physics part 1 class xii.pdf

7/27/2019 Physics Part 1 Class XII.pdf

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PHYSICSPART I

TEXTBOOKFORCLASSXII


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PHYSICSPART I

TEXTBOOKFORCLASSXII


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F i r s t E d i t i o n

December 200 6 Pausa 192 8

Rep r i n t e dDecember 2007 Agrahayana 192 9


PD 36 0T RNB

Na t i o na l Counc i l o f Educ a t i o na l

Res ea r c h a nd T r a i n i n g , 200 6

Rs . 11 5 .00

Printed on 80 GSM paper w ith NCERT

w atermark

Published at the Publication Departmentby the Secretary, National Council of

Educational Research and Training,Sri Aurobindo Marg, New Delhi 110 016and printed at Prabhat Printing Press,

D-23, Industrial Area Site-A, Mathura

ISBN 81-7450-631-4

ALL 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 publisher.

This book is sold subject to the condition that it shall not, by way of trade, be lent, re-

sold, hired out or otherwise disposed of without the publishers consent, in any formof binding or cover other than that in which it is published.

The correct price of this publication is the price printed on this page, Any revised

price indicated by a rubber stamp or by a sticker or by any other means is incorrectand should be unacceptable.

OFFICES OF THE PUBLICATION

DEPARTMENT, NCERT

NCERT CampusSri Aurobindo Marg

New Delhi 110 016 Phone : 011-26562708

108, 100 Feet RoadHosdakere Halli Extension

Banashankari III StageBangalore 560 085 Phone : 080-26725740

Navjivan Trust BuildingP.O.NavjivanAhmedabad 380 014 Phon e : 079-27541446

CWC CampusOpp. Dhankal Bus Stop

PanihatiKolkata 700 114 Phone : 033-25530454

CWC ComplexMaligaonGuwahati 781 021 Phone : 0361-2674869

Publicatio n Team

Head, Publication : Peyyet i Rajakuma rDepartment

Chief Production : Shiv Kuma r

Officer

Chief Editor : Shveta Uppal

Chief Business : Gautam GangulyManager

Assistant Editor : R.N. Bhard w aj

Production Assistant : Praka sh Veer Singh

Cover , La you ta n d I l l u s t r a t i o n s Shw eta Rao


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FOREWORD

The National Curriculum Framework (NCF), 2005 recommends that childrens life at school mustbe linked to their life outside the school. This principle marks a departure from the legacy of bookishlearning which continues to shape our system and causes a gap between the school, home andcommunity. The syllabi and textbooks developed on the basis of NCF signify an attempt to implementthis basic idea. They also attempt to discourage rote learning and the maintenance of sharp

boundaries between different subject areas. We hope these measures will take us significantlyfurther in the direction of a child-centred system of education outlined in the National Policy onEducation (NPE), 1986.

The success of this effort depends on the steps that school principals and teachers will take toencourage children to reflect on their own learning and to pursue imaginative activities and questions.We must recognise that, given space, time and freedom, children generate new knowledge by engagingwith the information passed on to them by adults. Treating the prescribed textbook as the sole basisof examination is one of the key reasons why other resources and sites of learning are ignored.Inculcating creativity and initiative is possible if we perceive and treat children as participants inlearning, not as receivers of a fixed body of knowledge.

These aims imply considerable change in school routines and mode of functioning. Flexibility inthe daily time-table is as necessary as rigour in implementing the annual calendar so that the

required number of teaching days are actually devoted to teaching. The methods used for teachingand evaluation will also determine how effective this textbook proves for making childrens life atschool a happy experience, rather than a source of stress or boredom. Syllabus designers have triedto address the problem of curricular burden by restructuring and reorienting knowledge at differentstages with greater consideration for child psychology and the time available for teaching. The textbookattempts to enhance this endeavour by giving higher priority and space to opportunities forcontemplation and wondering, discussion in small groups, and activities requiring hands-onexperience.

The National Council of Educational Research and Training (NCERT) appreciates the hardwork done by the textbook development committee responsible for this book. We wish to thank theChairperson of the advisory group in science and mathematics, Professor J.V. Narlikar and theChief Advisor for this book, Professor A.W. Joshi for guiding the work of this committee. Severalteachers contributed to the development of this textbook; we are grateful to their principals for

making this possible. We are indebted to the institutions and organisations which have generouslypermitted us to draw upon their resources, material and personnel. We are especially grateful tothe members of the National Monitoring Committee, appointed by the Department of Secondaryand Higher Education, Ministry of Human Resource Development under the Chairpersonship ofProfessor Mrinal Miri and Professor G.P. Deshpande, for their valuable time and contribution. Asan organisation committed to systemic reform and continuous improvement in the quality of itsproducts, NCERT welcomes comments and suggestions which will enable us to undertake furtherrevision and refinement.

Director

New Delhi National Council of Educational20 December 200 6 Research and Training


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TEXTBOOK DEVELOPMENT COMMITTEE

CHAIRPERSON, ADVISORYGROUPFOR TEXTBOOKS IN SCIENCEAND MATHEMATICS

J.V. Narlikar, Emeritu s Professor,Inter-University Centre for Astronomy and Astrophysics

(IUCAA), Ganeshkhind, Pune University Campus, Pune

CHIEF ADVISORA.W. Joshi, Honorary Visiting Scientist, National Centre for Radio Astrophysics (NCRA), Pune

University Campus, Pune (Formerly Professorat Department of Physics, University of Pune)

MEMBERS

A.K. Ghatak, Emeritu s Professor,Department of Physics, Indian Institute of Technology,

New Delhi

Alika Khare, Professor, Department of Physics, Indian Institute of Technology, Guwahati

Anjali Kshirsagar, Reader, Department of Physics, University of Pune, Pune

Anuradha Mathur, PGT, Modern School, Vasant Vihar, New Delhi

Atul Mody, Lectu rer (S.G.),VES College of Arts, Science and Commerce, MumbaiB.K. Sharma, Professor, DESM, NCERT, New Delhi

Chitra Goel, PGT,Rajkiya Pratibha Vikas Vidyalaya, Tyagraj Nagar, New Delhi

Gagan Gupta, Reader,DESM, NCERT, New Delhi

H.C. Pradhan, Professor,Homi Bhabha Centre of Science Education (TIFR), Mumbai

N. Panchapakesan, Professor(Retd. ), Department of Physics and Astrophysics, University of

Delhi, Delhi

R. Joshi, Lecturer(S.G.), DESM, NCERT, New Delhi

S.K. Dash, Reader,DESM, NCERT, New Delhi

S. Rai Choudhary,Professor,

Department of Physics and Astrophysics, University of Delhi, DelhiS.K. Upadhyay, PGT, Jawahar Navodaya Vidyalaya, Muzaffar Nagar

S.N. Prabhakara, PGT,DM School, Regional Institute of Education (NCERT), Mysore

V.H. Raybagkar,Reader, Nowrosjee Wadia College, Pune

Vishwajeet Kulkarni, Teacher (Grade I), Higher Secondary Section, Smt. Parvatibai Chowgule

College, Margao, Goa

MEMBER-COORDINATOR

V.P. Srivastava, Reader,DESM, NCERT, New Delhi


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CONSTITUTION OF INDIA

Fundamental Duties

Fundamental Duties It shall be the duty of every citizen of India

(a) to abide by the Constitution and respect its ideals and institutions, the National

Flag and the National Anthem;

(b) to cherish and follow the noble ideals which inspired our national struggle for

freedom;

(c) to uphold and protect the sovereignty, unity and integrity of India;

(d) to defend the country and render national service when called upon to do so;

(e) to promote harmony and the spirit of common brotherhood amongst all the peopleof India transcending religious, linguistic and regional or sectional diversities; to

renounce practices derogatory to the dignity of women;

(f) to value and preserve the rich heritage of our composite culture;

(g) to protect and improve the natural environment including forests, lakes, rivers,

wildlife and to have compassion for living creatures;

(h) to develop the scientific temper, humanism and the spirit of inquiry and reform;

(i) to safeguard public property and to abjure violence;

(j) to strive towards excellence in all spheres of individual and collective activity so

that the nation constantly rises to higher levels of endeavour and achievement;

(k) who is a parent or guardian, to provide opportunities for education to his child or,

as the case may be, ward between the age of six and fourteen years.

Part IV A (Artic le 5 1 A)


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ACKNOWLEDGEMENTS

The National Council of Educational Research and Training acknowledges the valuable

contribution of the individuals and organisations involved in the development of Physics Textbookfor Class XII. The Council also acknowledges the valuable contribution of the following academics

for reviewing and refining the manuscripts of this book:

Anu Venugopalan, Lecturer, School of Basic and Applied Sciences, GGSIP University, Delhi;A.K. Das, PGT, St. Xaviers Senior Secondary School, Delhi; Bharati Kukkal, PGT, Kendriya

Vidyalaya, Pushp Vihar, New Delhi; D.A. Desai, Lecturer (Retd.), Ruparel College, Mumbai;Devendra Kumar, PGT, Rajkiya Pratibha Vikas Vidyalaya, Yamuna Vihar, Delhi; I.K. Gogia, PGT,

Kendriya Vidyalaya, Gole Market, New Delhi; K.C. Sharma, Reader, Regional Institute of Education

(NCERT), Ajmer; M.K. Nandy, Ass ociate Professor, Department of Physics, Indian Institute ofTechnology, Guwahati; M.N. Bapat,Reader, Regional Institute of Education (NCERT), Mysore;

R. Bhattacharjee, Asst t. Professor, Department of Electronics and Communication Engineering,Indian Institute of Technology, Guwahati; R.S. Das, Vice-Principa l (Retd .), Balwant Ray Mehta

Senior Secondary School, Lajpat Nagar, New Delhi; Sangeeta D. Gadre, Reader, Kirori Mal College,

Delhi; Suresh Kumar, PGT, Delhi Public School, Dwarka, New Delhi; Sushma Jaireth, Reader,Department of Womens Studies, NCERT, New Delhi; Shyama Rath, Reader, Department of Physics

and Astrophysics, University of Delhi, Delhi; Yashu Kumar,PGT, Kulachi Hans Raj Model School,Ashok Vihar, Delhi.

The Council also gratefully acknowledges the valuable contribution of the following academics

for the editing and finalisation of this book: B.B. Tripathi,Professor (Retd .), Department of Physics,Indian Institute of Technology, New Delhi; Dipan K. Ghosh, Professor, Department of Physics,

Indian Institute of Technology, Mumbai; Dipanjan Mitra, Scientist, National Centre for RadioAstrophysics (TIFR), Pune; G.K. Mehta, Raja Rama nna Fel low, Inter-University Accelerator

Centre, New Delhi; G.S. Visweswaran, Professor, Department of Electrical Engineering, Indian

Institute of Technology, New Delhi; H.C. Kandpal, Head, Optical Radiation Standards, NationalPhysical Laboratory, New Delhi; H.S. Mani, Raja Rama nna Fel low, Institute of Mathematical

Sciences, Chennai; K. Thyagarajan, Professor, Department of Physics, Indian Institute ofTechnology, New Delhi; P.C. Vinod Kumar, Professor, Department of Physics, Sardar Patel

University, Vallabh Vidyanagar, Gujarat; S. Annapoorni, Professor, Department of Physics andAstrophysics, University of Delhi, Delhi; S.C. Dutta Roy, Emeritu s Professor, Department ofElectrical Engineering, Indian Institute of Technology, New Delhi; S.D. Joglekar, Professor,

Department of Physics, Indian Institute of Technology, Kanpur; V. Sundara Raja, Professor, SriVenkateswara University, Tirupati.

Special thanks are due to Hukum Singh,Professor and Head ,DESM, NCERT for his support.

The Council also acknowledges the support provided by the APC office and the administrativestaff of the DESM; Deepak Kapoor, Incharge,Computer Station; Inder Kumar, DTP Operator;

Mohd. Qamar Tabrez, Copy Editor ;Ashima Srivastava, Proof Read erin shaping this book.The contributions of the Publication Department in bringing out this book are also duly

acknowledged.


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CONSTITUTION OF INDIAPart III (Articles 12 35)

(Subject to certain conditions, some exceptionsand reasonable restrictions)

guarantees these

Fundamental Rights

Right to Equality

before law and equal protection of laws;

irrespective of religion, race, caste, sex or place of birth;

of opportunity in public employment;

by abolition of untouchability and titles.

Right to Freedom

of expression, assembly, association, movement, residence and profession;

of certain protections in respect of conviction for offences;

of protection of life and personal liberty;

of free and compulsory education for children between the age of six and fourteen years;

of protection against arrest and detention in certain cases.

Right against Exploitation

for prohibition of traffic in human beings and forced labour;

for prohibition of employment of children in hazardous jobs.

Right to Freedom of Religion

freedom of conscience and free profession, practice and propagation of religion;

freedom to manage religious affairs;

freedom as to payment of taxes for promotion of any particular religion;

freedom as to attendance at religious instruction or religious worship in educational

institutions wholly maintained by the State.

Cultural and Educational Rights

for protection of interests of minorities to conserve their language, script and culture;

for minorities to establish and administer educational institutions of their choice.

Right to Constitutional Remedies

by issuance of directions or orders or writs by the Supreme Court and High

Courts for enforcement of these Fundamental Rights.


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PREFACE

It gives me pleasure to place this book in the hands of the students, teachers and the public at

large (whose role cannot be overlooked). It is a natural sequel to the Class XI textbook which

was brought out in 2006. This book is also a trimmed version of the textbooks which existed so

far. The chapter on thermal and chemical effects of current has been cut out. This topic has also

been dropped from the CBSE syllabus. Similarly, the chapter on communications has beensubstantially curtailed. It has been rewritten in an easily comprehensible form.

Although most other chapters have been based on the earlier versions, several parts and

sections in them have been rewritten. The Development Team has been guided by the feedback

received from innumerable teachers across the country.

In producing these books, Class XI as well as Class XII, there has been a basic change ofemphasis. Both the books present physics to students without assuming that they would pursue

this subject beyond the higher secondary level. This new view has been prompted by the various

observations and suggestions made in the National Curriculum Framework (NCF), 2005.

Similarly, in todays educational scenario where students can opt for various combinations of

subjects, we cannot assume that a physics student is also studying mathematics. Therefore,physics has to be presented, so to say, in a stand-alone form.

As in Class XI textbook, some interesting box items have been inserted in many chapters.They are not meant for teaching or examinations. Their purpose is to catch the attention of the

reader, to show some applications in daily life or in other areas of science and technology, to

suggest a simple experiment, to show connection of concepts in different areas of physics, andin general, to break the monotony and enliven the book.

Features like Summary, Points to Ponder, Exercises and Additional Exercises at the end of

each chapter, and Examples have been retained. Several concept-based Exercises have beentransferred from end-of-chapter Exercises to Examples with Solutions in the text. It is hoped

that this will make the concepts discussed in the chapter more comprehensible. Several newexamples and exercises have been added. Students wishing to pursue physics further would

find Points to Ponder and Additional Exercises very useful and thoughtful. To provide resources

beyond the textbook and to encourage eLearn ing, each chapter has been provided with some

relevant website addresses under the title ePhysics. These sites provide additional materials onspecific topics and also provide learners the opportunites for interactive demonstrations/

experiments.The intricate concepts of physics must be understood, comprehended and appreciated.

Students must learn to ask questions like why, how, how do we know it. They will findalmost always that the question why has no answer within the domain of physics and science

in general. But that itself is a learning experience, is it not? On the other hand, the questionhow has been reasonably well answered by physicists in the case of most natural phenomena.

In fact, with the understanding of how things happen, it has been possible to make use of manyphenomena to create technological applications for the use of humans.

For example, consider statements in a book, like A negatively charged electron is attractedby the positively charged plate, or In this experiment, light (or electron) behaves like a wave.

You will realise that it is not possible to answer why. This question belongs to the domain ofphilosophy or metaphysics. But we can answer how, we can find the force acting, we can find


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the wavelength of the photon (or electron), we can determine how things behave under different

conditions, and we can develop instruments which will use these phenomena to our advantage.It has been a pleasure to work for these books at the higher secondary level, along with a

team of members. The Textbook Development Team, the Review Team and Editing Teams involvedcollege and university teachers, teachers from Indian Institutes of Technology, scientists from

national institutes and laboratories, as well as higher secondary teachers. The feedback and

critical look provided by higher secondary teachers in the various teams are highly laudable.

Most box items were generated by members of one or the other team, but three of them were

generated by friends and well-wishers not part of any team. We are thankful to Dr P.N. Sen ofPune, Professor Roopmanjari Ghosh of Delhi and Dr Rajesh B Khaparde of Mumbai for allowing

us to use their box items, respectively in Chapters 3, 4 (Part I) and 9 (Part II). We are very

thankful to the members of the Review and Editing Workshops to discuss and refine the first

draft of the textbook. We also express our gratitude to Prof. Krishna Kumar, Director, NCERT,for entrusting us with the task of presenting this textbook as a part of the national effort forimproving science education. I also thank Prof. G. Ravindra, Joint Director, NCERT, for his help

from time-to-time. Prof. Hukum Singh, Head, Department of Education in Science and

Mathematics, NCERT, was always willing to help us in our endeavour in every possible way.

We welcome suggestions and comments from our valued users, especially students and

teachers. We wish our young readers a happy journey into the exciting realm of physics.

A. W. JOSHIChie f Adv isor

Textbook Development Committee

xii


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CONTENTS

FOREWORD v

PREFACE xi

CHAPTER ONE

ELECTRICCHARGESANDFIELDS

1 .1 Introduction 1

1 .2 Electric Charges 11 .3 Conductors and Insulators 5

1 .4 Charging by Induction 6

1 .5 Basic Properties of Electric Charge 8

1 .6 Coulombs Law 10

1 .7 Forces between Multiple Charges 15

1 .8 Electric Field 18

1 .9 Electric Field Lines 23

1 . 1 0 Electric Flux 25

1 . 1 1 Electric Dipole 271 . 1 2 Dipole in a Uniform External Field 31

1 . 1 3 Continuous Charge Distribution 32

1 . 1 4 Gausss Law 33

1 . 1 5 Application of Gausss Law 37

CHAPTER TWO

ELECTROSTATICPOTENTIALANDCAPACITANCE

2 .1 Introduction 51

2 .2 Electrostatic Potential 53

2 .3 Potential due to a Point Charge 54

2 .4 Potential due to an Electric Dipole 55

2 .5 Potential due to a System of Charges 57

2 .6 Equipotential Surfaces 60

2 .7 Potential Energy of a System of Charges 61

2 .8 Potential Energy in an External Field 64

2 .9 Electrostatics of Conductors 67

2 . 1 0 Dielectrics and Polarisation 71

2 . 1 1 Capacitors and Capacitance 73

2 . 1 2 The Parallel Plate Capacitor 742 . 1 3 Effect of Dielectric on Capacitance 75


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2 . 1 4 Combination of Capacitors 78

2 . 1 5 Energy Stored in a Capacitor 80

2 . 1 6 Van de Graaff Generator 83

CHAPTER THREE

CURRENTELECTRICITY


3 .2 Electric Current 93

3 .3 Electric Currents in Conductors 94

3 .4 Ohms law 95

3 .5 Drift of Electrons and the Origin of Resistivity 97

3 .6 Limitations of Ohms Law 1013 .7 Resistivity of various Materials 101

3 .8 Temperature Dependence of Resistivity 103

3 .9 Electrical Energy, Power 105

3 . 1 0 Combination of Resistors Series and Parallel 107

3 . 1 1 Cells, emf, Internal Resistance 110

3 . 1 2 Cells in Series and in Parallel 113

3 . 1 3 Kirchhoffs Laws 115

3 . 1 4 Wheatstone Bridge 118

3 . 1 5 Meter Bridge 120

3 . 1 6 Potentiometer 122

CHAPTER FOUR

MOVING CHARGES ANDMAGNETISM


4 .2 Magnetic Force 133

4 .3 Motion in a Magnetic Field 137

4 .4 Motion in Combined Electric and Magnetic Fields 140

4 .5 Magnetic Field due to a Current Element, Biot-Savart Law 143

4 .6 Magnetic Field on the Axis of a Circular Current Loop 145

4 .7 Amperes Circuital Law 147

4 .8 The Solenoid and the Toroid 150

4 .9 Force between Two Parallel Currents, the Ampere 154

4 . 1 0 Torque on Current Loop, Magnetic Dipole 157

4 . 1 1 The Moving Coil Galvanometer 163

CHAPTER FIVE

MAGNETISMANDMATTER


5 .2 The Bar Magnet 174xiv


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5 .3 Magnetism and Gausss Law 181

5 .4 The Earths Magnetism 185

5 .5 Magnetisation and Magnetic Intensity 189

5 .6 Magnetic Properties of Materials 191

5 .7 Permanent Magnets and Electromagnets 195

CHAPTER SIX

ELECTROMAGNETICINDUCTION


6 .2 The Experiments of Faraday and Henry 205

6 .3 Magnetic Flux 206

6 .4 Faradays Law of Induction 207

6 .5 Lenzs Law and Conservation of Energy 210

6 .6 Motional Electromotive Force 212

6 .7 Energy Consideration: A Quantitative Study 215

6 .8 Eddy Currents 218

6 .9 Inductance 219

6 . 1 0 AC Generator 224

CHAPTER SEVEN

ALTERNATINGCURRENT


7 .2 AC Voltage Applied to a Resistor 234

7 .3 Representation of AC Current and Voltage byRotating Vectors Phasors 237

7 .4 AC Voltage Applied to an Inductor 237

7 .5 AC Voltage Applied to a Capacitor 241

7 .6 AC Voltage Applied to a Series LCR Circuit 244

7 .7 Power in AC Circuit: The Power Factor 252

7 .8 LC Oscillations 255

7 .9 Transformers 259

CHAPTER EIGHT

ELECTROMAGNETICWAVES


8 .2 Displacement Current 270

8 .3 Electromagnetic Waves 274

8 .4 Electromagnetic Spectrum 280

ANSWERS 288

xv


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COVERDESIGN(Adapted from http://nobelprize.org and

the Nobel Prize in Physics 2006)

Different stages in the evolution ofthe universe.

BACKCOVER(Adapted from http://www.iter.org and

http://www.dae.gov.in)

Cut away view of Interna tional Thermonuclear Experimenta l Reactor(ITER)device. The man in the bottom shows the scale.

ITER is a joint international research and development project that

aims to demonstrate the scientific and technical feasibility of fusion power.India is one of the seven full partners in the project, the others being

the European Union (represented by EURATOM), Japan, the PeoplesRepublic of China, the Republic of Korea, the Russian Federation and theUSA. ITER will be constructed in Europe, at Cadarache in the South of

France and will provide 500 MW of fusion power.

Fusion is the energy source of the sun and the stars. On earth, fusionresearch is aimed at demonstrating that this energy source can be used toproduce electricity in a safe and environmentally benign way, withabundant fuel resources, to meet the needs of a growing world population.

For details of Indias role, see Nuclear India, Vol. 39, Nov. 11-12/May-June 2006, issue available at Department of Atomic Energy (DAE)website mentioned above.


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F i r st E d i t i o n December, 2006 Pausa 1 928

Rep r i n t e d

December, 200 7 Agrahay ana 192 9


PD 3 60 T RNB

Na t i o na l Counc i l o f Educ a t i o na l

Res ea r c h a nd T r a i n i n g , 200 6

Rs . 115 .00

Printed on 80 GSM pap er w ith NCERT

watermark

Published at the Publication Departmentby the Secretary, National Council of

Educational Research and Training,Sri Aurobindo Marg, New Delhi 110 016and printed at Supreme Offset Press, K-5,Malvaya Nagar, New Delhi 110 017

ISBN 81-7450-631-4

ALL 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 publisher.

This book is sold subject to the condition that it shall not, by way of trade, be lent, re-

sold, hired out or otherwise disposed of without the publishers consent, in any formof binding or cover other than that in which it is published.

The correct price of this publication is the price printed on this page, Any revised

price indicated by a rubber stamp or by a sticker or by any other means is incorrectand should be unacceptable.

OFFICES OF THE PUBLICATION

DEPARTMENT, NCERT

NCERT CampusSri Aurobindo MargNew Delhi 110 016 Phone : 011-26562708

108, 100 Feet RoadHosdakere Halli Extension

Banashankari III StageBangalore 560 085 Phone : 080-26725740

Navjivan Trust Building

P.O.NavjivanAhmedabad 380 014 Phon e : 079-27541446

CWC CampusOpp. Dhankal Bus StopPanihati

Kolkata 700 114 Phone : 033-25530454

CWC Complex

MaligaonGuwahati 781 021 Phone : 0361-2674869

Publication Team

Head, Publication : Peyyet i Rajakuma rDepartment

Chief Production : Shiv KumarOfficer

Chief Editor : Shveta Uppal

Chief Business : Gautam GangulyManager

Assistant Editor : R.N. Bhard w aj

Production Assistant : Praka sh Veer Singh

Cover, Lay outa n d I l l u s t r a t i o n s Shw eta Rao


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Chapter One

ELECTRIC CHARGES

AND FIELDS

1.1 INTRODUCTIONAll of us have the experience of seeing a spark or hearing a crackle whenwe take off our synthetic clothes or sweater, particularly in dry weather.This is almost inevitable with ladies garments like a polyester saree. Haveyou ever tried to find any explanation for this phenomenon? Anothercommon example of electric discharge is the lightning that we see in thesky during thunderstorms. We also experience a sensation of an electricshock either while opening the door of a car or holding the iron bar of a

bus after sliding from our seat. The reason for these experiences isdischarge of electric charges through our body, which were accumulateddue to rubbing of insulating surfaces. You might have also heard thatthis is due to generation of static electricity. This is precisely the topic weare going to discuss in this and the next chapter. Static means anythingthat does not move or change with time. Electrostatics deals with thestudy of forces, fields and potentials arising from static charges.

1.2 ELECTRICCHARGEHistorically the credit of discovery of the fact that amber rubbed with

wool or silk cloth attracts light objects goes to Thales of Miletus, Greece,

around 600 BC. The name electricity is coined from the Greek wordelektronmeaning amber. Many such pairs of materials were known which


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2

Physics

on rubbing could attract light objects

like straw, pith balls and bits of papers.You can perform the following activityat home to experience such an effect.Cut out long thin strips of white paperand lightly iron them. Take them near a

TV screen or computer monitor. You willsee that the strips get attracted to thescreen. In fact they remain stuck to thescreen for a while.

It was observed that if two glass rodsrubbed with wool or silk cloth are

brought close to each other, they repeleach other [Fig. 1.1(a)]. The two strandsof wool or two pieces of silk cloth, with

which the rods were rubbed, also repeleach other. However, the glass rod and

wool attracted each other. Similarly, two plastic rods rubbed with catsfur repelled each other [Fig. 1.1(b)] but attracted the fur. On the otherhand, the plastic rod attracts the glass rod [Fig. 1.1(c)] and repel the silkor wool with which the glass rod is rubbed. The glass rod repels the fur.

If a plastic rod rubbed with fur is made to touch two small pith balls(now-a-days we can use polystyrene balls) suspended by silk or nylonthread, then the balls repel each other [Fig. 1.1(d)] and are also repelled

by the rod. A similar effect is found if the pith balls are touched with aglass rod rubbed with silk [Fig. 1.1(e)]. A dramatic observation is that apith ball touched with glass rod attracts another pith ball touched withplastic rod [Fig. 1.1(f )].

These seemingly simple facts were established from years of effortsand careful experiments and their analyses. It was concluded, after manycareful studies by different scientists, that there were only two kinds ofan entity which is called the electric charge. We say that the bodies likeglass or plastic rods, silk, fur and pith balls are electrified. They acquirean electric charge on rubbing. The experiments on pith balls suggestedthat there are two kinds of electrification and we find that (i) like charges

repeland (ii) unlike chargesattracteach other. The experiments alsodemonstrated that the charges are transferred from the rods to the pithballs on contact. It is said that the pith balls are electrified or are chargedby contact. The property which differentiates the two kinds of charges iscalled thepolarityof charge.

When a glass rod is rubbed with silk, the rod acquires one kind ofcharge and the silk acquires the second kind of charge. This is true forany pair of objects that are rubbed to be electrified. Now if the electrifiedglass rod is brought in contact with silk, with which it was rubbed, theyno longer attract each other. They also do not attract or repel other lightobjects as they did on being electrified.

Thus, the charges acquired after rubbing are lost when the charged

bodies are brought in contact. What can you conclude from theseobservations? It just tells us that unlike charges acquired by the objects

FIGURE 1.1Rods and pith balls: like charges repel andunlike charges attract each other.

Interactiveanim

ationonsimpleelectrostaticex

periments:

http://ephysics.physics.ucla.e

du/travoltage/HTML/


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Electric Charges

and Fields

3

neutralise or nullify each others effect. Therefore the charges were named

aspositiveand negativeby the American scientist Benjamin Franklin.We know that when we add a positive number to a negative number ofthe same magnitude, the sum is zero. This might have been thephilosophy in naming the charges as positive and negative. By convention,the charge on glass rod or cats fur is called positive and that on plasticrod or silk is termed negative. If an object possesses an electric charge, itis said to be electrified or charged. When it has no charge it is said to beneutral.

UNIFICATIONOFELECTRICITYANDMAGNETISM

In olden days, electricity and magnetism were treated as separate subjects. Electricitydealt with charges on glass rods, cats fur, batteries, lightning, etc., while magnetismdescribed interactions of magnets, iron filings, compass needles, etc. In 1820 Danishscientist Oersted found that a compass needle is deflected by passing an electric currentthrough a wire placed near the needle. Ampere and Faraday supported this observation

by saying that electric charges in motion produce magnetic fields and moving magnetsgenerate electricity. The unification was achieved when the Scottish physicist Maxwelland the Dutch physicist Lorentz put forward a theory where they showed theinterdependence of these two subjects. This field is calledelectromagnetism. Most of thephenomena occurring around us can be described under electromagnetism. Virtuallyevery force that we can think of like friction, chemical force between atoms holding thematter together, and even the forces describing processes occurring in cells of living

organisms, have its origin in electromagnetic force. Electromagnetic force is one of thefundamental forces of nature.

Maxwell put forth four equations that play the same role in classical electromagnetismas Newtons equations of motion and gravitation law play in mechanics. He also arguedthat light is electromagnetic in nature and its speed can be found by making purelyelectric and magnetic measurements. He claimed that the science of optics is intimatelyrelated to that of electricity and magnetism.

The science of electricity and magnetism is the foundation for the modern technologicalcivilisation. Electric power, telecommunication, radio and television, and a wide varietyof the practical appliances used in daily life are based on the principles of this science.

Although charged particles in motion exert both electric and magnetic forces, in theframe of reference where all the charges are at rest, the forces are purely electrical. Youknow that gravitational force is a long-range force. Its effect is felt even when the distance

between the interacting particles is very large because the force decreases inversely asthe square of the distance between the interacting bodies. We will learn in this chapterthat electric force is also as pervasive and is in fact stronger than the gravitational force

by several orders of magnitude (refer to Chapter 1 of Class XI Physics Textbook).

A simple apparatus to detect charge on a body is the gold-leafelectroscope [Fig. 1.2(a)]. It consists of a vertical metal rod housed in a

box, with two thin gold leaves attached to its bottom end. When a chargedobject touches the metal knob at the top of the rod, charge flows on to

the leaves and they diverge. The degree of divergance is an indicator ofthe amount of charge.


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Students can make a simple electroscope as

follows [Fig. 1.2(b)]: Take a thin aluminium curtainrod with ball ends fitted for hanging the curtain. Cutout a piece of length about 20 cm with the ball atone end and flatten the cut end. Take a large bottlethat can hold this rod and a cork which will fit in theopening of the bottle. Make a hole in the corksufficient to hold the curtain rod snugly. Slide therod through the hole in the cork with the cut end onthe lower side and ball end projecting above the cork.Fold a small, thin aluminium foil (about 6 cm inlength) in the middle and attach it to the flattened

end of the rod by cellulose tape. This forms the leavesof your electroscope. Fit the cork in the bottle withabout 5 cm of the ball end projecting above the cork.

A paper scale may be put inside the bottle in advanceto measure the separation of leaves. The separationis a rough measure of the amount of charge on theelectroscope.

To understand how the electroscope works, usethe white paper strips we used for seeing theattraction of charged bodies. Fold the strips into halfso that you make a mark of fold. Open the strip andiron it lightly with the mountain fold up, as shown

in Fig. 1.3. Hold the strip by pinching it at the fold.You would notice that the two halves move apart.

This shows that the strip has acquired charge on ironing. When you foldit into half, both the halves have the same charge. Hence they repel eachother. The same effect is seen in the leaf electroscope. On charging thecurtain rod by touching the ball end with an electrified body, charge istransferred to the curtain rod and the attached aluminium foil. Both thehalves of the foil get similar charge and therefore repel each other. Thedivergence in the leaves depends on the amount of charge on them. Letus first try to understand why material bodies acquire charge.

You know that all matter is made up of atoms and/or molecules.

Although normally the materials are electrically neutral, they do containcharges; but their charges are exactly balanced. Forces that hold themolecules together, forces that hold atoms together in a solid, the adhesiveforce of glue, forces associated with surface tension, all are basicallyelectrical in nature, arising from the forces between charged particles.

Thus the electric force is all pervasive and it encompasses almost eachand every field associated with our life. It is therefore essential that welearn more about such a force.

To electrify a neutral body, we need to add or remove one kind ofcharge. When we say that a body is charged, we always refer to thisexcess charge or deficit of charge. In solids, some of the electrons, beingless tightly bound in the atom, are the charges which are transferred

from one body to the other. A body can thus be charged positively bylosing some of its electrons. Similarly, a body can be charged negatively

FIGURE 1.2 Electroscopes: (a) The gold leafelectroscope, (b) Schematics of a simple

electroscope.

FIGURE 1.3 Paper stripexperiment.


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by gaining electrons. When we rub a glass rod with silk, some of the

electrons from the rod are transferred to the silk cloth. Thus the rod getspositively charged and the silk gets negatively charged. No new charge iscreated in the process of rubbing. Also the number of electrons, that aretransferred, is a very small fraction of the total number of electrons in thematerial body. Also only the less tightly bound electrons in a material

body can be transferred from it to another by rubbing. Therefore, whena body is rubbed with another, the bodies get charged and that is why

we have to stick to certain pairs of materials to notice charging on rubbingthe bodies.

1.3 CONDUCTORSANDINSULATORS

A metal rod held in hand and rubbed with wool will not show any sign ofbeing charged. However, if a metal rod with a wooden or plastic handle isrubbed without touching its metal part, it shows signs of charging.Suppose we connect one end of a copper wire to a neutral pith ball andthe other end to a negatively charged plastic rod. We will find that thepith ball acquires a negative charge. If a similar experiment is repeated

with a nylon thread or a rubber band, no transfer of charge will takeplace from the plastic rod to the pith ball. Why does the transfer of chargenot take place from the rod to the ball?

Some substances readily allow passage of electricity through them,others do not. Those which allow electricity to pass through them easilyare called conductors. They have electric charges (electrons) that arecomparatively free to move inside the material. Metals, human and animal

bodies and earth are conductors. Most of the non-metals like glass,porcelain, plastic, nylon, wood offer high resistance to the passage ofelectricity through them. They are called insulators.Most substancesfall into one of the two classes stated above*.

When some charge is transferred to a conductor, it readily getsdistributed over the entire surface of the conductor. In contrast, if somecharge is put on an insulator, it stays at the same place. You will learn

why this happens in the next chapter.This property of the materials tells you why a nylon or plastic comb

gets electrified on combing dry hair or on rubbing, but a metal article

like spoon does not. The charges on metal leak through our body to theground as both are conductors of electricity. When we bring a charged body in contact with the earth, all the

excess charge on the body disappears by causing a momentary currentto pass to the ground through the connecting conductor (such as our

body). This process of sharing the charges with the earth is calledgrounding or earthing. Earthing provides a safety measure for electricalcircuits and appliances. A thick metal plate is buried deep into the earthand thick wires are drawn from this plate; these are used in buildingsfor the purpose of earthing near the mains supply. The electric wiring inour houses has three wires: live, neutral and earth. The first two carry

* There is a third category called semiconductors, which offer resistance to themovement of charges which is intermediate between the conductors andinsulators.


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electric current from the power station and the third is earthed by

connecting it to the buried metal plate. Metallic bodies of the electricappliances such as electric iron, refrigerator, TV are connected to theearth wire. When any fault occurs or live wire touches the metallic body,the charge flows to the earth without damaging the appliance and withoutcausing any injury to the humans; this would have otherwise beenunavoidable since the human body is a conductor of electricity.

1.4 CHARGINGBYINDUCTIONWhen we touch a pith ball with an electrified plastic rod, some of thenegative charges on the rod are transferred to the pith ball and it alsogets charged. Thus the pith ball is charged by contact. It is then repelled

by the plastic rod but is attracted by a glass rod which is oppositelycharged. However, why a electrified rod attracts light objects, is a question

we have still left unanswered. Let us try to understand what could behappening by performing the following experiment.(i) Bring two metal spheres, A and B, supported on insulating stands,

in contact as shown in Fig. 1.4(a).(ii) Bring a positively charged rod near one of the spheres, say A, taking

care that it does not touch the sphere. The free electrons in the spheresare attracted towards the rod. This leaves an excess of positive chargeon the rear surface of sphere B. Both kinds of charges are bound inthe metal spheres and cannot escape. They, therefore, reside on thesurfaces, as shown in Fig. 1.4(b). The left surface of sphere A, has an

excess of negative charge and the right surface of sphere B, has anexcess of positive charge. However, not all of the electrons in the sphereshave accumulated on the left surface of A. As the negative chargestarts building up at the left surface of A, other electrons are repelled

by these. In a short time, equilibrium is reached under the action offorce of attraction of the rod and the force of repulsion due to theaccumulated charges. Fig. 1.4(b) shows the equilibrium situation.

The process is called induction of charge and happens almostinstantly. The accumulated charges remain on the surface, as shown,till the glass rod is held near the sphere. If the rod is removed, thecharges are not acted by any outside force and they redistribute totheir original neutral state.

(iii) Separate the spheres by a small distance while the glass rod is stillheld near sphere A, as shown in Fig. 1.4(c). The two spheres are foundto be oppositely charged and attract each other.

(iv) Remove the rod. The charges on spheres rearrange themselves asshown in Fig. 1.4(d). Now, separate the spheres quite apart. Thecharges on them get uniformly distributed over them, as shown inFig. 1.4(e).In this process, the metal spheres will each be equal and oppositely

charged. This is charging by induction. The positively charged glass roddoes not lose any of its charge, contrary to the process of charging bycontact.

When electrified rods are brought near light objects, a similar effect

takes place. The rods induce opposite charges on the near surfaces ofthe objects and similar charges move to the farther side of the object.

FIGURE 1.4 Chargingby induction.


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EXAMPLE

1.1

[This happens even when the light object is not a conductor. The

mechanism for how this happens is explained later in Sections 1.10 and2.10.] The centres of the two types of charges are slightly separated. Weknow that opposite charges attract while similar charges repel. However,the magnitude of force depends on the distance between the chargesand in this case the force of attraction overweighs the force of repulsion.

As a result the particles like bits of paper or pith balls, being light, arepulled towards the rods.

Example 1.1 How can you charge a metal sphere positively withouttouching it?

Solution Figure 1.5(a) shows an uncharged metallic sphere on aninsulating metal stand. Bring a negatively charged rod close to themetallic sphere, as shown in Fig. 1.5(b). As the rod is brought closeto the sphere, the free electrons in the sphere move away due torepulsion and start piling up at the farther end. The near end becomespositively charged due to deficit of electrons. This process of chargedistribution stops when the net force on the free electrons inside themetal is zero. Connect the sphere to the ground by a conductingwire. The electrons will flow to the ground while the positive chargesat the near end will remain held there due to the attractive force ofthe negative charges on the rod, as shown in Fig. 1.5(c). Disconnectthe sphere from the ground. The positive charge continues to beheld at the near end [Fig. 1.5(d)]. Remove the electrified rod. Thepositive charge will spread uniformly over the sphere as shown in

Fig. 1.5(e).

FIGURE 1.5

In this experiment, the metal sphere gets charged by the processof induction and the rod does not lose any of its charge.

Similar steps are involved in charging a metal sphere negativelyby induction, by bringing a positively charged rod near it. In thiscase the electrons will flow from the ground to the sphere when thesphere is connected to the ground with a wire. Can you explain why?

In

teractiveanimationoncharging

atwo-spheresystembyinduction:

http://www.physicsclassroom.com/m

media/estatics/estaticTOC.html


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1.5 BASICPROPERTIESOFELECTRICCHARGEWe have seen that there are two types of charges, namely positive andnegative and their effects tend to cancel each other. Here, we shall nowdescribe some other properties of the electric charge.

If the sizes of charged bodies are very small as compared to thedistances between them, we treat them as point charges. All thecharge content of the body is assumed to be concentrated at one pointin space.

1.5.1 Additivity of charges

We have not as yet given a quantitative definition of a charge; we shall

follow it up in the next section. We shall tentatively assume that this canbe done and proceed. If a system contains two point charges q1and q2,the total charge of the system is obtained simply by adding algebraicallyq1and q2,i.e., charges add up like real numbers or they are scalars likethe mass of a body. If a system contains ncharges q1,q2,q3,, qn, thenthe total charge of the system is q1+ q2+ q3+ + qn . Charge hasmagnitude but no direction, similar to the mass. However, there is onedifference between mass and charge. Mass of a body is always positive

whereas a charge can be either positive or negative. Proper signs have tobe used while adding the charges in a system. For example, thetotal charge of a system containing five charges +1, +2, 3, +4 and 5,in some arbitrary unit, is (+1) + (+2) + (3) + (+4) + (5) = 1 in thesame unit.

1.5.2 Charge is conserved

We have already hinted to the fact that when bodies are charged byrubbing, there is transfer of electrons from one body to the other; no newcharges are either created or destroyed. A picture of particles of electriccharge enables us to understand the idea of conservation of charge. When

we rub two bodies, what one body gains in charge the other body loses.Within an isolated system consisting of many charged bodies, due tointeractions among the bodies, charges may get redistributed but it isfound that the total charge of the isolated system is always conserved.

Conservation of charge has been established experimentally.It is not possible to create or destroy net charge carried by any isolated

system although the charge carrying particles may be created or destroyedin a process. Sometimes nature creates charged particles: a neutron turnsinto a proton and an electron. The proton and electron thus created haveequal and opposite charges and the total charge is zero before and afterthe creation.

1.5.3 Quantisation of charge

Experimentally it is established that all free charges are integral multiplesof a basic unit of charge denoted by e. Thus charge qon a body is always

given byq = ne


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where nis any integer, positive or negative. This basic unit of charge is

the charge that an electron or proton carries. By convention, the chargeon an electron is taken to be negative; therefore charge on an electron is

written as e and that on a proton as +e.The fact that electric charge is always an integral multiple ofeis termed

as quantisation of charge. There are a large number of situations in physicswhere certain physical quantities are quantised. The quantisation of chargewas first suggested by the experimental laws of electrolysis discovered byEnglish experimentalist Faraday. It was experimentally demonstrated byMillikan in 1912.

In the International System (SI) of Units, a unit of charge is called acoulomband is denoted by the symbol C. A coulomb is defined in terms

the unit of the electric current which you are going to learn in asubsequent chapter. In terms of this definition, one coulomb is the chargeflowing through a wire in 1 s if the current is 1 A (ampere), (see Chapter 2of Class XI, Physics Textbook , Part I). In this system, the value of the

basic unit of charge is

e = 1.602192 1019 C

Thus, there are about 6 1018 electrons in a charge of 1C. Inelectrostatics, charges of this large magnitude are seldomencounteredand hence we use smaller units 1 C(micro coulomb) = 106C or 1 mC(milli coulomb) = 103C.

If the protons and electrons are the only basic charges in the universe,all the observable charges have to be integral multiples of e. Thus, if a

body contains n1electrons and n2protons, the total amount of chargeon the body is n2 e + n1 (e) = (n2 n1) e.Since n1and n2are integers,their difference is also an integer. Thus the charge on any body is alwaysan integral multiple of eand can be increased or decreased also in stepsof e.

The step size eis, however, very small because at the macroscopiclevel, we deal with charges of a few C.At this scale the fact that charge ofa body can increase or decrease in units of eis not visible. The grainynature of the charge is lost and it appears to be continuous.

This situation can be compared with the geometrical concepts of points

and lines. A dotted line viewed from a distance appears continuous tous but is not continuous in reality. As many points very close toeach other normally give an impression of a continuous line, manysmall charges taken together appear as a continuous chargedistribution.

At the macroscopic level, one deals with charges that are enormouscompared to the magnitude of charge e. Since e= 1.6 1019C, a chargeof magnitude, say 1 C, contains something like 1013times the electroniccharge. At this scale, the fact that charge can increase or decrease only inunits of eis not very different from saying that charge can take continuous

values. Thus, at the macroscopic level, the quantisation of charge has no

practical consequence and can be ignored. At the microscopic level, wherethe charges involved are of the order of a few tens or hundreds of e, i.e.,


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EXAMPLE

1.3

EXAMPLE1

.2

they can be counted, they appear in discrete lumps and quantisation of

charge cannot be ignored. It is the scale involved that is very important.

Example 1.2 If 109 electrons move out of a body to another bodyevery second, how much time is required to get a total charge of 1 Con the other body?

SolutionIn one second 109 electrons move out of the body. Thereforethe charge given out in one second is 1.6 1019 109 C= 1.6 1010 C.The time required to accumulate a charge of 1 C can then be estimatedto be 1 C (1.6 1010C/s)= 6.25 109s= 6.25 109 (365 24 3600) years = 198 years. Thus to collect a charge of one coulomb,from a body from which 109electrons move out every second, we willneed approximately 200 years. One coulomb is, therefore, a very large

unit for many practical purposes.It is, however, also important to know what is roughly the number ofelectrons contained in a piece of one cubic centimetre of a material.A cubic piece of copper of side 1 cm contains about 2.5 1024

electrons.

Example 1.3 How much positive and negative charge is there in acup of water?

Solution Let us assume that the mass of one cup of water is250 g. The molecular mass of water is 18g. Thus, one mole(= 6.02 1023 molecules) of water is 18 g. Therefore the number ofmolecules in one cup of water is (250/18) 6.02 10 23.

Each molecule of water contains two hydrogen atoms and one oxygenatom, i.e., 10 electrons and 10 protons. Hence the total positive andtotal negative charge has the same magnitude. It is equal to(250/18) 6.02 1023 10 1.6 1019C= 1.34 107C.

1.6 COULOMBSLAWCoulombs law is a quantitative statement about the force between twopoint charges. When the linear size of charged bodies are much smallerthan the distance separating them, the size may be ignored and thecharged bodies are treated aspoint charges.Coulomb measured theforce between two point charges and found that it varied inversely asthe square of the distance between the charges and was directly

proportional to the product of the magnitude of the two charges and

acted along the line joining the two charges. Thus, if two point chargesq1, q2are separated by a distance r in vacuum, the magnitude of theforce (F) between them is given by

212

q qF k

r= (1.1)

How did Coulomb arrive at this law from his experiments? Coulombused a torsion balance*for measuring the force between two charged metallic

* A torsion balance is a sensitive device to measure force. It was also used laterby Cavendish to measure the very feeble gravitational force between two objects,to verify Newtons Law of Gravitation.


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spheres. When the separation between two spheres is much

larger than the radius of each sphere, the charged spheresmay be regarded as point charges. However, the chargeson the spheres were unknown, to begin with. How thencould he discover a relation like Eq. (1.1)? Coulombthought of the following simple way: Suppose the chargeon a metallic sphere is q. If the sphere is put in contact

with an identical uncharged sphere, the charge will spreadover the two spheres. By symmetry, the charge on eachsphere will be q/2*. Repeating this process, we can getcharges q/2, q/4, etc. Coulomb varied the distance for afixed pair of charges and measured the force for different

separations. He then varied the charges in pairs, keepingthe distance fixed for each pair. Comparing forces fordifferent pairs of charges at different distances, Coulombarrived at the relation, Eq. (1.1).

Coulombs law, a simple mathematical statement,was initially experimentally arrived at in the mannerdescribed above. While the original experimentsestablished it at a macroscopic scale, it has also beenestablished down to subatomic level (r ~1010m).

Coulomb discovered his law without knowing theexplicitmagnitude of the charge. In fact, it is the other

way round: Coulombs law can now be employed to

furnish a definition for a unit of charge. In the relation,Eq. (1.1), kis so far arbitrary. We can choose any positive

value of k. The choice of kdetermines the size of the unitof charge. In SI units, the value of kis about 9 109.

The unit of charge that results from this choice is calleda coulomb which we defined earlier in Section 1.4.Putting this value of k in Eq. (1.1), we see that forq1= q2= 1 C, r= 1 m

F= 9 109 NThat is, 1 C is the charge that when placed at a

distance of 1 m from another charge of the same

magnitude in vacuumexperiences an electrical force ofrepulsion of magnitude 9 109 N. One coulomb isevidently too big a unit to be used. In practice, inelectrostatics, one uses smaller units like 1 mC or 1 C.

The constant k in Eq. (1.1) is usually put ask = 1/40for later convenience, so that Coulombs law is written as

0

1 22

14

q qF

r=

(1.2)

0is called thepermittivity of free space . The value of 0in SI units is

0 = 8.854 1012C2N1m2

* Implicit in this is the assumption of additivity of charges and conservation:two charges (q/2 each) add up to make a total chargeq.

Charles Augustin deCoulomb (1736 1806)Coulomb, a Frenchphysicist, began his careeras a military engineer inthe West Indies. In 1776, hereturned to Paris andretired to a small estate todo his scientific research.He invented a torsionbalance to measure thequantity of a force and used

it for determination offorces of electric attractionor repulsion between smallcharged spheres. He thusarrived in 1785 at theinverse square law relation,now known as Coulombslaw. The law had beenanticipated by Priestley andalso by Cavendish earlier,though Cavendish neverpublished his results.Coulomb also found the

inverse square law of forcebe tween unlike and likemagnetic poles.

CHARLESAUGUSTIND

ECOULOMB

(17361

806)


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Since force is a vector, it is better to write

Coulombs law in the vector notation. Let theposition vectors of charges q1and q2be r1and r2respectively [see Fig.1.6(a)]. We denote force onq1due to q2by F12and force on q2due to q1byF21. The two point charges q1and q2have beennumbered 1 and 2 for convenience and the vectorleading from 1 to 2 is denoted by r21:

r21= r2 r1

In the same way, the vector leading from 2 to1 is denoted by r12:

r12= r1 r2= r21

The magnitude of the vectors r21and r12isdenoted by r21 and r12,respectively (r12 =r21). Thedirection of a vector is specified by a unit vectoralong the vector. To denote the direction from 1to 2 (or from 2 to 1), we define the unit vectors:

2121

21

r

=r

r ,12

12 21 1212

,r

= =r

r r r

Coulombs force law between two point charges q1and q2located atr1and r2is then expressed as

1 221 212

21

1 4 o

q q

r=

F r (1.3)

Some remarks on Eq. (1.3) are relevant: Equation (1.3) is valid for any sign of q1and q2whether positive or

negative. If q1and q2are of the same sign (either both positive or bothnegative),F21is along r 21, which denotes repulsion, as it should be forlike charges. If q1and q2are of opposite signs, F21is along r 21(= r 12),

which denotes attraction, as expected for unlike charges. Thus, we donot have to write separate equations for the cases of like and unlikecharges. Equation (1.3) takes care of both cases correctly [Fig. 1.6(b)].

The force F12on charge q1due to charge q2, is obtained from Eq. (1.3),by simply interchanging 1 and 2, i.e.,

1 212 12 212

0 12

1

4q q

r= =

F r F

Thus, Coulombs law agrees with the Newtons third law.

Coulombs law [Eq. (1.3)] gives the force between two charges q1andq2in vacuum. If the charges are placed in matter or the interveningspace has matter, the situation gets complicated due to the presence

of charged constituents of matter. We shall consider electrostatics inmatter in the next chapter.

FIGURE 1.6 (a)Geometry and(b) Forces between charges.


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EXAMPLE

1.4

Example 1.4Coulombs law for electrostatic force between two pointcharges and Newtons law for gravitational force between twostationary point masses, both have inverse-square dependence onthe distance between the charges/masses. (a) Compare the strengthof these forces by determining the ratio of their magnitudes (i) for anelectron and a proton and (ii) for two protons. (b) Estimate theaccelerations of electron and proton due to the electrical force of theirmutual attraction when they are 1 (= 10-10m) apart? (m

p= 1.67

1027 kg, me= 9.11 1031kg)

Solution(a) (i) The electric force between an electron and a proton at a distance

rapart is:2

20

1

4ee

F r=

where the negative sign indicates that the force is attractive. Thecorresponding gravitational force (always attractive) is:

2p e

G

m mF G

r=

where mp and m

e are the masses of a proton and an electron

respectively.2

39

0

2.4 104

e

G p e

F e

F Gm m = =

(ii) On similar lines, the ratio of the magnitudes of electric forceto the gravitational force between two protons at a distance r

apart is :2

04e

G p p

F e

F Gm m = =

1.3 1036

However, it may be mentioned here that the signs of the two forcesare different. For two protons, the gravitational force is attractivein nature and the Coulomb force is repulsive . The actual valuesof these forces between two protons inside a nucleus (distancebetween two protons is ~ 10-15m inside a nucleus) are Fe~ 230 Nwhereas FG~ 1.9 10

34 N.The (dimensionless) ratio of the two forces shows that electricalforces are enormously stronger than the gravitational forces.

(b) The electric force Fexerted by a proton on an electron is same inmagnitude to the force exerted by an electron on a proton; however

the masses of an electron and a proton are different. Thus, themagnitude of force is

|F|=2

20

14

e

r=8.987 109Nm2/C2 (1.6 1019C)2/ (1010m)2

= 2.3 108 NUsing Newtons second law of motion, F = ma, the accelerationthat an electron will undergo isa=2.3108 N / 9.11 1031 kg = 2.5 1022 m/s2

Comparing this with the value of acceleration due to gravity, wecan conclude that the effect of gravitational field is negligible onthe motion of electron and it undergoes very large accelerationsunder the action of Coulomb force due to a proton.

The value for acceleration of the proton is2.3 108 N / 1.67 1027 kg = 1.4 1019 m/s2

Interac

tiveanimationonCoulombslaw:

http://w

ebphysics.davidson.edu/physlet_resources/bu_semester2/menu_sem

ester2.html


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EX

AMPLE

1.5

Example 1.5 A charged metallic sphere A is suspended by a nylonthread. Another charged metallic sphere B held by an insulatinghandle is brought close to A such that the distance between theircentres is 10 cm, as shown in Fig. 1.7(a). The resulting repulsion of Ais noted (for example, by shining a beam of light and measuring thedeflection of its shadow on a screen). Spheres A and B are touchedby uncharged spheres C and D respectively, as shown in Fig. 1.7(b).C and D are then removed and B is brought closer to A to adistance of 5.0 cm between their centres, as shown in Fig. 1.7(c).What is the expected repulsion of A on the basis of Coulombs law?Spheres A and C and spheres B and D have identical sizes. Ignorethe sizes of A and B in comparison to the separation between theircentres.

FIGURE 1.7


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EXAMPLE

1.5

Solution Let the original charge on sphere A be qand that on B beq. At a distance r between their centres, the magnitude of theelectrostatic force on each is given by

20

14

qqF

r

=

neglecting the sizes of spheres A and B in comparison to r. When anidentical but uncharged sphere C touches A, the charges redistributeon A and C and, by symmetry, each sphere carries a charge q/2.Similarly, after D touches B, the redistributed charge on each isq/2. Now, if the separation between A and B is halved, the magnitudeof the electrostatic force on each is

2 20 0

1 ( /2)( /2) 1 ( )4 4( /2)

q q qq F F

r r

= = =

Thus the electrostatic force on A, due to B, remains unaltered.

1.7 FORCESBETWEENMULTIPLECHARGESThe mutual electric force between two charges is givenby Coulombs law. How to calculate the force on acharge where there are not one but several chargesaround? Consider a system of nstationary charges

q1, q2, q3, ...,qnin vacuum.What is the force on q1dueto q2, q3, ..., qn? Coulombs law is not enough to answerthis question. Recall that forces of mechanical originadd according to the parallelogram law of addition. Isthe same true for forces of electrostatic origin?

Experimentally it is verified that force on anychargedue to a number of other charges is the vectorsum of all the forces on that charge due to theothercharges, taken one at a time. The individual forcesare unaffected due to the presence of other charges.

This is termed as theprinciple of superposition.To better understand the concept, consider a

system of three charges q1,q2 andq3, as shown inFig. 1.8(a).The force on one charge, say q1, due to twoother charges q2, q3 can therefore be obtained byperforming a vector addition of the forces due to eachone of these charges. Thus, if the force on q1due to q2is denoted by F12, F12is given by Eq. (1.3) even thoughother charges are present.

Thus, F121 2

1220 12

1

4q q

r=

r

In the same way, the force on q1due to q3, denotedby F13, is given by

1 313 132

0 13

1 4

q qr

=

F r

FIGURE 1.8 A system of (a)threecharges (b) multiple charges.


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EX

AMPLE

1.6

which again is the Coulomb force on q1due to q3, even though other

charge q2is present.Thus the total force F1 on q1 due to the two charges q2and q3 is

given as

1 31 21 12 13 12 132 2

0 012 13

1 1

4 4q qq q

r r = + = +

F F F r r (1.4)

The above calculation of force can be generalised to a system ofcharges more than three, as shown in Fig. 1.8(b).

The principle of superposition says that in a system of charges q1,q2,..., qn,the force on q1due to q2is the same as given by Coulombs law,i.e., it is unaffected by the presence of the other charges q3, q4, ..., qn. The

total force F1on the charge q1, due to all other charges, is then given bythe vector sum of the forces F12, F13, ..., F1n:

i.e.,

1 3 11 21 12 13 1n 12 13 12 2 2

0 12 13 1

1 = + + ...+ ...

4n

n

n

q q q q q q

r r r

= + + +

F F F F r r r

112

20 1

4

ni

i

i i

qq

r ==

r (1.5)

The vector sum is obtained as usual by the parallelogram law ofaddition of vectors. All of electrostatics is basically a consequence ofCoulombs law and the superposition principle.

Example 1.6Consider three charges q1, q2, q3each equal to qat thevertices of an equilateral triangle of side l. What is the force on acharge Q (with the same sign as q) placed at the centroid of thetriangle, as shown in Fig. 1.9?

FIGURE 1.9

Solution In the given equilateral triangle ABC of sides of length l, ifwe draw a perpendicular AD to the side BC,

AD = AC cos 30 = ( 3/2 ) l and the distance AO of the centroid Ofrom A is (2/3) AD = (1/ 3 ) l. By symmatry AO = BO = CO.


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EXAMPLE

1.6

Thus,

Force F1on Qdue to charge q at A =0

34

Qq

lalong AO

Force F2 on Qdue to charge qat B =0

34

Qq

lalong BO

Force F3

on Qdue to charge qat C =0

34

Qq

lalong CO

The resultant of forces F2 and F3 is 20

34

Qq

l along OA, by the

parallelogram law. Therefore, the total force on Q = ( )20

3

4

Qq

l

r r

= 0, where r is theunit vector along OA.It is clear also by symmetry that the three forces will sum to zero.Suppose that the resultant force was non-zero but in some direction.Consider what would happen if the system was rotated through 60about O.

Example 1.7 Consider the charges q, q,and qplaced at the verticesof an equilateral triangle, as shown in Fig. 1.10. What is the force oneach charge?

FIGURE 1.10

Solution The forces acting on charge q at A due to charges q at Bandqat C are F12along BA and F13along AC respectively, as shownin Fig. 1.10. By the parallelogram law, the total force F1onthechargeqat A is given by

F1= F 1r where 1r is a unit vector along BC.The force of attraction or repulsion for each pair of charges has the

same magnitude2

204

qF

l=

The total force F2on charge qat B is thus F2=F r 2, where r 2 is aunit vector along AC.

EXAMPLE

1.7


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EXAMPLE

1.7

Similarly the total force on charge qat CisF3 = 3 Fn , where n isthe unit vector along the direction bisecting the BCA.

It is interesting to see that the sum of the forces on the three chargesis zero, i.e.,

F1+F2+F3= 0

The result is not at all surprising. It follows straight from the factthat Coulombs law is consistent with Newtons third law. The proofis left to you as an exercise.

1.8 ELECTRICFIELDLet us consider a point charge Qplaced in vacuum, at the origin O. If we

place another point charge qat a point P, whereOP= r, then the charge Qwill exert a force on qas per Coulombs law. We may ask the question: Ifcharge q is removed, then what is left in the surrounding? Is therenothing? If there is nothing at the point P, then how does a force act

when we place the charge qat P. In order to answer such questions, theearly scientists introduced the concept offield. According to this, we saythat the charge Qproduces an electric field everywhere in the surrounding.

When another charge qis brought at some point P, the field there acts onit and produces a force. The electric field produced by the charge Q at apoint r is given as

( )2 20 0

1 1 4 4

Q Q

r r = =

E r r r

(1.6)where =r r/r, is a unit vector from the origin to the point r. Thus, Eq.(1.6)specifies the value of the electric field for each value of the position

vector r. The word field signifies how some distributed quantity (whichcould be a scalar or a vector) varies with position. The effect of the chargehas been incorporated in the existence of the electric field. We obtain theforce Fexerted by achargeQon a charge q, as

20

1 4

Qq

r=

F r (1.7)

Note that the charge q also exerts an equal and opposite force on thecharge Q.The electrostatic force between the charges Q and qcan be

looked upon as an interaction between charge qand the electric field ofQ and vice versa. If we denote the position of charge qby the vector r,itexperiences a force F equal to the charge qmultiplied by the electricfield Eat the location of q.Thus,

F(r)= q E(r) (1.8)Equation (1.8) defines the SI unit of electric field as N/C*.Some important remarks may be made here:

(i) From Eq. (1.8), we can infer that if qis unity, the electric field due toa charge Qis numerically equal to the force exerted by it. Thus, theelectric field due to a chargeQ at a point in space may be definedas the force that a unit positive charge would experience if placed

* An alternate unit V/m will be introduced in the next chapter.

FIGURE 1.11 Electricfield (a) due to a

charge Q, (b) due to a

charge Q.


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Electric Charges

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at that point. The charge Q,which is producing the electric field, is

called a source chargeand the charge q,which tests the effect of asource charge, is called a test charge. Note that the source charge Qmust remain at its original location. However, if a charge qis broughtat any point aroundQ, Qitself is bound to experience an electricalforce due to qand will tend to move. A way out of this difficulty is tomake qnegligibly small. The force Fis then negligibly small but theratio F/q is finite and defines the electric field:

0limq q

=

FE (1.9)

A practical way to get around the problem (of keepingQundisturbed

in the presence of q) is to hold Qto its location by unspecified forces!This may look strange but actually this is what happens in practice.When we are considering the electric force on a test charge qdue to acharged planar sheet (Section 1.15), the charges on the sheet are held totheir locations by the forces due to the unspecified charged constituentsinside the sheet.(ii) Note that the electric field Edue to Q, though defined operationally

in terms of some test charge q,is independent of q. This is becauseFis proportional to q, so the ratio F/qdoes not depend on q. Theforce Fon the charge q due to the charge Qdepends on the particularlocation of charge qwhich may take any value in the space around

the charge Q.Thus, the electric field Edue to Qis also dependent onthe space coordinate r.For different positions of the charge q all overthe space,we get different values of electric field E. The field exists atevery point in three-dimensional space.

(iii) For a positive charge, the electric field will be directed radiallyoutwards from the charge. On the other hand, if the source charge isnegative, the electric field vector, at each point, points radially inwards.

(iv) Since the magnitude of the force Fon charge q due to charge Qdepends only on the distance rof the charge q from charge Q,the magnitude of the electric field Ewill also depend only on thedistance r. Thus at equal distances from the charge Q, the magnitude

of its electric field E is same.The magnitude of electric field Edue toa point charge is thus same on a sphere with the point charge at itscentre; in other words, it has a spherical symmetry.

1.8.1 Electric field due to a system of charges

Consider a system of charges q1, q2, ..., qnwith position vectors r1,r2, ..., rnrelative to some origin O. Like the electric field at a point inspace due to a single charge, electric field at a point in space due to thesystem of charges is defined to be the force experienced by a unittest charge placed at that point, without disturbing the originalpositions of charges q1, q2,...,qn. We can use Coulombs law and the

superposition principle to determine this field at a point P denoted byposition vector r.


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Electric field E1at rdue to q1at r1is given by

E1=1

1P2

0 1P

1 4

q

rr

where 1Pr is a unit vector in the direction from q1to P,and r1Pis the distance between q1and P.In the same manner, electric field E2at rdue to q2atr2is

E2=2

2P2

0 2P

1 4

q

rr

where 2Pr is a unit vector in the direction from q2to P

and r2P is the distance between q2 and P. Similarexpressions hold good for fields E3, E4, ...,Endue tocharges q3, q4, ..., qn.By the superposition principle, the electric field Eat rdue to the system of charges is (as shown in Fig. 1.12)

E(r) = E1(r) + E2(r) + + En(r)

= 1 21P 2P P2 2 20 0 01P 2P P

1 1 1 ...

4 4 4n

n

n

qq q

r r r + + +

r r r

E(r) i P210 P

1

4

ni

i i

q

r ==

r (1.10)

Eis a vector quantity that varies from one point to another point in spaceand is determined from the positions of the source charges.

1.8.2 Physical significance of electric field

You may wonder why the notion of electric field has been introducedhere at all. After all, for any system of charges, the measurable quantityis the force on a charge which can be directly determined using Coulombslaw and the superposition principle [Eq. (1.5)]. Why then introduce thisintermediate quantity called the electric field?

For electrostatics, the concept of electric field is convenient, but notreally necessary. Electric field is an elegant way of characterising the

electrical environment of a system of charges. Electric field at a point inthe space around a system of charges tells you the force a unit positivetest charge would experience if placed at that point (without disturbingthe system). Electric field is a characteristic of the system of charges andis independent of the test charge that you place at a point to determinethe field. The termfieldin physics generally refers to a quantity that isdefined at every point in space and may vary from point to point. Electricfield is a vector field, since force is a vector quantity.

The true physical significance of the concept of electric field, however,emerges only when we go beyond electrostatics and deal with time-dependent electromagnetic phenomena. Suppose we consider the force

between two distant chargesq1, q2in accelerated motion. Now the greatest

speed with which a signal or information can go from one point to anotheris c, the speed of light. Thus, the effect of any motion of q1on q2cannot

FIGURE 1.12 Electric field at apoint due to a system of charges isthe vector sum of the electric fields

at the point due to individualcharges.


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Electric Charges

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arise instantaneously. There will be some time delay between the effect

(force on q2) and the cause (motion of q1). It is precisely here that thenotion of electric field (strictly, electromagnetic field) is natural and veryuseful. The field picture is this: the accelerated motion of charge q1

produces electromagnetic waves, which then propagate with the speed

c, reach q2and cause a force on q2. The notion of field elegantly accountsfor the time delay. Thus, even though electric and magnetic fields can bedetected only by their effects (forces) on charges, they are regarded asphysical entities, not merely mathematical constructs. They have anindependent dynamics of their own, i.e., they evolve according to lawsof their own. They can also transport energy. Thus, a source of time-dependent electromagnetic fields, turned on briefly and switched off, leaves

behind propagating electromagnetic fields transporting energy. Theconcept of field was first introduced by Faraday and is now among thecentral concepts in physics.

Example 1.8 An electron falls through a distance of 1.5 cm in auniform electric field of magnitude 2.0 104N C1 [Fig. 1.13(a)]. Thedirection of the field is reversed keeping its magnitude unchangedand a proton falls through the same distance [Fig. 1.13(b)]. Computethe time of fall in each case. Contrast the situation with that of freefall under gravity.

FIGURE 1.13

Solution In Fig. 1.13(a) the field is upward, so the negatively chargedelectron experiences a downward force of magnitude eE where E isthe magnitude of the electric field. The acceleration of the electron is

ae = eE/m

e

where meis the mass of the electron.

Starting from rest, the time required by the electron to fall through a

distance his given by22

e

e

e

h mht

a e E= =

For e= 1.6 1019C, me= 9.11 1031kg,

E= 2.0 104N C1, h= 1.5 102m,

te= 2.9 109s

In Fig. 1.13 (b), the field is downward, and the positively chargedproton experiences a downward force of magnitude eE. Theacceleration of the proton is

ap = eE/m

p

where mpis the mass of the proton; mp= 1.67 10

27

kg. The time offall for the proton is

EXAMPLE

1.8


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EX

AMPLE

1.9

EXAMPLE

1.8

722 1 3 10 sppp

h mht .a e E

= = =

Thus, the heavier particle (proton) takes a greater time to fall throughthe same distance. This is in basic contrast to the situation of freefall under gravity where the time of fall is independent of the mass ofthe body. Note that in this example we have ignored the accelerationdue to gravity in calculating the time of fall. To see if this is justified,let us calculate the acceleration of the proton in the given electricfield:

p

p

e Ea

m=

19 4 1

27(1 6 10 C) (2 0 10 N C )

1 67 10 kg. .

.

=

12 21 9 10 m s.= which is enormous compared to the value of g (9.8 m s2), theacceleration due to gravity. The acceleration of the electron is evengreater. Thus, the effect of acceleration due to gravity can be ignoredin this example.

Example 1.9Two point charges q1and q2, of magnitude +108C and

108C, respectively, are placed 0.1 m apart. Calculate the electricfields at points A, B and C shown in Fig. 1.14.

FIGURE 1.14

Solution The electric field vector E1Aat A due to the positive chargeq1points towards the right and has a magnitude

9 2 -2 8

1A 2

(9 10 Nm C ) (10 C)(0.05m)

E

= = 3.6 104 N C1

The electric field vectorE2Aat A due to the negative charge q2pointstowards the right and has the same magnitude. Hence the magnitudeof the total electric field EAat A is

EA= E1A+ E2A= 7.2 104N C1

EA is directed toward the right.


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Electric Charges

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The electric field vector E1Bat B due to the positive charge q1pointstowards the left and has a magnitude9 2 2 8

1B 2

(9 10 Nm C ) (10 C)(0.05m)

E

= = 3.6 104N C1

The electric field vector E2Bat B due to the negative charge q2pointstowards the right and has a magnitude

9 2 2 8

2B 2

(9 10 Nm C ) (10 C)(0.15m)

E

= = 4 103 N C1

The magnitude of the total electric field at B isEB= E1B E2B= 3.2 10

4N C1

EBis directed towards the left.

The magnitude of each electric field vector at point C, due to chargeq1and q2is

9 2 2 8

1C 2C 2

(9 10 Nm C ) (10 C)(0.10m)

E E

= = = 9 103 N C1

The directions in which these two vectors point are indicated inFig. 1.14. The resultant of these two vectors is

1 2cos cos3 3CE E E

= + = 9 103 N C1

ECpoints towards the right.

1.9 ELECTRICFIELDLINESWe have studied electric field in the last section. It is a vector quantityand can be represented as we represent vectors. Let us try to representEdue to a point charge pictorially. Let the point charge be placed at theorigin. Draw vectors pointing along the direction of the electric field withtheir lengths proportional to the strength of the field ateach point. Since the magnitude of electric field at a pointdecreases inversely as the square of the distance of thatpoint from the charge, the vector gets shorter as one goesaway from the origin, always pointing radially outward.Figure 1.15 shows such a picture. In this figure, eacharrow indicates the electric field, i.e., the force acting on a

unit positive charge, placed at the tail of that arrow.Connect the arrows pointing in one direction and theresulting figure represents a field line. We thus get manyfield lines, all pointing outwards from the point charge.Have we lost the information about the strength ormagnitude of the field now, because it was contained inthe length of the arrow? No. Now the magnitude of thefield is represented by the density of field lines.Eis strongnear the charge, so the density of field lines is more nearthe charge and the lines are closer. Away from the charge,the field gets weaker and the density of field lines is less,resulting in well-separated lines.

Another person may draw more lines. But the number of lines is notimportant. In fact, an infinite number of lines can be drawn in any region.

FIGURE 1.15 Field of a point charge.

EXAMPLE

1.9


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It is the relative density of lines in different regions which is

important.We draw the figure on the plane of paper, i.e.,in two-

dimensions but we live in three-dimensions. So if one wishesto estimate the density of field lines, one has to consider thenumber of lines per unit cross-sectional area, perpendicularto the lines. Since the electric field decreases as the square ofthe distance from a point charge and the area enclosing thecharge increases as the square of the distance, the numberof field lines crossing the enclosing area remains constant,

whatever may

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