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ComprehensiveObjective

PHYSICSFor Competitive Examinations

Volume—II

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PHYSICSFor Competitive Examinations

Volume—II

By

NARINDER KUMARM.Sc. PES (I)

Department of PhysicsS.D. Govt. College

Ludhiana

&

Dr. J.K. JUNEJAM.Sc., M.Phil., Ph.D.

Department of PhysicsHindu College

Sonepat

RST

RST

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GBC-5009-495-OBJECTIVE PHYSICS II

All rights reserved with the Publisher.

Revised Edition, 2006Reprint, 2007

C—129/06/06

Laser Typesetted at : Goswami Printers, Delhi Printed at : Ajit Printers, Delhi.


PHYSICSVolume—I

Comprehensive Objective Physics is essential for all the students preparing for various Engineering & Medical En-trance Examinations given below and also for students preparing for other State Services Exams.

• IIT—JEE• AIIMS• DPMT• BVP, Pune• CPMT, U.P.• JEE, Orissa• CEE, Assam• CEE, Kerala• AFMC, Pune• CMC, Vellore• CBSE—AIEEE• CBSE—PMT• UPSEAT, U.P.• PET/PMT, M.P.• BHU, Varanasi• CMC, Ludhiana• CEET, Haryana• CET, Karnataka• MGIMS, Wardha• JEE, West Bengal• PET/PMT, Rajasthan• DCE, NSIT, Delhi• JIPMER, Pondicherry• Aligarh Entrance Exam.• Manipal Entrance Exam.• GGSIP University, Delhi• EAMCET, Andhra Pradesh• CET/TNPCEE, Tamil Nadu• Indian School of Mines, Dhanbad• MLNR, Engineering Entrance Exam.• CET/PMT, Punjab & UT Chandigarh• Birla Institute of Technology Mesra, Ranchi• Other State Level Competitive Examinations

List of Chapters in Volume—I and Volume—II

Volume—I

Unit 0 MATHEMATICAL TOOLS

Unit I INTRODUCTION AND MEASUREMENT

1.01 Introduction, Units, Measurement and Dimension

1.02 Significant Figures and Error Analysis

Unit II DESCRIPTION OF MOTION IN ONE DIMENSION

Unit III DESCRIPTION OF MOTION IN TWO AND THREE DIMENSIONS

3.01 Vectors

3.02 Motion in Two and Three Dimensions

Unit IV LAWS OF MOTION

Unit V WORK, ENERGY AND POWER

Unit VI ROTATIONAL MOTION (Circular Motion, Centre of Mass and Rotational Mechanics)

Unit VII GRAVITATION

Unit VIII PROPERTIES OF MATTER

8.01 Elasticity

8.02 Fluids at Rest

8.03 Surface Tension

8.04 Fluids in Motion

8.05 Kinetic Theory of Gases

Unit IX HEAT AND THERMODYNAMICS

Unit X OSCILLATION AND WAVES

3 Practice Papers

Volume—II

Unit XI ELECTROSTATICS

Unit XII CURRENT ELECTRICITY

Unit XIII MAGNETIC EFFECT OF CURRENT AND MAGNETISM

Unit XIV ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

Unit XV OPTICS

Unit XVI DUAL NATURE OF MATTER AND RADIATIONS

Unit XVII ATOMIC NUCLEUS

Unit XVIII SOLIDS AND SEMICONDCUTOR DEVICES, ELECTROMAGNETIC WAVES ANDPRINCIPLES OF COMMUNICATION

3 Practice Papers

3 Model Test Papers based on Full Syllabus

PREFACE TO THE SECOND EDITION

There is no dearth of competition books for engineering and medical entrance examinations. But there is no singlebook which completely satisfies the intelligent student. The present book is a serious attempt in this direction. We haveleft no stone unturned to get ‘EXTREMELY SATISFACTORY’ grade from the readers of the book.

Some salient features of the book are as under :(i) No superfluous question. Only those questions have been included which have either been already set in different

examinations or are expected to be set.(ii) Most systematic presentation. It is the only book in the market which has systematically categorised the study

material of each unit. The study material has been clearly demarcated in the following seven segments.1. SYNOPSIS2. SET I [Contains MCQs based on Memory Work, Hard Facts, Important Terms, Important Formulae etc.]3. SET II [Contains MCQs based on Important Basic Concepts, Application of Formulae and Brain Teasers]4. SET III [Contains MCQs with more than one correct alternative]5. SET IV [Contains MCQs based on Typical Numerical Bank]6. SELF-EVALUATION TEST I [Contains Expected Questions for Forthcoming Examinations]7. SELF-EVALUATION TEST IIIn addition to the above, ‘Knowledge Plus’ has also been included at some places.

(iii) Time-saving solutions. Special techniques have been used in solving questions. These techniques have been high-lighted at different places in the book. If the reader tries to grasp these techniques, considerable time will be saved.

The book has been divided into two volumes. The divisions are as under :

Units

Volume—I I—XTopics included

Mathematical Tools ; Introduction, Units, Measurements and Dimension ; Description of Motion in One Dimension ;Description of Motion in Two and Three Dimensions (Vectors ; Motion in Two and Three Dimensions) ; Laws ofMotion ; Work, Energy and Power ; Rotational Motion (Circular Motion ; Centre of Mass and Rotational Mechanics) ;Gravitation ; Properties of Matter (Elasticity ; Fluids at Rest ; Surface Tension ; Fluids in Motion ; Kinetic Theoryof Gases) ; Heat and Thermodynamics ; Oscillations and Waves.

Units

Volume—II XI—XVIIITopics included

Electrostatics ; Current Electricity ; Magnetic Effect of Current and Magnetism ; Electromagnetic Induction andAlternating Current ; Optics ; Dual Nature of Matter and Radiations ; Atomic Nucleus ; Solids and SemiconductorDevices, Electromagnetic Waves and Principles of Communication.3 Practice Papers are designed in such a way so as to enable the students to evaluate their skills in Volume—I andVolume—II separately.Model Test Papers based on full syllabus are included in Volume—II for Self Assessment.

Utmost effort has been made to make this book as best as possible. But it is our firm conviction that there is alwaysa scope for improvement. So, we invite your suggestions for the further improvement of the book. It would be ourearnest endeavour to incorporate all good suggestions in the next edition.

—AUTHORS

Unit XI ELECTROSTATICS

11. Electrostatics

CONTENTS

• Synopsis 3• Question Bank with Answers/Solutions

Set I : MCQs based on Memory work, Hard 10Facts, Important Terms, ImportantFormulae etc.

Set II : MCQs based on Important Basic 33Concepts, Application of Formulae,Brain Teasers

Set III : MCQs with one or more than one 73Correct Alternative

Set IV : MCQs based on Typical Numerical 77Bank (Exclusively for EngineeringEntrance Tests)

• Self-Evaluation Test I with Answers/ 92Solutions (Expected Questions forForthcoming Examinations)

• Self-Evaluation Test II with Answers/ 99Solutions

Unit XII CURRENT ELECTRICITY

12. Current Electricity• Synopsis 111• Question Bank with Answers/Solutions

Set I : MCQs based on Memory Work, Hard 123Facts, Important Terms, ImportantFormulae etc.






Unit XIII MAGNETIC EFFECT OF CURRENT AND MAGNETISM

13. Magnetic Effect of Current andMagnetism• Synopsis 231• Question Bank with Answers/Solutions







Unit XIV ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

14. Electromagnetic Induction and AlternatingCurrent• Synopsis 343• Question Bank with Answers/Solutions







Unit XV OPTICS

15. Optics• Synopsis 429• Question Bank with Answers/Solutions







Unit XVI DUAL NATURE OF MATTER AND RADIATIONS

16. Dual Nature of Matter and Radiations• Synopsis 631• Question Bank with Answers/Solutions

Set I : MCQs based on Memory work, Hard 637Facts, Important Terms, ImportantFormulae etc.




• Self-Evaluation Test I with Answers/ 668Solutions (Expected Questions forForthcoming examinations)


Unit XVII ATOMIC NUCLEUS

17. Atomic Nucleus• Synopsis 683• Question Bank with Answers/Solutions







18. Solids and Semiconductor Devices, Electro-magnetic Waves and Principles of Communi-cation• Synopsis 763• Question Bank with Answers/Solutions







Unit XVIII SOLIDS AND SEMICONDUCTOR DEVICES, ELECTROMAGNETIC WAVESAND PRINCIPLES OF COMMUNICATION

• Practice Paper 1 1• Practice Paper 2 7• Practice Papers 3 13

PRACTICE PAPERS BASED ON UNITS XI—XVIII

• Model Test Paper 1 1• Model Test Paper 2 10• Model Test Paper 3 18

MODEL TEST PAPERS BASED ON FULL SYLLABUS

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UNIT XI

ELECTROSTATICS

� Frictional electricity � Charges and their conservation � Coulomb’s law � Forces be-tween two point electric charges � Forces between multiple electric charges � Superpositionprinciple and continuous charge distribution � Electric field and its physical significance � Electricfield due to a point charge � Electric field lines � Electric dipole � Electric field due to adipole and behaviour of dipole in a uniform electric field �� Electric potential-Physicalmeaning � Potential difference � Electric potential due to a point charge � A dipole and sys-tem of charges � Equipotential surfaces � Electrical potential energy of a system of two pointcharges and of electric dipoles in an electrostatic field � Electric flux � Statement of Gauss’stheorem and its applications to find field due to an infinitely long straight wire, uniformly chargedinfinite plane sheet and uniformly charged thin spherical shell (field inside and outside) � Conductorsand insulators � Presence of free charges and bound charges inside a conductor � Dielectricsand electric polarisation � General concept of a capacitor and capacitance � Combination ofcapacitors in series and in parallel � Energy stored in a capacitor � Capacitance of a parallelplate capacitor with and without dielectric medium between the plates � Van de Graff generator.

UNIT DETAILS

1. Synopsis Points 65 Plus

2. Illustrations 10 Plus

3. MCQs from Competitive Examinations 280 Plus

4. Self-Evaluation Tests 2

5. Total Number of MCQs 580 Plus

6. Total Number of Solutions 570 Plus

CHAPTER 11

ELECTROSTATICS

SYNOPSIS

1. The existence of two types of charges was discoveredby Du Fay.

2. It was Benjamin Franklin who first assigned positiveand negative signs to the charges.

3. The fact that like charges repel each other and unlikecharges attract each other can be easily demonstratedby using pith balls.

4. Electric charge is additive, quantised and conserved.5. According to Coulomb’s law of electrostatics,

F = 14

1 22πε

q qr

Here, ε = ε0εr , where the letters have usual meanings.6. When a dielectric is introduced between two point

charges, the force between the two point charges isreduced.

7. A material is suitable for use as dielectric if its dielec-tric constant and dielectric strength has large val-ues.

8. 1 emu of charge = c esu of chargeor 1 emu of charge = 3 × 1010 esu of charge.

9. 1 coulomb of charge = 3 × 109 statcoulomb, 1 abcoulomb= 10 coulomb.

10. 1 abcoulomb = 10 coulomb.11. Electric field intensity at a point on the axial line of

the electric dipole is :

E = 1

42

2 2 2πεpr

r l( )−where p is the electric dipole moment, “2l” is the lengthof the dipole and r is the distance of the observationpoint from the mid-point of the dipole.

12. Electric field intensity at a point on the equatorialline of the electric dipole is :

E = 1

4 2 2 3 2πεp

r l( ) /+

3

13. Electric field intensity at general point due to a dipoleis :

E = 1

43 1

03

2

πεθ

pr

cos +

Here, θ is the angle between the line joining the ob-servation point with the mid-point of the dipole andthe axial line of the dipole.

14. Torque experienced by an electric dipole in uniform

electric field is : τ→ → →

= ×p E .15. The time period of angular SHM of a dipole of mo-

ment of inertia I and dipole moment p in electric fieldE is

T = 2π IpE

.

16. According to Gauss’ law in electrostatics, Electric flux,

φE = E

Ez ∑→ →

=

=. dS qii

n1

0 1ε

17. Dimensional Formulae of Electric Field E andElectric Flux φ

[E] = [ [ ][

Force][Charge]

MLTAT]

=−2

= [MLT–3 A–1]

[φ] = [E] [Area] = [MLT–3 A–1] [L2]= [ML3 T–3 A–1]

18. The electric field due to infinite line charge of linear

charge density λ is 1

42

0πελr

.

19. The electric field due to an infinite plane sheet of charge

is σε2 0

, where σ is surface density of charge.

4 COMPREHENSIVE OBJECTIVE PHYSICS

20. The electric field near a conductor of any shape is σε0

.

21. Line integral of electric field between two points rep-resents the work done by electric field in moving aunit positive charge between two points in the field.

22. Electric potential at a point in an electric field,

V = −∞

→ →

zr

drE . .

23. If the charge is distributed uniformly along a line oflength l and λ is the linear charge density, then

V = 1

4 0πελdlrlz

24. If the charge is distributed uniformly over an area Sand σ is the charge per unit area, then

V = 1

4 0πεσd

rS

Sz25. If the charge is uniformly distributed over a volume

V and ρ is the charge per unit volume, then

V = 1

4 0περd

rV

Vz .

26. Electric potential due to an electric dipole at point onthe axial line of the dipole is :

V = 1

4 02 2πε

p

r l−27. Electric potential due to an electric dipole at point on

equational line is zero.28. Electric potential at a general point due to dipole is :

V = 14 0

2πεθp

r

cos

29. The electric lines of force and equipotential surfacesconstitute a mutually perpendicular network.

30. No work is required to be done in moving a chargeover an equipotential surface.

31. Equipotential surfaces indicate regions of strong andweak electric fields.

32. Short dipole(i) Potential at equator is zero

(ii) Electric field at a point on equator = 14 0

3πεpr

(iii) Potential at a point on axial line = 1

4 02πεpr

(iv) Electric field at a point on axial line = 1

42

03πεp

r.

33. Uniformly Charged Non-Conducting Sphere ofCharge Q and Radius R

(i) Electric field (at r > R) = 1

4 02πε

Qr

Note that E ∝ 12r

Also note that the charge on the sphere behavesas if concentrated at the centre.

(ii) Electric field (at r = R) = 1

4 02πε

QR

(iii) Electric field (at r < R) = 1

4 0πεQR3

r

Note that E ∝ r.

(iv) Electric potential (at r > R) = 1

4 0πεQr

(v) Electric potential (at r = R) = 1

4 0πεQR

.

34. Charged Spherical Conductor of Charge Q andRadius R

(i) Electric field (at r > R) = 14 0

2πεQr

(ii) Electric field (at r = R) = 1

4 0πεQR2

(iii) Electric field (at r < R) = 0

(iv) Electric potential (at r > R) = 14 0πε

Qr

(v) Electric potential (at r = R) = 14πε0

QR

.

(vi) Electric potential (at r < R) = 14πε0

QR

Note that the electric potential at every point in-side the conductor is the same as on the surface of theconductor.

35. Uniformly Charged Ring of Radius r

(i) Electric field at a point on the axis = 1

4 02 2πεqx

r x( )+Here x is the distance of the observation point fromthe centre of the ring.

(ii) Electric field at the centre of the charged ring iszero.

(iii) Potential at a point on the axis = 1

4 2 2πε0

q

r x+.

ELECTROSTATICS 5

36. Potential at a point, inside an uniformly charged non-conducting sphere of charge Q and radius R, at a dis-

tance r is 14 2

2

πε0

2

3Q (3R

R− r ) .

37. The potential difference between two points at dis-tances r1 and r2 from an infinite line charge of linear

charge density is 14

2 2

1πελ

0loge

rr

.

38. Electric field, due to a point charge q, at a distanced1 + d2 where d1 is thickness of medium of dielectricconstant k1 and d2 is thickness of medium of dielec-tric constant k2.

E = 1

4 1 22πε0 1 2K K

qd d( )+

Note. Potential, V = 14 1 2πε0 1 2

q

d k d k+

39. The Electric Field at a Point is Equal to theNegative Gradient of the Electric Potential. Thenegative sign indicates that the direction of E

→ is al-

ways in the direction of decrease of electric potential.The SI unit of potential gradient is Vm–1.

40. Electrostatic potential energy due to point charges q1

and q2 separated by a distance r is 14

1 2

πε0

q qr

.

41. Work done in rotating an electric dipole through anangle θ is : W = pE(1 – cos θ).

42. Electric potential energy of an electric dipole in a uni-

form electric field is : W = −→ →p . E = – pE cos θ.

43. Binding energy of an electric dipole = – (potential en-ergy of charges of the dipole)

= − −F

HGI

KJ=1

4 21

4 2

2 2

πε πε0 0

ql

ql

.

44. Electrostatic potential energy is the product of chargeand electrostatic potential.

45. The electrostatic self-energy of a charged dielectric

sphere of charge q and radius r is 14

35

2

πε0

qr

.

46. Method of Electrical Images(i) Force between point charge ‘+ q’ and an earthed

conductor = Force between charges + q and – qseparated by distance 2l.

= 14 2

2

2πε0

ql( )

+ q – q

l l

Fig. 1

(ii) Interaction energy of the system mentioned in (i),

U = − = −14 2 8

2 2

0πε πε0

ql

ql.

47. The electric force be-tween two short dipolesof dipole moments p1and p2 at separation r,when they are co-axial,

is ‘ – 1

46 1 2

4πε0

p pr

’.

The couple is zero. The potential energy is

− 14

2 1 23πε0

p p

r.

48. The electric force between twoshort dipoles of dipole moments

p1

→ and p2

→ at separation r,

when they are parallel, is

‘+1

43 1 2

4πε0

p pr

’. The couple is

zero. The potential energy is

‘ 14

1 23πε0

p p

r’.

49. The electric force betweentwo short dipoles of dipolemoments p1 and p2, whenthey are mutually perpen-

dicular, is ± 14

2 1 24πε0

p p

r.

Couple on p1 is 1

42 1 2

3πε0

p pr

.

Couple on p2 is 14

1 23πε0

p pr

. The potential energy is

zero.

®p1

®p2

r

Fig. 2

®p1

®p2

r

Fig. 3

®p1 ®

p2

F

F

r

Fig. 4

Comprehensive Objective Physics Vol.II For Competitive Examinations

Publisher : Laxmi Publications ISBN : 9788179681749Author : Prof. Narinderkumar, Dr. J. K. Juneja

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