12

CBSE

PHYSICS

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Preface Physics-12 is based on the latest curriculum guidelines specified by the CBSE. It will certainly prove to be a torch-bearer for those who toil hard to achieve their goal. This All-in-one Question Bank has been developed keeping in mind all the requirement of the students for Board Examinations preparations like learning, practicing, revising and assessing. Salient Features of the Book: ●● Each chapter is designed in ‘Topic wise’ manner where each topic is briefly explained with sufficient Examples and Exercise. Exercise which covers all the possible variety of Questions. ●● Answers with hints are provided separately after the exercise. ●● Importance of Each Topic and Frequently Asked Types of Questions provides an idea to the students on which type they should focus more. ●● Assignment is provided at the end of each chapter. ●● Previous years’ Board Questions have been covered in every chapter. ●● 10 Unsolved Sample Papers for mock test are given with hints & answers for self assessment. ●● Latest CBSE Board Question Paper has been given with hints & answers. ●● Common Errors by the students are provided to make students aware what errors are usually done unknowingly. ●● Excerpts from Model Answers Sheet of topper candidates have been given to provide an idea how to attempt the paper. ●● The book has been well prepared to build confidence in students. uggestions for further improvement of the book, pointing out printing errors/mistakes which might S have crept in spite of all efforts, will be thankfully received and incorporated in the next edition. —Publisher

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Syllabus Time : 3 Hours  Unit No. I II III IV V VI VII VIII IX X

Marks : 70 Unit

No. of Periods

Electrostatics Chapter–1. Electric Charges and Fields Chapter–2. Electrostatic Potential and Capacitance Current Electricity Chapter–3. Current Electricity Magnetic Effects of Current and Magnetism Chapter–4. Moving Charges and Magnetism Chapter–5. Magnetism and Matter Electromagnetic Induction and Alternating Currents Chapter–6. Electromagnetic Induction Chapter–7. Alternating Current Electromagnetic Waves Chapter–8: Electromagnetic Waves Optics Chapter–9. Ray Optics and Optical Instruments Chapter–10. Wave Optics Dual Nature of Radiation and Matter Chapter–11. Dual Nature of Radiation and Matter Atoms and Nuclei Chapter–12. Atoms Chapter–13. Nuclei Electronic Devices Chapter–14. Semiconductor Electronics: Materials, Devices and Simple Circuits Communication Systems Chapter–15. Communication Systems Total

22

Marks

15

20 22 16 20 04 25

17

08 14 15

10

12

10 160

70

Unit I:  Electrostatics 22 Periods Chapter–1. Electric Charges and Fields Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric fleld. Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Chapter–2. Electrostatic Potential and Capacitance Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.

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Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Unit II:  Current Electricity 20 Periods Chapter–3. Current Electricity Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity, Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel, Kirchhoff’s laws and simple applications, Wheatstone bridge, metre bridge. Potentiometer - principle and its applications to measure potential difference and for comparing EMF of two cells; measurement of internal resistance of a cell. Unit III:  Magnetic Effects of Current and Magnetism 22 Periods Chapter–4. Moving Charges and Magnetism Concept of magnetic field, Oersted’s experiment. Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire. Straight and toroidal solenoids (only qualitative treatment), force on a moving charge in uniform magnetic and electric fields, Cyclotron. Force on a current-carrying conductor in a uniform magnetic field, force between two parallel currentcarrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter. Chapter–5. Magnetism and Matter Current loop as a magnetic dipole and its magnetic dipole moment, magnetic dipole moment of a revolving electron, magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; earth’s magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths, permanent magnets. Unit IV:  Electromagnetic Induction and Alternating Currents 20 Periods Chapter–6. Electromagnetic Induction Electromagnetic induction; Faraday’s laws, induced EMF and current; Lenz’s Law, Eddy currents. Self and mutual induction. Chapter–7. Alternating Current Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, power factor, wattless current. AC generator and transformer. Unit V:  Electromagnetic waves 04 Periods Chapter–8. Electromagnetic Waves Basic idea of displacement current, Electromagnetic waves, their characteristics, their Transverse nature (qualitative ideas only). Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.

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Unit VI:  Optics 25 Periods Chapter–9. Ray Optics and Optical Instruments Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula, magnification, power of a lens, combination of thin lenses in contact, refraction and dispersion of light through a prism. Scattering of light - blue colour of sky and reddish apprearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Chapter–10. Wave Optics Wave optics: Wave front and Huygen’s principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen’s principle. Interference, Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light, diffraction due to a single slit, width of central maximum, resolving power of microscope and astronomical telescope, polarisation, plane polarised light, Brewster’s law, uses of plane polarised light and Polaroids. Unit VII:  Dual Nature of Radiation and Matter 08 Periods Chapter–11. Dual Nature of Radiation and Matter Dual nature of radiation, Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de-Broglie relation, DavissonGermer experiment (experimental details should be omitted; only conclusion should be explained). Unit VIII:  Atoms and Nuclei 14 Periods Chapter–12. Atoms Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Chapter–13. Nuclei Composition and size of nucleus, Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion. Unit IX:  Electronic Devices 15 Periods Chapter–14. Semiconductor Electronics: Materials, Devices and Simple Circuits Energy bands in conductors, semiconductors and insulators (qualitative ideas only) Semiconductor diode - I-V characteristics in forward and reverse bias, diode as a rectifier; Special purpose p-n junction diodes: LED, photodiode, solar cell and Zener diode and their characteristics, zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor and transistor as an amplifier (common emitter configuration), basic idea of analog and digital signals, Logic gates (OR, AND, NOT, NAND and NOR). Unit X:  Communication Systems 10 Periods Chapter–15. Communication Systems Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation, satellite communication. Need for modulation, amplitude modulation.

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Question Paper Design for Science (Class XII) Time : 3 Hours S. No. 1.

2.

3.

4.

5.

Max. Marks : 70 Very Short Short Value Long Short Answer I Answer based Answer % Total Answer (VS-I) II question I Weight Marks (VSA) (VS-II) (VBQ) (L-I) age 1 Mark 2 Marks 3 Marks 4 Marks 5 Marks

Typology of Questions

Remembering (Knowledge based—Simple recall questions, to know specific facts, terms, concepts, principles, or theories; Identify, define, or recite, information) Understanding (Comprehension—To be familiar with meaning and to understand conceptually, interpret, compare, contrast, explain, paraphrase, information) Application (Use abstract information in concrete situation, to apply knowledge to new situations, use given content to interpret a situation, provide an example, or solve a problem) High Order Thinking Skills (Analysis & Synthesis— Classify, compare, contrast or differentiate between different pieces of information; Organize and/or integrate unique pieces of information from a variety of sources) Evaluation (Appraise, judge, and/or justify the value or worth of a decision or outcome, or to predict outcomes based on values) TOTAL

2

1

1

—

—

7

10%

—

2

4

—

1

21

30%

—

2

4

—

1

21

30%

2

—

1

—

1

10

14%

1

—

2

1

—

11

16%

5×1=5

5×2=10 12×3=36

1×4=4

3×5=15 70(26) 100%

QUESTION WISE BREAK UP Type of Question VSA SA-I SA-II VBQ LA Total

Mark per Question 1 2 3 4 5

Total No. of Questions 5 5 12 1 3 26

Total Marks 05 10 36 04 15 70

1. Internal Choice: There is no overall choice in the paper. However, there is an internal choice in one question of 2 marks weightage, one question of 3 marks weightage and all the three questions of 5 marks weightage. 2. The above template is only a sample. Suitable internal variations may be made for generating similar templates keeping the overall weightage to different form of questions and typology of questions same.

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OVERVIEW OF A CHAPTER Physics XII

1

Electric Charges and Fields

3. Gauss’s Law and its Applications

Topics covered 1. Electric Charges and Electric Fields

Continuous Charge Distribution

2. Electric Dipole

• Linear Charge Density λ: It is the charge per unit length λ =

3. Gauss’s Law and its Applications

FLOW CHART Charge (Coulomb)

Combination of charges

 F=

1 qQ  r 4πε 0 r 2   F = Eq  E=

dq . dA dq . • Volume Charge Density r: It is the charge per unit volume of the body r = dV • Electric flux: It is the measure of number of electric field lines crossing that area, normally.

• Surface Charge Density σ: It is the amount of charge per unit surface area σ =

Distribution of charges

n

∑ qi  E = K i =1 2 × r | ri |

→ →

Mathematically df = E ⋅ dS Electric flux is a scalar quantity. S.I. unit of electric flux is Nm2C–1 or Vm.

 σ.ds ρ.dv E = K ∫ | r |2 × r or K ∫ | r |2 × r s V

Electric Field

Gauss Law Field Intensity  E (N/C)

1 • Gauss theorem: The total flux through a closed surface, enclosing a volume, in vacuum is, ε0 times the net charge, enclosed by the surface. → → qenclosed f = � ∫ E ⋅ dS = ε0 s • Gaussian surface: Any closed surface imagined around the charge distribution, so that Gauss theorem can be conveniently applied to find electric field due to the given charge distribution. • Electric field due to infinitely long straight charged wire of linear charge density l: λ E= , where r is the perpendicular distance, of the observation point from the wire. 2pε 0 r • Electric field due to an infinite plane sheet of charge of surface charge density σ. σ E= 2ε 0 • Electric field due to a spherical shell of surface charge density σ and radius R: 1 q for r > R Outside the shell, E = 4pε 0 r 2 Inside the shell, E = 0 for r < R q At the surface, E= , r=R 4pε 0 R 2

  d φ = E.ds

Electric Flux (Nm2/C) Gauss’s Theorem ∑q φ= ε0

1 Q r 4πε 0 r 2

E=

dq . dl

λ 2πε 0 r

Electric field due to charge distributions

E=

E=

1 q 4πε 0 r 2

σ 2ε 0

V = Ed(OR) E = −

dV dr

✎ Each chapter is divided into topics and each concept is dealt separately. ✎ Flowchart representation of the chapter.

EXERCISE 1.3

✎ All concepts are presented in points, which can be easily learnt and remember. ✎ Each concept is well explain by relevant diagrams, tables and illustrations for better understanding.

(Questions 1 to 13 Carrying 1 Mark)

1. A metallic spherical shell has an inner radius R1 and outer radius R2. A charge Q is placed at the centre of the spherical cavity. What will be the surface charge density on (i) the inner surface and (ii) the outer surface? [NCERT Exemplar][HOTS] 2. Define the term ‘electric flux’.Write its S.I. unit. 3. Is electric flux a scalar or a vector? 4. Name a physical quantity whose unit is Vm. 5. Two charges of magnitude –2Q and +Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius ‘3a’ with its centre at origin? [AI 2013] 6. A charge q is placed at the centre of a cube of side l. What is the electric flux passing through

8. A spherical rubber balloon carries a charge that is uniformly distributed over its surface. As the balloon is blown up and increases in size, how does the total electric flux coming out of the surface change? Give reason. 9. The figure shows three charges +2q, – q and +3q. Two charges +2q and –q are enclosed within a surface ‘S’. What is the electric flux due to this configuration through the surface ‘S’? [Delhi 2010] 2q +3q

✎ Also included HOTS Questions that test the mental ability of the learner. ✎ Exercise to each topic has been dealt separately and important NCERT Textual and NCERT Exemplar Questions included, segregated into 1 Mark, 2 Marks, 3 Marks and 5 Marks Questions. 

S –q

10. An arbitrary surface encloses a dipole. What is the electric flux through this surface? [NCERT Exemplar] 11. State Gauss theorem in electrostatics. [Delhi 2008 C] 12. If the radius of the Gaussian surface enclosing a charge q is halved, how does the electric flux through the Gaussian surface change? [AI 2008] 3 2 13. If Coulomb’s law involved 1/r dependence (instead of 1/r ), would Gauss’s law be still true? [NCERT]

(Questions 14 to 22 Carrying 2 Marks)

14. A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q. A charge q is placed at the centre of the shell, (a) What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell? (b) Write expression for the electric field at point x > r2 from the centre of the shell. [AI 2010] 15. Charges of magnitude 2Q and –Q one located at points (a, 0, 0) and (4a, 0, 0). Find the ratio of the flux of electric field, due to these charges, through concentric spheres of radii 2a and 8a centred at the origin. [S.P. 2011] A charge is placed at the open end of a cylinder of length l and radius as shown in the figure.

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VALUE BASED QUESTIONS

REVISION CHART

1. During a thunderstorm the ‘live’ wire of the transmission line fell down on the ground. A group of boys passing through noticed it and some of them wanted to place the wire by the side. As they were approaching the wire and trying to lift it, Hari noticed it and immediately pushed them away to prevent them from touching the wire. Two of them got hurt in the processes. Hari took them to a doctor to get medical aid. Based on the above paragraph, answer the following: (a) Write two values which Hari displayed during the incident. (b) Why is it that a bird can sit over a suspended ‘live’ wire without any harm whereas touching it on the ground can give a fatal shock? (c) the electric power from a power plant is set up to a very high voltage before transmitting it to distant consumers. Write the reason for it. [AI 2016] 2. One day Pooja went to see an exhibition. She was already running late she forgot to switch off the car headlights. When she returned, she could not start the car. Anuj a passerby, came to her for help. After knowing about her problem, he went to a nearby garage and called mechanic Ram. Ram noticed that the car battery has been discharged as the headlights were left on for a long time. He brought another battery from his garage and connected its terminals to the terminals of the car battery. He succeeded in starting the engine and then disconnected his battery. This is called ‘jump starting’, Pooja felt happy and thanked both Anuj and Ram. Answer the following questions based on the above information. (a) What values were displayed by Anuj? (b) A storage battery of emf 8.0V and internal resistance 0.5W is being charged by a 120V d.c.

Quantization of electric charge: The charge on a body, is an integral multiple of, a basic quantity of charge, which is the charge on an electron.

1. q = ± Ne 2.

F= k

Electric charge

Methods of producing charge on an body by (i) friction (ii) Induction (iii) Conduction

q1q2 r2

  5. φ = E ⋅ d S = E dS cos θ E ∫ ∫

7. 8. 9.

φE = E=

∑q

E=

−dV dr

q1q2 r12

λ 2pε 0 R

q (a) outside the shell: E = k 2 r (b) on the shell: q 2 E = k 2 As q = 4pR σ R E = σ / ε0 (c) inside the shell: E = 0 11. σ (a) E = 2ε 0 1 P (b) E equator = 4pε 0 r 3 1 2P (b) E axis = 4pε 0 r 3

10.

Application

k=

E = Electric Field 1 , r = distance 4pε 0 e0 = Absolute permittivity

Relation between F and E Electric field due to a point charge

dS = small area

to find electric flux

dV/dr = dipole gradient

Relation between electric field and potential

U = Potential Energy W = Work done

Potential energy of a system of two point charges

COMMON ERRORS S.No. Errors 1. Confusion between Electric field intensity & Electric Potential due to electric dipole 2. Method for finding the directions of Electric field. 3. Effect of dielectric in capacitors 4. Variation of charge potential, energy, field, capacitance etc. on connected and disconnected with battery condition. 5. Numeric Problems based on combination of capacitors

l = linear charge density

Field intensity due to infinitely long straight uniformly charged wire r = radius of Gaussian surface Field intensity due to uniformly charged spherical shell (outside the shell) R = Radius of shell σ = surface charge density

E = Electric field e0 = electric permittivity

Field intensity due to thin infinite plane sheet of charge

12. τ = p × E = pE sin q

p = dipole moment τ = torque

Electric dipole in a uniform electric field

13. p = q × 2a

2a = dipole length

Dipole moment in electric field

6.

Area Vector concept in Gauss Theorem.

Corrections Read the question properly before attempting. Direction motion of positive charges or decreasing direction of electric potential Proper polarity for dielectric slab While connected p.d is constant and while disconnected charge is constant. Three ways of solving networks: 1. Solve from one end of the circuit if possible. 2. re-draw the circuit in a simpler way 3. Apply wheatstone’s principle if applicable Area vector is always perpendicular to the surface.

✎ Common errors and corrections have been tagged to clear the confusion with cautions answers for productive learning.

✎ Important formulae, Symbols and applications in the chapter are provided at one place for recapitulation.

ASSIGNMENTS 1. State one basic property of electric charge. 2. Name the physical quantity whose unit is (i) V/m, (ii) Vm.

1 1

3. What is the ratio of the strength of the electric field at a point on the equator and at a point some distance on the axis of a very short electric dipole. 1 4. Define electric line of force and mention three properties of electric lines of force. 2 3 2 –1 5. An electric flux of –1.0 × 10 Nm C is passing through a sphere of radius 10.0 cm due to

IMPORTANCE OF EACH TOPIC AND FREQUENTLY ASKED TYPES OF QUESTIONS

change placed at it’s centre. (i) What is the value of the point charge?

 Important topIcs 1. 2. 3. *

Conservation of charge: The net electric charge in an isolated system is always constant.

✎ Have the complete essence of the chapter; ✎ Quite effective for a quick revision before exams.

Gauss theorem f = Electric flux Charge enclosed ∑ q = Net within the surface

ε0

U = W= k

Additivity of electrical charges: The total charge on a system is the algebraic sum of all the charges in different parts of the body.

q = Charge, N = number of Quantization of charges Charge particle To find force between two point q1, q2 are point charges, charges F = Force

3. F = qE 4. q E= k 2 r

6.

Symbols

Insulators: The substances that do not allow the charges to flow through them are called insulators.

It is an intrinsic property of elementary particles like electrons and protons because of which they exert electrical force and are able to respond to electrical force. Electric charge is a scalar quantity.

IMPORTANT FORMULAE Formula

Relative permitivity is ratio of force b/w two point charges placed certain distance apart in vacuum to the force b/w the same two charges placed some distance apart in the given medium.

Questions based on Electric field due to a dipole. Questions based on Gauss theorem and its application. Short questions on the dipole moment and torque. Maximum weightage is of Application of Gauss’s Law.

(ii) If the radius of the Gaussian surface is doubled, how much electric flux will pass through the surface? [NCERT] 2  6. Find the strength and direction of electric field E required to keep a charged drop of mass m, just to remain suspended in vacuum. 2

1. A pendulum bob of mass 80 mg and carrying charge of 3 × 10–8 C is placed in an horizontal electric field. It comes to equilibrium position at an angle of 37° with the vertical. Calculate the [Ans. 2 × 10–4 N/C] intensity of electric field. (g = 10 m/s2) 2. Eight charged droplets each of radius 1 mm and charge 10 × 10–10 C coalesce to form a single drop. Calculate the potential of the bigger drop. [Ans. 3600 V] 3. What potential difference must be applied to produce an electric field that can accelerate an electron to 1/10 of velocity of light. [Ans. 2.6 × 103 V] 4. A 10 µF capacitor can withstand a maximum voltage of 100 V across it, whereas another 20 µF capacitor can withstand a maximum voltage of only 25 V. What is the maximum voltage that can be put across their series combination? [Ans. 75 V] 5. Three concentric spherical metallic shells A < B < C of radii a, b, c (a < b < c) have surface densities σ, – σ and σ respectively. Find the potential of three shells A, B and C. If shells A and C are at the same potential, obtain relation between a, b, c. [Ans. c = a + b]

7. State Gauss theorem in electrostatics. Using Gauss theorem, find out an expression for electric field at a point due to an infinitely long line change distribution of linear charge density l. 3 8. Define electric field intensity at a point. Two point charges q and –q are placed at a distance 2a apart in vacuum. Calculate the electric field at a distance ‘r’ along the perpendicular bisector of the line joining the charges. What will be the direction of electric field at that point? 3 9. (a) What is the force on an electric dipole placed in a uniform electric field? ½ (b) Obtain an expression for the torque acting on an electric dipole placed in a uniform electric field. 2

✎ Repeatedly asked numerical problem types has been given separately for better preparation.

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✎ Chapterwise Assignment appended for self evaluation.

CONTENTS 1. Electric Charges and Fields.......................................................................................................11 2. Electrostatic Potential and Capacitance....................................................................................47 3. Current Electricity.....................................................................................................................93 4. Moving Charges and Magnetism............................................................................................149 5. Magnetism and Matter............................................................................................................202 6. Electromagnetic Induction......................................................................................................238 7. Alternating Current.................................................................................................................284 8. Electromagnetic Waves...........................................................................................................326 9. Ray Optics...............................................................................................................................350 10. Wave Optics............................................................................................................................426 11. Dual Nature of Radiation and Matter......................................................................................485 12. Atoms......................................................................................................................................520 13. Nuclei......................................................................................................................................546 14. Semiconductor Devices..........................................................................................................585 15. Communication Systems........................................................................................................658

Answers to Chapterwise Assignments.....................................................................................686 Sample Papers (1 to 10).............................................................................................................689 • Answers to Sample Papers (1 to 10)...............................................................................743 Model Answers by Topper Candidate.....................................................................................792 CBSE Board Question Paper-2018 (Solved)......................................................................... 796

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1

Electric Charges and Fields

Topics Covered 1.  Electric Charges and Electric Fields

2.  Electric Dipole

3.  Gauss’s Law and its Applications

CHAPTER MAP Combination of charges

Charge (Coulomb)

Distribution of charges

n

 E=K

∑ qi i =1

| ri |2

 F=

1 qQ  r 4πε 0 r 2   F = Eq  E=

 σ.ds ρ.dv E = K ∫ | r |2 × r or K ∫ | r |2 × r s V

Electric Field

× r

Field Intensity  E (N/C)

   d φ = E.ds

Electric Flux (Nm2/C) Gauss’s Theorem

1 Q r 4πε 0 r 2

n

φ =

closed surface

E=

λ 2πε 0 r

∑ qi i =1

ε0

Electric field due to charge distributions

E=

σ 2ε 0

V = Ed (or) E = −

11

dV dr

Quick Revision Notes 1.  Electric Charges and Electric Fields •• Electrostatics: It is the branch of physics which deals with the forces between the charges at rest, electric fields and potentials due to the charges at rest. •• Electric charge: It is an intrinsic property of elementary particles like electrons and protons because of which they exert electrical force and are able to respond to electrical force. Electric charge is a scalar quantity. •• There are two kind of charges (a) Positive charge, (b) Negative charge. Like charges repel each other but unlike charges attract each other. •• Method of producing charge on a body By friction: When we rub two bodies together, there is, transfer of electrons from one body to another, which causes the charging of bodies. By friction, both bodies acquire equal but opposite kind of charge. By induction: It is the process of charging an uncharged body, by keeping a charged body near it, without making a physical contact. In this process the charge produced on the body, is opposite to the body, used to charge it. By conduction: It is also called charging by physical contact. If an uncharged body in brought in, electrical contact, with the charged body, some electrons, are shared between the bodies. The uncharged body acquire a charge similar to the charged body. •• Conductors: The substances through which electric charges can flow easily are called conductors. They contain large number of free electrons. e.g. silver is the best conductor of electricity. •• Insulators: The substances that do not allow the charges to flow through them are called insulators. •• Basic Properties of Electric Charges (a) Quantization of electric charge: The charge on a body, is an integral multiple of, a basic quantity of charge, which is the charge on an electron. (b) Additivity of electrical charges: The total charge on a system is the algebraic sum of all the charges in different parts of the body. If a system contains, n charges, q1, q2, ..., qn then the total charge of the system q = q1 + q2 + ... + qn (c) Conservation of charge: The net electric charge in an isolated system is always constant. •• Coulomb’s law of electrostatic: The force of attraction/repulsion between two stationary point charges is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them. Force is along the line joining the two q1 q2 charges r F ∝ q1q2 A B 1 F ∝ 2 r q q F ∝ 1 2 2 rq q 1 2 F = K 2 r The value of ‘k’ depends upon the medium chosen and system of units taken. For vacuum, K = 9 × 109 Nm2/C2 Note: Coulomb’s law is experimental law. It is applicable for macroscopic and microscopic distance. Electrostatic force is a conservative force.

12

Physics-12

•• SI unit of charge: 1 Coulomb q1 q2 F = K 2 r q1 = 1 C, q2 = 1 C, r = 1 m

F = K = 9 × 109 N It is that amount of charge that repels an equal and similar charge with a force of 9 × 109 N, when placed in vacuum at a distance of 1 m from it. The CGS unit is ‘Stat Coulomb’ or ‘esu of charge’. 1 C = 3 × 109 stat coulomb Dimensional formula of charge q I = t q = It [q] = [AT] K in Coulomb’s laws in also written as 1 K = 4pε m where em = permittivity of the medium. •• Coulomb’s law in vector form: Consider 2 point charges q1 and q2 separated by a distance r.  F12

 F21

 r12

q1

 r21

q2

Force on q1 due to q2. 1 q1 q2  r 21 4pε 0 → 2 | r 12 | Let magnitude of r12 = r = r21

→ F12

=



→ F12

=

Force on q2 due to q1

→

→

F 21 =

Comparing (1) and (3) →

...(1)

1 q1 q2  1 q1 q2  r12  2 2 r12 = 4pε 4pε 0 | r21 | 0 r = − r 21

F 21 =

But r12 Equation (2) becomes

1 q1 q2  r 21  4pε 0 r 2

−1 q1 q2  r 21  4pε 0 r 2

...(2)

...(3)

→

F12 = – F 21 Coulomb’s law is in accordance with Newton’s 3rd law of motion which states that every action has equal and opposite reaction.

Electric Charges and Fields 13

•• Permittivity is measure of effectiveness of the medium in transmitting the electric field. Relative permittivity (er) [no unit]: Also called dielectric constant, (dielectric – insulator). It is ratio of permittivity of medium to the permittivity of vacuum ε er = m ε0 Relative permittivity in terms of force b/w charges: If 2 charges are placed certain distance apart in vacuum then 1 q1 q2 F0 =  ...(1) 4pε 0 r 2 1 q1 q2 In given medium Fm =  ...(2) 4pε m r 2 4pε m ε m F0 = = = er 4pε 0 ε 0 Fm Relative permitivity is ratio of force b/w two point charges placed certain distance apart in vacuum to the force b/w the same two charges placed same distance apart in the given medium. •• Principle of superposition of forces: The total force acting on a given charge due to a number of charges around it is the vector sum of the individual forces acting on it due to all the charges. Consider the charges q1, q2, q3 and so on ... qn. The net force on q1.

→

→

→

→

→

F1 = F12 + F13 + F14 + ... + F1n Note: The force b/w two charges is unaffected by the presence of other charges in its vicinity.

Electric Field Intensity •• Electric field: The region/space around a charged body within which its influence can be felt is called electric field. Electric field intensity/strength is defined as the force experienced per unit +ve test charge →

(vanishingly small) placed at that point. It is denoted by E . →

F dq → 0 dq dq should be vanishingly small so that it does not alter the field which it is being used to measure. →

E = lim →

E is a vector quantity SI unit → N/C. →

Expression for E due to point charge. →

Consider a point charge +q placed at origin. To find E at point P let us place a test charge q0 at that point. → q0 1 Q q0  +Q ⋅ r  F =  O P 4pε 0 r 2 r →

→

E = Lt

q0 → 0

14

F Q Q 1 = ⋅ r = ⋅ 2 ⋅ r 2 q0 4pε 0 r 4pε 0 r

Physics-12

E

E

1/r

r

2

•• Electric Field Lines: It is a curve, the tangent to which at any point gives the direction of force acting on a test charge placed at that point. •• Properties of Electric Field Lines: – Continuous smooth curves without breaks. – Start at +ve charge, end at –ve charge cannot form closed loops. If there is a single charge, they start/end at infinity. →

– Tangent to an electric field line at any point gives direction of E at that point. – NO two lines of force can cross each other. (If they do, there will be two tangents at that point, →

two direction of E not possible). – They are always normal to surface of conductor on which the charges are in equilibrium. (It not, →

component of E parallel to surface will set up a current which is not possible in equilibrium condition). – They have tendency to contract lengthwise which explains attraction b/w unlike charges. – They have tendency to expand laterally. This explains repulsion b/w two like charges. →

– They give measure of strength of E (closer in strong field, far apart about in weak field, parallel →

and equally spaced in uniform E ).

→

– They do not pass through conductor since E inside a conductor is 0.

EXERCISE 1.1 I.  Very Short Answer Type Questions

(1 Mark)

1. Ordinary rubber is an insulator. But the special rubber tyres of aircrafts are made slightly conducting why is it necessary? [NCERT] 2. A glass rod held in hand can be charged by rubbing it with silk but a copper rod cannot be charged like this. Why? 3. Is the force acting between two point charges q1 and q2 kept at some distance in air, attractive or repulsive when: (i) q1q2 > 0, (ii) q1q2 < 0?  [CBSE 2007] 4. What does q1 + q2 = 0 signify in electrostatics?  5. Name any two basic properties of electric charges. 6. What do you understand by quantisation of electric charges? 7. State the principle of conservation of charge. 8. A point charge (+q) is kept in the vicinity of uncharged conducting plate. Sketch electric field lines between the charge and the plate. [Delhi 2014]

Electric Charges and Fields 15

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