Electricity & Magnetism for JEE [3 ed.]

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BalaJi

Electricity^ (Main & Advanced)

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^ 1Ek Amurag Mishra '5; i"' B:TfecH(Mech:'Eng&.)

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SHRI BALAJI PUBLICATIONS (EDUCATIONAL PUBLISHERS & DISTRIBUTDRS)

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AN ISO 9001-2008 CERTIFIED ORGAN^TlbN •£ Muzaffamagar (U.P.) - 251001

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Published by:

SHRI BALAJI PUBLICATIONS^ (EDUCATIONAL PUBLISHERS & DISTRIBUTORS)

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0pp. Mahalaxmi Enclave, Jansath Road, Muzaffarnagar (U.P.) Phone : 0131-2660440 (0), 2600503 (R) website: www.shrlbalajibooks.com email: [email protected] Xr' -

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First edition

:2010

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Third edition : April 2012

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© All Right Reserved with Author

: April 2017

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All the rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted. In any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the author and publisher. Any violation/breach shall be taken into legal action.

A.

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Preface My interaction with students, sincerely preparing for IIT-JEE motivated me to write this book on electricity &magnetism.

Electricity and Magnetism is also as important as Mechanics because in all the competitive examinations, this part is given same or even more weightage than A- --V

mechanics. Like Mechanics I & II this book "Electricity and Magnetism is alsodesigned to clear the concepts through numerical approach. This book will help the students in building analytical and quantitative skills, addressing key misconceptions and developing confidence in problem solving.

I sincerely wish that this book will fulfill all the aspirations of the readers. Although utmost full care has been taken to make the book free from error but some 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, my wife Manjari, my sister Parul, my little kids Vrishank and Ira for giving their valuable time which I utilized during the writing of this book and people of Moradabad, who supported me throughout my career. I am also thankful to Mr. T. Kondala Rao, Mr. Abhishek Sinha (Ranchi), Mr.

Sunil Manohar, Mr. S.P. Sharma, Mr. Sudhir Sharma and Mr. R Narendra Reddy for their valuable suggestions in improving the book.

In the last, 1 also pay my sincere thanks to all the esteemed rmembers of Shri Balaji Publications in bringingoutthis bookinthe present form.- ••"

Anurag Mishra

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Following are some doubts which arise in the mind of almost all the students but may face them by taking some care. 1.

/ can not solve numerical because my concepts are not clear. In fact numerical solving itselfis an exercise to learn concepts.

2.

/ can not study because I am in depression, I fell into it because I was not studying] Depression is escape mechanism ofpeople afraid of facing failures. Failure is integral part oflearning.

3.

/ understand everything in class but can not solve on my own. WRITING work is vital. It is a multiple activity initially idea comes in mind then we put into language to express it, we are focUssed in hand eye coordination, eyes create visual impression on brain which is recorded there. WRITING WORKS ARE EMBOSSEDON BRAIN LIKE CARVINGS OFAJANTA CAVES.

4.

In exams my brain goes blank, but I can crack them at home. Home attempt is your second attempt! you are contemplating about it while home back. You do not behave differently in exam you replicate your instincts. Once a fast bowler was bowling'no balls-. His coach placed a stump on crease, in fear of injury he got it right. CONCEPTUALIZATION, WRITING EQUATION, SOLVING, THEN PROBLEM GETS TO CONCLUSION!

5.

1 •

/ am an average student. It is a rationalization used by people afraid of hard work. In their reference frame Newton's first law applies "if 1 have a misconception 1 will continue with it unless pushed by an external agent even 1 will surround him in my web of misconception yielding zero resultant." AVERAGE IS NOT DUE TO CAPACITY LACUANE BUT DUE TO LACK OF DETERMINATION TO SHED INERTNESS.

6.

A famous cliche "I do not have luck in myfavour" PRINCIPLE OF CAUSALITY: 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. Sow a seed of aspiration in mind, water it with passion, dedication-it will bear fruit, luck can give you sweeter fruit.

1.

Do not take study as a burden actually its a skill like singing and dancing. It has to be honed by proper devotion and dedication.

2.

Without strong sense of achievement 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 ender batting in front of Steyn's bouncers.

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 their is desire and passion to learn you can not discover new ideas. It requires patience and hard work, whose fruits may be tangible later on.

4.

Some students realize very late that they are studying for acquiring skills and honing them. Their is a feeling that they can ride at the back of instructor and achieve excellence. Study comes as torturous exercise enforced on them and their is some mechanism that can take this burden ofthem.

5.

Science is not about gaining good marks, up to Xth by reading key points good marks are achieved but beyond that only those survive who have genuine interest in learning and exploring. Self study habit is must.

6.

IF YOU WANTTO GAIN LEAD START EARLY. Majority of successful students try to finish major portion elementary part of syllabus before they enter Coaching Institute. Due to this their maturity level as compared to others is more they get ample time to adjust with the fast pace. They are less traumatized by the scientific matter handed over. For those who enter fresh must be counselled to not get bullied by early starters but work harder initially within first two months initial edge is neutralized.

7.

Once a student lags behind due to some forced or unforced errors his mind

i

begins to play rationalization remarks like I am an average student, my mind

^ 1 is not sharp enough,1 havelow IQ etc. Thesewords are mechanisms used to i'"

avoid hard work. These words are relative terms a person who has early start maybe intelligent relative to you.

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.

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I. GLGCTROSTATICS Electric Charge (1); What is Charge (2); Charging by Rubbing (5); Insulators andConductors (5); Charging by Contact (6); Charging byInduction (6); Polarization (8); Properties ofCharge (8); Coulomb's law (11); The Electric Field (19); Point Charge Distribution (20); Principle ofSuperposition (21); Electric Field lines (22); Continuous charge Distribution (27), Important Graphs (29); Flux (47); Electric Flux (47); AreaVectors (48);

Solid Angle (52); Developing Gauss's Law from Coulomb's Law (53); Statement of Gauss's Law (55); -Coulomb's Law from Gauss's Law (58); Electric Potential Energy and Electric Potential (74); Acceleration of Charged Particles the Influence ofElectric Forces(82); Equipotentiais and Electric Field Lines (84); TheVan DeGraaff Generator (86); Potential Energy ofa Dipole in a Uniform Field (102); Electric Field and Potential due toADipole (104); The Energy ofa Point Charge Distribution (113); Energy ofElectric Field (114); Energy for a Continuous Distribution ofCharge (116); Properties ofConductor (119); Charge Distribution on a Conducting Sheet (126); Earthing of a Conductor (128); Field between Oppositely Charged Parallel Conducting Plates (136); Level-1: OnlyOneAlternatlveisCorrect(145):Answers(163):Solution(164). Level-2: More than OneAlternative is/ areCorrect (172); Answers (183); Solutions (184); Level-3: Comprehension Based Problems (191); Matching Type Problems (198); Assertion-Reason Type Problems (202); Answers

(204); Solutions (205).

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B. GLGCTRIC CURRGNT Electric Current (211); Electric Current Density (212); Current Density and Drift Speed(214); Expression for Resistance (216); Electromotive, Force and Its Sources (218); EMF and Internal Resistance of a Battery (221); Electric Energy and Power,(222); Series,and Parallel Combination ofBulbs (225); One Dimensional Conduction (231); Two Dimensional .Conduction (232); Kirchhoffs Laws, for "Circuit Analysis (234); KirchhofTs Rules (235); Combination of Cells (236); Net Work Analysis (238); Nodal Analysis (244); Equivalent Resistance (245); Folding Symmetry.(260); Ammeter and Voltmeter (264); Wheat Stone bridge (267);ThePostOfficeBox(273). Level-1: OnlyOneAlternativeisCorrect (285);Answers(296);Solutions(297).' ' Level-2: More thanOneAlternative is/areCorrect (305); Answers (309); Solutions (310); Level-3: Comprehension Based Problems (314); Matching Type Problems (317); Assertion-Reason Type Problems (321); Answers

(322); Solutions (323).

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3. CAPACITORS Sources ofEMF (326); Capacitors (327); ASpherical Capacitor (328); ACylindrical Capacitor (329); Energy Storage in a Capacitor (329); Combination ofCapacitors (331); Capacitors and Dielectrics (332); Gauss's Law and the Electric Field Vectors (334); Charge Sharing between Conductors (335); Analysis ofSimple Capacitive Circuits (352); Nodal Analysis for Capacitive Circuits (356); An Introduction to Transients in Circuits (370); ADischarging Capacitor (372); EquivaienttheTlmeConstant (373); TimeConstant (380) Level-1: Only Onealternative iscorrect(305); Answers (393); Solutions (394).' Level-2: More than OneAlternative is/are Correct (401); Answers (409); Solutions (410).

Level-3: Comprehension Based Problems (417); Matching Type Problems (424); Assertion-Reason Type Problems (427); Answers (428); Solutions (429).

4. THE MAGNETIC FIELD Magnets and Magnetic Poles (436); The Magnetic Field (438); Force and Field for v1B (439); The Force Exerted by Moving Charge in a Magnetic Field (439); The Cyclotron (441); Bubble Chamber (441); Moving Charges in Non-uniform Magnetic Fields (442); The Lorentz Force (447); Force on a Current Carrying Conductor (455); Can Magnetic Force Perform Work (457); Torque on a Current Loop in a Magnetic Field (460); Magnetic Moment of a Circular Coil (461); Galvanometer (469); The Biot-Savart Law (470); Direction of Magnetic Field due to Current Carrying Wire (471); Magnetic Field of Moving Point Charges (471);

Magnetic Force and Conservation ofMomentum (471); Magnetic Field Lines (473); Magnetic Field due to Regular Polygon atits Centre (478); Force between Current Carrying Parallel Wires (482); Ampere's Law (489); Magnetic Field due to an Infinitely Long Cylindrical 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); Paramagnetism andDiamagnetism (512);

Level-1: Only One Alternative Is Correct (524); Answers (544); Solution (545); Level-2: More than OneAlternative is/are Correct (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 Magnetic Flux (578); Induced EMF (580); Motional EMF (584); The Nature of EMF (585); Generators (594); Induced EMF, and Electric Fields (607); Eddy Current (613); Inductance (614); Series and Parallel

Combination of Inductors (616); Self-Inductance and the Modified Kirchhoffs Loop Rule (616); ASeries LR Circuit (618); Energy Stored in an Inductor (623); Mutual Inductance (629); AParallel LC Circuit (639); AC Circuit (650): ACapacitor in an AC Circuit (651); An Inductor In an AC Circuit (652); Phaser Diagram (653); Analysis of Series In AC Circuits (655); SeriesAC RL Circuit (656); Series AC CR Circuit (657); Power in AC Circuits (657); Resonance in Series LCR Circuit (658); Choke Coil (660); Symbolic Notation of Phasors (663); Relation between the Phasors Iand V(664); Kirchhoffs Rules forAC Circuits (665);

Level-1: Only One Alternative isCorrect (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 In ancient time the Greeks noticed that amber, a

yellow-brown material (fossilized pine tree re.in) when rubbed with cloth or fur, it attracts small bits of straw, hair, etc. The word electric derives from the Greek word for amber I

ielectron). By the mid-seventeenth century it was established that a substance, activated by rubbing, possessed some sort of "amber stuff' or electricity. A piece of hard

rubber, a glass rod or a plastic comb or ruler after being vigorously rubbed with a towel can pick up small pieces of paper. From our knowledge of the laws of mechanics we conclude that there exists another force, electric force. The

physical attribute responsible for such electric interaction is electromagnetic charge (electric and magnetic phenomena both are manifestations of charge). In this chapter we will study phenomena due to charges that are stationary, called electrostatics, or static electricity. In this chapter, we focus on the physics of electrostatics, the study of the interactions between electric charges that are at rest (or at most moving very slowly). Though the electric and magnetic forces are distinct, they are intimately related. That is why

we speak of electromagnetism as a unified subject.

Electromagnetism is one of the parts of physics in which we distinguish between electrostatics and magnetostatics and study the two subjects separately. Then we study the remarkable connection between electricity and

magnetism that becomes clear in moving systems.

. • •' -:- ->---i-'-l-'?

Finally, we come to see how electricity and magnetism are two' manifestations of the same basic phenomenon, electromagnetism. Some of the basic characteristics of electrostatics are :

1. Physical quantity responsible for static electricity is electric charge.2. There are two types of charges, one called positive and the other called negative. 3. Like charges repel, whereas unlike charges attract. 4. The net amount of charge produced in any

process is zero. Whenever a certain amount of charge is produced on one body in a process, an equal amount of the opposite type of charge is produced on another body. The positive and negative charges are to be treated algebraically. When a plastic ruler is rubbed with a paper towel, the plastic acquires a negative charge 'and the towel an equal amount of positive charge; the sum of these two charges is zero. If one object or one region of space acquires a positive charge, then an equal amount of negative charge will be established in the neighbouring areas or objects. There are two types of charges, positive and negative. This fact can be easily verified by a simple experiment. When glass is rubbed with silk, the glass becomes positively charged and the silk negatively charged [Fig. 1.1 (a)]. Since the glass and silk have opposite charges, they attract one another. Two glass rods rubbed in this manner repel one another, since each rod has positive charge on it [Fig. 1.1(b)]. Similarly two silk cloths so rubbed repel each other because both cloths have negative charge [Fig. 1.1(c)].

ELECTRICITY &MAGNETISM

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Fig. 1.2 (d) An electrified glass rod attracts an electrified rubber or amber rod

Two different kinds of electrification properties are needed to explain all of these observations.

All electrical phenomena can be described by assuming

only two different kinds of electrification properties. Dufay

called the two types of electrification properties vitreous

(c)

electricity (that similar to glass) and resinous electricity (that

Fig. 1.1

' The normal matter ismadeof atoms, and atoms contain

similar to amber). One never observes an electrified

positive and negative charge in equal amounts. An electron

material that repels (or attracts) both an electrified glass rod

is negatively charged; itrepels other electrons and it attracts protons"which are positively charged.

and an electrified rubber rod; such an observation would

imply a third type, of electrified, state or electrification

WHAT IS CHARGE ?

Furthermore, electrical forces are quite distinct from gravitational forces in several respects:

Fig, i.2 (a) to (d) show certain observations about a charged body

property.

1. Electrical forces between electrified materials are

quite apparent even with small pieces of electrified 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 only when one orboth ofthe masses in huge by laboratory standards). 2. Gravitation is always and only observed as an

Fig. 1.2 (a) Two pieces ofrubbed amber always repel each

other, regardless of which way they face each other.

attractive force, and so we have need for only one kind of

mass, positive inass. Electrical forces are observed to be

either attractive orrepulsive, hence the need for two types of electrification property, the vitreous and resinous electrifications of Dufay. The electric and gravitational forces are similar in two ways:

(i) Both are observed tobe centralforces. They act along the line connecting point like materials causing the force. (ii) Both are conservative forces. The work done by the force around a closed path is zero (equivalently, the work done by the force along a path connecting any two points in

space is independent of the path between the two points).

Fig. 1.2 (b)

Two glass rods rubbed with silk repel each other

Fig. 1.2 (c) Two rubber or amber

rods rubbed with fur

repel each other

It was Benjamin Franklin who introduced the two properties of electrification :

Aparticle or mass is said to be positively electrified if it is repelled by a glass rod that has been freshly rubbed with silk.

ELECTROSTATICS

All glass rods thus rubbed also have positive electrification, since they individually-repel each other.

A particle or niass'is said to be negatively electrified if it is repelled by rubber or amber that has been freshly rubbed with fur.

Hence the rubber or amber itself has a negative electrification property. The names for the electrification properties are .

arbitrary. Dufay called them vitreous and resinous electricity; Franklin- called them positive and negative electricity. One could have called the two electrification properties Ram and Shyam and lean and fat electricity, Jai and Veeru, haired and bald electricity, or even male and female electricity. The two electrification properties are easily transferred through and shared among materials. Some materials easily let the electrification property move from one place to another; these materials are called conductors. With other materials the electrical property lacks mobility (atTeast over short time intervals); these are called insulators. Insulators also are called dielectrics.

We designate the electric charge property of matter symbolically by q (or Q), which may be either a positive or negative scalar according to Franklin's convention. Mass itself quantifies the property we called, inertia or resistance to a change in motion. Both concepts thus are defined operationally by experiment. The concept of mass more real and tangible than charge. Mass and charge both are abstractions used to describe the' way things in nature

behave in certain experiments. The terms mass and charge are our ways of describing the response- of a simple or complex system to certain types or classes of experiments. Thus, when we say an object has a positive charge, we mean the object has the elecmfication property-that makes it repelled by a glass rod that has been freshly rubbed with silk Fig. 1.3 (a). When we say an object has a negative

charge, we mean the object has the electrificatiohproperty that makes it repelled by a rubber rod that has been freshly

rubbed by fur Fig 1.3 (b).This is what we mean Bythe terms positive of negative charge; fundamental particles horizero mass are the only kinds of fundamental particleis that'exhibit electric charge (1.6., can have one or the other electrification property), but that not all particles with mass have nonzero total charge (e.g., the neutron has zero total charge). If an electrified conducting sphere and an identical but un- electrified conducting sphere [see Fig; 1.3 (a)] are brought into contact [Fig. 1.3 (b)], and then separated [Fig. 1.3 (c)]

A

A

B

A

B

(b) Touch them together

(a) An electrified conducting and an unelectrified conducting sphere

B

(c) Separate them.

Fig. 1.3'Transferrlng Charge

We find that both spheres how are electrified and repel each other. We can measure the repulsive force that exists between the two spheres at a fixed separation. If two more identical conducting but unelectrified spheres are each now

brought into contact with one of the identically electrified spheres, we find that the repulsive force between any two of the four elecmfjed spheres,-when, separated by the same distance, is one-fourth what it-was between the original two electrified spheres, , < . , ' The condition of electrification thus is qua,ntifiable as measured by the-forces.

Combining materials havihg equal amounts of opposite electrification properties exactly cancels "their total effectiveness.

•' The two" electrification states or properties •thus are

quantifiable and behave algebraically and arithmetically as scalars.

Analogously to gravitation, we could call the electrification properties of matter' the positive or negative electrical masses, but to avoid confusion with gravitation, the name used for the two electrification properties is electrical charge. ' ^The word charge-means to endow with electricity (or the electrification'property); '

Two particles with the same electrification property seither both positive or both negative, will feel repulsive electrical forces- of equal magnitude on each. We say the charges like'charges; this does not mean that charges are of equal magnitude, only that they have the same type of electrification property. If the two particles have opposite electrification (one positive, one negative), we say the charges are unlike. charges; these produce attractive electrical forces of equal magnitude on each other.

4

ELECTRICITY & IM6NETISM

Atom

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Most of the atom's volume 'm->

is occupied sparsely by electron.

(b) A negative charge is repelled by a rubber rod freshly rubbed with fur

(a) A positive charge is repelled by a glass rod freshly rubbed with silk

Tiny compared with the rest of the atom, the

Nucleus

nucleus contains over

99.9% of the atom's mass.

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Proton:

(T) Neutron:

No charge

0

Negative charge Mass = 9.109x10-21 kg

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(c) Unlike charges attract each other (d) Like charges repel each other with forces of equal magnitude with forces of equal magnitude

Electron:

Fig. 1.4

The electrical forces that two charged masses exert on each other are of equal magnitude and opposite in direction, regardless of the quantity of charge each has, in accordance with Newton's third law of motion.

These experimental results (and others like them) lead us to the following general rules: 1. When two bodies are rubbed together, it is not possible to create electric charge on only one of them. Either neither is charged or both are. 2. Two bodies rubbed together and thus charged exert attractive forces on one another.

Mass = 1.675 x io-27 kg

Fig. 1.5 The structure of an atom

The nucleus is positive due to the presence of positive protons. The nucleus also contains a neutral particle neutron whose properties will be discussed in later chapters. Other charge particles are observed in cosmic rays and nuclear decay, which are very short lived. The charges of electron and proton are identical in magnitude but opposite in sign. All the charges in nature are integral multiples of a basic unit of charge. All the charges are formed by combinations of electrons and protons. The magnitude of this basic charge is

|qJ =1.60xl0"^^C

3. When two bodies made of the same material are

charged in the same way (say, by rubbing with the same kind of cloth), each exerts a repulsive force on the other. 4. The force exerted by a charged body on an uncharged body is always attractive. Fig. 1.5 shows a simple model of an atom with negative electrons orbiting the nucleus.

Positive charge Mass =1.673 X10-27 kg

The symbol q is commonly used for charge. The SI unit of charge is Coulomb (C). O Protons (+) "> Neutrons O Electrons (-)

6P

(a) Neutral iithiuin atom (Li): 3 protons(3+)

(b) Positivelithium ion (Li^): (c) Negative lithium ion (Ll~): 3 protons (3+) _3 protons (3+)

4 neutrons

4 neutrons

4 neutrons

3 electrons(3-)

2 electrons (2-

4electrons!^)

Electronsequal protons:

lesser electronsthan protons:

More electronsthan protons:

Zero net charge

Positive net charge

Negative net charge

Fig. 1.6

ELECTROSTATICS

or electrons in a neutral atom of an element is called the atomic number of the-element. If one or more electrons

acceptor metal. The plastic which has lost electrons now contains a number of immobile positive ions on-its surface and has become charged. The positive plastic attracts the negative metal and the two cling to each other.When a hard rubber rod is stroked with a piece of fur, the rod draws off electrons, becoming negatively charged, and the donor fur becomes equally positively charged. The rubbing mainly increases the area of contact between the

are removed, the remaining positively charged structure is

bodies.

The negative charge of the electron has (within experimental error) exactly the same magnitude as the positive charge of the proton. In a neutral atom the number of electrons equals'the number of protons in the nucleus, and the net electric.charge (the algebraic sum of all the charges) is exactly zero [Fig. 1.6(a)]. The number of protons

called a positive ion [Fig. 1.6(b)]. A negative ion is an A substance that can attract electrons form a material atom that has gained one or more electrons [Fig. 1.6 (c)]. may serve as a donor in another situation. Glass rubbed with This gaining or losing of electrons is called ionization. asbestos draws off electrons from the fibrous material, Following a convention established by Benjamin becoming negative, but if stroked with persistence against Franklin, we call the two kinds of charge positive and silk or flannel, the glass will emerge positively charged negative. When the two are present in a body in equal having lost electrons. amounts, a body is electrically neutral; that is, it does not The table known as triboelectric sequence shows the exhibit the behavior of charged bodies described in the behaviour of various materials. preceding list. If an excess of either positive or negative When a negatively charged object (that has an excess of charge is present, the body is positively or negatively electrons) is placed in contact with a neutral body, some of charged and does exhibit such behavior. Which kind of these electrons are transferred to the neutral body, charging charge we call positive and which negative is entirely it negatively. Similarly, a positively charged body has a arbitrary, but Franklin's convention has been universally deficiency of electrons or an excess of positive ions. When adopted: When a glass rod is rubbed with a silk cloth, we say placed in contact with a neutral body it attracts and draws that the glass becomes positively' charged and the silk • off electrons becominig less positive, while the neutral body becomes negatively charged. Rubbing results in a'liet becomes positive due toToss of electrons: Only electrons are transfer of one land of charge from one body to transferred but the system behaves exactly' as though the other. This leaves one of the bodies with an • positive charge'is being transferred from the'charged one to excess of positive charge and the other body with the neutral one. ' '

an excess of negative charge. Implicit in ^s picture is an important point: The charging process neither creates nor destroys charge; it only redistributes it. This is one statement of the

principle of conservation of charge. According to contemporary physicists most of heavy subatomic particles are actually compositesystems made up of several varieties of smaller fundamental entities called

quarks. These are supposed to have charges or ±-qg and 3

INSULATORS AND CONDUCTORS Substances which do not allow the charges to move

timough them are called insulators, nonconductors, dielectrics. The electrons and ions in insulator are bound

in place; they have limited mobility. They will move only when their mutual repulsion is great enough to overcome

the tendency to be held in place by the host atoms. The charges received by insulators are confined within two regions in which it was introduced.

2

±- 0,. It is believed that quarks cannot ordinary exist in the 3

free state, so the observable unit of charge is indeed q^, the electronic charge.

CHARGING BY RUBB|NG Most of us have the common experience that a plastic

Wheh' a' drarge is introduced anywhere within a conductor it allows the charges to flow freely and redistribute.

The conductors and insulators are distinguished'by the

relative mobility of, charge within the material. In metal atoms the outermost electrons are weakly held, so a bulk

electrons and protons. But the outer electrons are the least

sample contains a tremendous number of free electrons. Pure water and dry table salt are insulators whereas molten salt and salty water are conductors. Air is good insulator even though it contains some 300 ions per cubic

strongly bound and they can be easily shed. The process of transfer is not entirely understood till date. Different

the mutual repulsion may propel them into the surrounding

wrap clings to a container, a rubbed balloon on a shirt sticks to the wall, the cloths cling in a dryer. . Atoms are neutral and they have equal number of

materials have different affinities for electrons. When two substances are in close contact one of them may give up some of its loose electrons while the other may accept them.

When a plastic sheet is pressed down onto a metal plate, electrons will be transferred from the donor plastic to the

centimetre. If large negative charge builds up on an object, air. The air will have some of its own electrons removed

from it, becoming ionized. The ionized space may create a

temporary conductive pathway along which the bulk of the charge then flows. Collisions with the gas increase its

ELEaRICITY &MAGNETISm

temperature and cause some of the atoms to emit light, known as spark. When a charge is introduced on a conductor, under mutual repulsion they move until they are as distant from

one another as possible. Irrespective of the shape of the conductor excess charge always resides on its outer surface. On a metal sphere the charges are uniformly distributed and at rest on the outer surface. With a non-spherical conductor the charge distribution will be non-uniform.

Concept ; insulator = Dielectric

1. The use of the word insulator as a synonym for dielectric is based on Gray's demonstration. The insulator

isolates the conductor from the out side world bypreventing theflow of charge onto or offthe conducting body, analogous to the way a thermal insulator isolates a body from the outside world bypreventing theflow of heat into or out of it. 2. It is easy to see why an electrical conductor—a body made of a substance that conducts electric

charge—cannot be charged by rubbing in the ordinaryway.

Fig. 1.7

An electroscope is an instrument that can be used for

detecting charge (Fig. 1.8). It is made with gold foil leaves

Suppose, for example, that you hold a lump of copper in one

hung from a metal stem and is insulated from the air in a glass-availed container. .

hand and rub it against a piece of glass held in your other hand. Electric charge that is transferred to the copper surface where it rubs against the glass can flow away through the

an electroscope [Fig. l.SCa)]. The glass rod is an insulator, so it must be brought, into contact with the electroscope to

copper and then through your body (also a conductor) to the

transfer charge to or from it. The electrons can move in

A positively charged glass is brought into contact with

ground, thus dispersing so widely that no electricforce can be

metals; they are attracted to the top of the electroscope and

detected. Indeed, Gray showed that conductors could be

some are transferred to the positive rod by touch, which leaves the electroscope positively charged.

charged by rubbing, if they were supported on good dielectrics.

3. The difference between dielectrics and conductors has

to do with the mobility of the charge, which is a property of the particular substance. In conductors, at least one kind of [charge can flow freely. In dielectiics, both kinds ofcharge are bound inplace andcanflow only with difficulty. Although no dielectric isperfect, there is a factor of roughly 10^° between the rates at which charge flows through a conductor such as copper and through a dielectric such as glass. CHARGING BY CONTACT Consider -a negative conductor made to touch an

uncharged metal body. Electrons are [transferred onto the neutral body by their mutual repulsion, which depends on

how densely packed the charges were initially. The charge

(a)

(b) Fig. 1.8

flows similar to fluid flow from a filled container into a

The positively charged leaves of the electroscope

connecting container of arbitrary shape. The gravity driven

separate against the force of gravity. Similarly the

flow continues until the liquid levels are the same, the

electroscope can be negatively charged by contact with a negatively charged object [Fig. 1.8(b)].

pressures equalize and equilibrium is reached. Similarlyif a total excess charge Q is placed on one of two identical metal

spheres and those spheres are brought into contact and then separated, a charge Cl/2)Q will end upon each of them (Fig. 1.7).

CHARGING BY INDUCTION

Consider a positively charged object brought close to

ELECTROSTATICS

neutral metal rod, without any contact. The electrons in the

many purposes it may be thought of as a limitless reservoir

metal can move within the metal towards the positively

of charge. To ground a conductor means to provide a conducting

D

c

Metal rod still neutral, but

path between it and the ground (or to another charge reservoir). A charged conductor and onto the Earth. A buildup of even a relatively small amount of charge on a truck that delivers could be dangerous—a spark could trigger an explosion. To prevent such a charge buildup, the truck grounds its tank before starting to deliver petrol to the

with a separation of charge

service station.

Neutral metal rod

(a)

D (b) Fig. 1.9; Inducting a charge on an object connected to ground

charged object (electrostatic attraction) which leaves a positive charge at the opposite end. A charge is said to be

The third opening of modem electrical outlets is called ground. It is literally connected by a conducting wire to the ground, either through a metal rod driven into the Earth or through underground metal water pipes. The purpose of the ground connection is that it prevents static charges from building up on the conductor that is grounded.

induced at the two ends of the metal rod. Note that no net Metal sphere

charge has been created in the rod. A charge redistribution has taken place. The net charge on the metal rod is still zero. Glass rod

If we break the rod in the middle we could have two charged

objects, one charged positively and the other negatively. Charge separation in electrically neutral materials caused by presence of another nearly charged object, is called electrical polarization.

Silk cloth Insulated base

We take a fixed negatively charged object near an

uncharged conductor. The uncharged conductor is polarized. The electrons move to the far end of the conductor, since they are repelled by the negatively charged object. Nextwe connect the conductor with conductingwire to the ground. Connecting a conductor to Earth by means of

(a) Electron flow

from ground through wire to sphere

another conductor is called grounding the conductor, or

Negative charges

earthing. The Earth is gigantic and can conduct, can easily give up or accept electrons; hence it acts like a reservoir of charge. The electrons in the conductor repelled by negatively charged object can escape to Earth. This leaves the conductor positively charged. If the wire is now removed

are attracted towards rod

(c)

c

Disconnecting +1 ground wire

(a)

(V •

Rod IS removed

equilibrium attained

;

(b)

dZLlB-(C) Fig. 1.10

the electrons cannot get back into the conductor from which they escaped earlier. So the conductor now has a positive

charge and is no longer electrically neutral. The negatively charged object can be removed and the initially neutral conductor remains positively charged. This process is called charging by induction. The Earth is a conductor because of the presence of metal ions and moisture. The Earth is large enough that for

• Fig. 1.11:The symbol y represents a connection toground. Charging by induction. (a) Aglass rod Is charged by rubbing itwith silk, (b) The positively charged glass rod is held near a metal sphere, but does not touch it. The sphere Is polarized as free electrons within the sphere are attracted toward the' glass rod. (c) When the sphere is grounded, electrons from the ground move ontothe sphere, attracted there by positive charges on the sphere (d) The ground connection is broken without moving theglass rod. (e) Now

the glass rod Isremoved. Charge spread over the metal surface as thelike charges repel each other. The sphere is left witii a netnegative charge '

because of the excess electrons.

In case of insulator the electrons are not free for

macroscopic charge separation.

In this case local

ELECTRICITY &MAGNETKMj

8

polarization occurs only on local atomic or molecular scale.

When a charged object is brought near an insulator the distribution of charge in atoms and molecules is shifted slightly. Opposite charge is attracted nearer the external charged object while two like charges are repelled. The small shift of charge position for each atom or molecule is balanced out by the same effect on all its nearest neighbours. But at the surface the cancellation is not

complete. The excess of positive or negative charge over the near and far surfaces gives a resultant force of attraction towards the charged object. The polar molecules like water have natural separation of charge, although they are neutral overall. Polar molecules show greater polarization effects than the molecules with uniform charge distribution. POLARIZATION

An electrically neutral object may have regions of positive and negative charge within it, separated from one another. Such an object is polarized. Apolarized objectcan experience an electric force even though its net charge is zero. A rubber rod charged negatively after being rubbed

with fur attracts smallbits of.paper. So does a glass rod that is positively charged after being rubbed with silk [Fig. 1.12]. The bits of paper are electrically neutral, but a charged rod polarizes the paper—it attracts the unlike charge in the paper a bit closer and pushes the like charge in the paper a bit farther away [Fig. 1.12(c)]. The attraction between the

rod and the unlike charge then becomes a little stronger than the repulsion between the rod and the like charge, since the electrical force gets-weaker as the separation

On a dry day, run a comb through your hair or rub the comb on a wool sweater., go to a sink and turn the water on .so that a thin stream of water comes out. It does not matter

if the stream breaks up into droplets near the bottom..Hold the charged comb near the stream of water. You should see

that the water experiences a force due to the charge on the comb. Is the force attractive or repulsive? Does this mean that the water coming from the tap has a net charge? Explain your observations. Ordinary tape has an adhesive that allows it to stick to

paper and many other materials. Since the sticking force is electrical in nature,. Ifyou have everpeeled a rollof tape too quickly and noticed that the strip of tape curls around and behavesstrangely, the strip of tape has a net charge (and so does the tape left behind, but of opposite sign). Tape pulled slowly off a surface does not tend to have a net charge. A similar phenomenon occurs on a dry day when you walk across a carpeted room wearing rubber-soled shoes. Chargeis transferred between the carpet and your shoes and

between yourshoes and your body. Sonie of the charge you have'accumulated may be unintentionally transferred from your fingertips to a doorlmob or to a friend—accompanied by the sensation of a-shock. Electrons in each molecule of the neutral

Insulator shift away from the comb.

Negatively

'charged comb

increases and the like charge is farther away. Thus, the net

As a result, the

force oilthe paperis always attractive, regardless ofthe sign

(+) charges in each molecule are closer to

of charge on the rod.

the comb than are the (-) charges and so experience a stronger force from the comb. Therefore the net force Is attractive.

Paper bits Paper bits Magnifier

This time, electrons in the molecules shift toward the comb.... •Rubber rod

Glass rod

Positively charged comb

Fig. 1.12

In this case, we say that the paper is polarized by induction; the polarization of the paper is induced by the

charge on the nearby rod. When the rod is moved away, the paper is no longer polarized. Some objects, including some molecules, are intrinsically polarized. Anelectrically neutral water molecule, for example, equal amounts of positive and negative charge (10 protons and 10 electrons), but the center of positive charge and the center of negative charge do not coincide. The electrons in the molecule are shared in such a way that the oxygen end of the molecule has a

negative charge, while the hydrogen atoms are positive.

molecule are closer to

^

the comb, and experience a stronger force from It, than the (+) charges. The net force is attractive.

Fig. 1.13

PROPERTIES OF CHARGE

1. Charge: It is the property associatedwith matter due

to which it produces and experiences electrical and magnetic ejfects. The excess or deficiency ofelectrons in a body gives the

^_ concept ofcharge. Soa negatively charged body means that the

body has gained electrons while a positively charged body means that the body has lost some of its electrons.

•

=^ emu of charge

^^

9|

is converted into mass while in annihilation mass is

converted into energy. In pair production 'presence of

nu^eus is a must to conserye momentum. In absence of

1coulomb = 3X10^ esu of charge

•_


F, = F 12 + F13+F14 + ...+

constant of medium, or relative permittvity of medium

F-liV =y.F,, t=2

This result is called principal of superposition.

So

Remember that the Coulomb's force

s = permittivity of medium Eq = permittivity of vacuum Er = relative permittivity Thus,

than the distance between them. Ideally it is precise for 1

iFl=

qi'32

4'K&o&r r For vacuum

= 1

point charges, whose spatial size is negligible as compared to other distances. In case of finite size objects, it is always not possible to identify value of r, particularly when

there

is

nonuniform

charge

distribution.

For

For air 8^=1 For conductivity medium 8^=00

conducting spheres the charge is uniformly

For water

centres.

s- = 80

3. Coulombic force between two charges is an action

reaction pair, conservative in nature, central force. It acts along line joining two point charges:

distributed, then r

is the distance between

Coulomb's law describe the force between charges at

rest. In this chapter our discussion is restricted to charges at rest, the study of which is called electrostatics. When charges are in motion additional forces come into play, whidi will be discussed in later chapters.

\

equation is

precisely applicable to objects whose size is much smaller

ELECTROSTATICS

Concepts: 1.^ To make the study of the distance

'To express Coulomb's law as an equation, we must deal

.dependence as simple as possible, consider theforce exerted by

i

with an additional problem. When we developed Newton's law of gravitation, we had already defined mass as one of

point charge 1 onpoint charge 2. Apoint charge—afinite charge locateU' at a geometric point—is an idealization analogous to that of a point mass (a particle). Ifwe consider two point charges. We can precisely define the vector ^hat extends from body 1 to body 2. (We approximate this ideal

the basic dimensions—mass, length, and time—of SI and

had established a unit ofmass, the kilogram. Electric charge q, which appears in Proportionality cannot be expressed in terms of these basic dimensions. Consequently, we must expand our set of basic dimensions to include a fourth

.situation when the distance between the two

dimension, electric charge, for which we must then establish

charged bodies is large compared with the size of

•an SI unit. With this in mind, we proceed in two steps: 1. As a preliminaiy to defining it, we give the unit of electric charge a name, the coulomb (C). This is , the quantities and q2 that appear in our desired equation will be expressed in coulombs. With this in mind, we use a

either).

, 2. The forces that any two point like charges exert on .each otherare of equal magnitude but in opposite directions, in accordance with Newton's third law. The force on each

.charge has the same magnitude even if q and Q are of different magnitude^ as shown in Fig. 2.23

proportionality constant to rewrite Coulomb's law as an equation:

= (constant) Q1Q2

4^2,

From this equation, it follows that the SI units of the proportionality constant are N -

/ C^. For reasons that will

be clear later on, we write the constant in theform

constant =—^ 47180

Fig. 1.23 •

,

The electrical force on each of two charges satisfies

Newton's third law.

3,

If the

electric force

is

likewise

The quantity eQ("epsilon-zero") that appedrs in this definition is called thepermittivity offree space. We can now write Coulomb's law in its most requently used form, -

an

.