsimilarto glass) and resinous electricity (that
Fig.1.1
similar to amber). One never observes an electrified
' Thenormalmatterismadeofatoms, andatoms contain
materialthatrepels (orattracts) bothan electrifiedglassrod
positive and negative charge in equal amounts. An electron
and an electrified rubber rod; such an observation would
is negativelycharged; itrepels otherelectronsanditattracts
imply a third type, of electrified, state or electrification
protons"which are positively charged.
property.
WHAT IS CHARGE ?
Furthermore, electrical forces are quite distinct from
Fig, i.2 (a) to (d) show certain observations about a
gravitational forces inseveral respects:
charged body 1. Electrical forces between electrified materials are
quite apparent even with small pieces ofelectrified matter,
whereas the gravitational force between such small masses
is almost negligible and detectable only with the most
sensitive types of equipment. Thus electrical forces
evidently are intrinsically much stronger than gravitational
forces (which are appreciable onlywhen one orbothofthe
masses inhugebylaboratorystandards).
2. Gravitation is always and only observed as an
attractive force, and so we have need for only one kind of
Fig.1.2(a)Twopiecesofrubbedamberalwaysrepeleach
mass, positive inass. Electrical forces are observed to be
other, regardlessofwhichwaytheyfaceeachother.
eitherattractiveorrepulsive,hencetheneedfortwotypesof
electrification property, the vitreous and resinous
electrifications of Dufay. The electric and gravitational
forces are similar in two ways:
(i) Bothareobservedtobecentralforces. Theyactalong
theline connecting pointlike materials causing theforce.
(ii) Both are conservativeforces. The work done by the
force around a closed pathiszero (equivalently, thework
donebythe force along apathconnectinganytwo pointsin
space is independent ofthe path between the two points).
It was Benjamin Franklin who introduced the two
Fig. 1.2 (b) Fig. 1.2(c) propertiesofelectrification :
Twoglassrodsrubbed Tworubberoramber Aparticle ormass is said tobe positively electrified
with silkrepeleach other rodsrubbedwithfur
repeleachother ifitisrepelled byaglass rodthathas been freshly rubbed
with silk.