ll ne - Arihant Book
Transcription
ll ne - Arihant Book
CHAPTER ONE Electric Charges and Fields TOPIC 1 Electric Charges Introduction When a glass rod is rubbed with silk, it acquires a power to attract light bodies such as, small pieces of paper. The agencies which acquire the attracting power are said to be electrified or charged. The electricity produced by friction is called frictional electricity. If the charge in a body does not move, then the frictional electricity is known as static electricity. The branch of Physics which deals with static electricity is called electrostatics. Electric Charge The property of protons and electrons, which gives rise to electric force between them is called electric charge. Electric charge is a characteristic that accompanies fundamental particles, wherever they exist. According to William Gilbert, charge is something possessed by material objects that makes it possible for them to exert electrical force and to respond to electrical force. Electric charge is a scalar quantity. A proton possesses positive charge while an electron possesses an equal negative charge (where the value of the electric charge, e is 1.6 ´ 10 -19 C) . Unlike charges attract each other, whereas like charges repel each other. A simple apparatus used to detect charge on a body is the gold leaf electroscope. There are two kinds of charges such as positive charge and negative charge. An object can attain positive charge by loosing electrons while other can attain negative charge by gaining electrons. Charges with same sign, i.e. like charges repel each other while charges with opposite sign, i.e. unlike charges attract each other. Charges always reside on the surface of the charged conducting object. An object can be charged by different methods like friction, conduction and induction. Charge is a scalar quantity, it can be added and subtracted as a number. Its SI unit is coulomb. Dimensional formula for electric charge is [M 0L0 TA]. Chapter Checklist Electric Charges Coulomb's Law and Electrostatic Field Electric Dipole Electric Flux ll 2 Conductors and Insulators Conductors are those substances which can be used to carry or conduct electric charge/electron from one point to other. They have electric charges that are comparatively free to move inside the material. They allow electricity to pass through them easily, e.g. silver, copper, iron, aluminium, etc. Insulators are those substances which cannot conduct electricity. They are also called dielectrics. They offer high resistance to the passage of electricity through them, e.g. glass, rubber, plastic, ebonite, mica, etc. Difference between Dielectrics and Conductors Dielectrics are non-conductors and do not have free electrons at all, while conductors have free electrons in their any volume which makes them able to pass the electricity through them. Charging by Induction The process of charging a neutral body by bringing a charged body nearby it without making contact between the two bodies is known as charging by induction. Using the process of charging by induction, a conductor may be charged permanently. For charging an uncharged conducting sphere positively by induction, a negatively charged rod is brought close to it. The near end of the sphere becomes positively charged, while its far end becomes negatively charged. Now, the sphere is connected to the earth, keeping the negatively charged rod in its position. The electrons will flow to the ground, while positive charges will remain held at near end because of attractive force of negative charges on rod. Now, disconnect the sphere from the ground. The positive charges still continues to be held at near end. When the negatively charged rod is removed, the positive charge will spread uniformly over the sphere. Example 1. Attraction by a Comb A comb run through one’s hair attracts small bits of paper. What happens, if the hair are wet or if it is a rainy day? Sol. If the hair are wet or it is a rainy day, then the friction between the hair and the comb reduces. The comb does not get charged and it will not attract small bits of paper. ne Physics Class 12th Basic Properties of Electric Charge As discussed above, we know that there are two types of charges, namely positive and negative and their effects tend to cancel each other. Now, we shall discuss some other properties of the electric charge. Additive Nature of Electric Charge Electric charge is additive in nature. It means if a system consists of two charges q1 and q 2 , then the total charge of the system will be q1 + q 2 . In general, if a system consists of n charges q1 , q 2 , q3 , ¼, qn , then the total charge of the system will be q1 + q 2 + q3 + ¼+ qn . In order to calculate the net charge on a system, we have to just add algebraically, all the charges present in the system. This is known as the principle of superposition of charge. If the sizes of charged bodies are very small as compared to distance between them, they are considered as point charges. Conservation of Electric Charge During any process, the net electric charge of an isolated system remains constant (i.e. conserved). In simple words, charge can neither be created nor be destroyed. In any physical process, the charge may get transferred from one part of the system to another, but the net charge will always remain the same. It is impossible to create or destroy net charge carried by an isolated system although charge carrying particles may be created or destroyed in a process. Nature creates charged particles, i.e. a neutron turns into an electron and proton. Thus, the electron and proton have created equal and opposite charges and total charge is zero, before and after their creation. Quantisation of Electric Charge The charge on any body can be expressed as the integral multiple of basic unit of charge, i.e. charge on one electron. This phenomena is called quantisation of electric charge. It can be written as q = ± ne . where, n = 1, 2, 3, ××× is any integer, positive or negative and e is the basic unit of charge. Charge is said to be quantised because it can have only discrete values rather than any arbitrary value, i.e. free particle has no charge at all or a charge of +10 e or - 6 e but not a free particle with a charge of, say 3.57 e. ll ne 3 Electric Charges and Fields Origin of Electric Charge: Electron Theory of Electrification Experiment shows that an object becomes charged, when a very tiny fraction of the mobile electrons with their negative charge are transferred from one object to another. This is why we must rub, stroke or make significant contact between two objects for the objects to become charged. In ordinary matter, a positive charge is much less mobile than negative charge. For this reason, an object becomes positively charged through the removal of negatively charged electrons rather than through the addition of positively charged protons. Example 2. Discrete Nature of Charge Is a charge of 5. 8 ´ 10 -18 C possible? Sol. From q = ne Þ n = q e = 5.8 ´ 10 -18 1.6 ´ 10 -19 Worked Out Problem A paisa coin is made up of Al-Mg alloys and weighs 0.75 g. It has a square shape and its diagonal measures 17 mm. It is electrically neutral and contains equal amounts of positive and negative charges. Treating the paisa coins made up of only Al, find the magnitude of equal number of positive and negative charges. What conclusion do you draw from this magnitude? NCERT Exemplar Step I Write the given quantities in the question. Mass of a paisa coin, m = 0.75 g Atomic mass of aluminium, M = 26.9815 g Length of the diagonal of square shaped paisa coin =17 mm = 36.25 Avogadro’s number, N A = 6.023 ´ 10 23 As, n is not an integer, this value of charge is not possible. Difference between Charge and Mass Step II Calculate the number of aluminium atoms in one paisa coin. NA ´m M 6.023 ´ 10 23 = ´ 0.75g 26.9815 g n= The differences between mass and charge is given in the following table: Charge Mass Mass of a body is a positive quantity. Electric charge on a body may be positive, negative or zero. Charge carried by a body does not depend upon velocity of the body. Mass of a body increases with its velocity m0 as m = where, c is velocity of v2 1- 2 c light in vacuum, m is the mass of the body moving with velocity v and m 0 is rest mass of the body. Charge is quantised. The quantisation of mass is yet to be established. Electric charge is always conserved. Mass is not conserved as it can be changed into energy and vice-versa. The gravitational force between two Force between charges can be either masses is always attractive. attractive or repulsive, as charges are unlike or like charges. Þ n = 1.6742 ´ 10 22 Step III Since, atomic number ( Z ) of Al is 13, therefore, each atom of Al contains 13 protons and 13 electrons. Now, find out the magnitude of positive and negative charges present in one paisa coin. nZe = 1.6742 ´ 10 22 ´ 13 ´ 1.6 ´ 10 -19 C = 3.48 ´ 10 4 C = 34.8 kC Step VI Now, write the conclusion drawn from this magnitude of charge. 34.8 kC is a very large amount of charge. This concludes that ordinary neutral matter contains an enormously large amount of positive and negative charges. ll ne EXAM Practice Very Short Answer Type Questions 1. Which is bigger, a coulomb or a charge on an electron? Sol. A coulomb of charge is bigger than the charge on an electron. 2. An ebonite rod held in hand can be charged by rubbing with flannel but a copper rod cannot be charged like this, why? Sol. Both the human body and the copper rod conduct electricity. When it is attempted to charge a copper rod by rubbing, the charge flows from the rod to the earth through the hand. However, when ebonite rod is charged by rubbing, the charges so produced stay on the ebonite rod as it is bad conductor of electricity. 3. What does q1 + q2 = 0 signify in electrostatics? Sol. The charges q1 and q2 are equal and opposite. 4. Can a body has charge 1.5 e, where e is the electronic charge? Sol. No, because the physically existing charge is always an integral multiple of e = 1.6 ´ 10 -19 C. 5. Consider three charged bodies A, B and C. If A and B repel each other and A attracts C, what is nature of the force between B and C? Sol. It is also attractive. 6. A metal sphere has a charge of – 6 mC. When 5 ´ 10 12 electrons are removed from the sphere, what would be net charge on it? Sol. Here, q1 =- 6 mC and q2 = ne = 5´1012 (1.6 ´10 -19) C = 8 .0 ´10 -7 C = 0 .8 ´10 -6 C = 0 .8 mC Since, electrons are removed from the sphere, q2 is positive. Therefore, net charge on the sphere, q = q1 + q2 = (- 6 .0 + 0 .8) mC =-5 .2 mC 7. A glass rod when rubbed with silk cloth acquires a charge 1.6 ´10-13 C. What is the charge on the silk cloth? Sol. Silk cloth will also acquire a charge 1.6 ´10 -13 C. However, it will be negative in nature. [1 Mark] 8. What is the basic cause of quantisation of charge? Sol. The basic cause of quantisation of charge is only the integral number of electrons which is transferred from one body to another, i.e. ± ne. 9. Quarks are the building blocks of nucleons and possess fractional electronic charge. Does this discovery violate the principle of quantisation of charge? Sol. If the quarks are detected in any experiment with concrete practical evidence, then the minimum value 1 2 of quantum of charge will be either e or e. 3 3 However, the law of quantisation will hold good. 10. A glass object is charged to +3 nC by rubbing, it with a silk cloth. In this rubbing process, have protons been added to the object or have electrons been removed from it? Sol. Electrons have been removed from the object. 11. Two insulated charged copper spheres A and B of identical size have charges qA and qB respectively. A third sphere C of the same size but uncharged is brought in contact with the first and then in contact with the second and finally removed from both. What are the new charges on A and B? Foreign 2011 Sol. When sphere C is brought in contact with A : Charge on sphere C, q + 0 qA qC = A = 2 2 and new charge on sphere A, q q¢A = A 2 When sphere C is brought in contact with B : Charge on sphere C, q + qB q¢C = C 2 q A / 2 + qB = 2 q A + 2 qB = 4 q + 2 qB \ New charge on sphere B, q¢B = A 4 ll ne 5 Electric Charges and Fields Short Answer Type Questions [2 Marks] 1. Ordinary rubber is an insulator. But the special rubber tyres of aircrafts are made slightly conducting. Why is this necessary? Sol. During landing or take off, the tyres of aircrafts get charged due to the friction between tyres and ground. In case, the tyres are slightly conducting, the charge developed on the tyres will not stay on them and it finds its way to the earth. [1+1] 7. A copper slab of mass 2 g contains 2 ´ 1022 atoms. The charge on the nucleus of each atom is 29 e. What fraction of the electrons must be removed from the sphere to give it a charge of +2 mC? Sol. Total number of electrons in the slab = 29 ´ 2 ´ 10 22 Number of electrons removed q 2 ´10 -6 = 1.25 ´ 10 13 = = e 1.6 ´ 10 -19 Fraction of electrons removed 1.25 ´ 10 13 = 2 .16 ´ 10 -11 = 29 ´ 2 ´ 10 22 2. Automobile ignition failure occurs in damp weather. Explain, why? Sol. The insulating porcelain of the spark plugs accumulates a film of dirt. The surface dirt is hygroscopic and picks up moisture from the air. Therefore, in humid weather, the insulating porcelain of the plugs becomes quasi-conductor. This allows an appreciable proportion of the spark to leak across the surface of the plug instead of discharging across the gap. [1+1] [1] [1] 8. Why does a charged glass rod attract a piece of paper? Sol. Paper is a dielectric, so when a positively charged glass rod is brought near it, atoms of paper get polarised, with centre of negative charge of atoms coming closer to the glass rod. [1/2] 3. Can a charged body attract another uncharged body? Explain. Sol. Yes, because when a charged body is brought infront of the uncharged body, opposite kind of induced charge is produced on the uncharged body. Therefore, the charged body attracts the uncharged body. [1+1] Fr 4. A and B have identical size and same mass. ++ and B becomes B - - . Will A + + and HOTS A becomes A -B still have the same mass? Why? Sol. No, they will not have same mass. B- - has more mass as, it has gained two electrons, whereas A + + has lost [1+1] two electrons. 5. Can two balls having same kind of charge on them attract each other? Explain. Sol. Yes, two balls having same kind of charge also attract each other. If any one of them has more charge as compared to the other. Then, due to the induction, they induce opposite kind of charges on the faces of each other when they are brought nearer. Therefore, they behave as oppositely charged balls and hence they attract each other. [1+1] 6. Can ever the whole excess charge of a body be transferred to the other? If yes, how and if not, why? All India 2011 Sol. Yes, the whole charge of a body P can be transferred to a conducting body Q, when P is enclosed by Q and is connected to it. This is because the charge always [1+1] resides on the outer surface of the conductor. + + + + – –– – Paper ++ ++ Fa Glass rod [1/2] Therefore, force of attraction Fa between glass rod and piece of paper becomes greater than the force of repulsion Fr between the glass rod and the piece of paper. This results in attraction of the piece of paper toward the glass rod. [1] 9. In filling the gasoline tank of an aeroplane, the metal nozzle of hose from the gasoline truck is always carefully connected to the metal of the aeroplane by a wire, before the nozzle is inserted in the tank. Explain, why? Sol. Since, the aeroplane and the gasoline truck usually have wheels with rubber tyres, they are insulated from the ground. Further, the service ramps are usually made of concrete and are not necessary good conductors to the earth. Therefore, inspite of grounding metallic ropes, the aeroplane and the truck could remain charged. A spark may jump and ignite the explosive gasoline, when the metal nozzle is brought near the aeroplane. The connection of metal of the aeroplane and the nozzle of the hose with a wire avoids any unbalance of charge and hence the risk of gasoline. [1+1] ll ne 7 Electric Charges and Fields For the neutron, the charge on neutron is 0. Let the number of up quarks are b and the number of down quarks are 3 - b. [1] So, b ´ up quark charge + (3 - b) down quark charge = 0 æ 2e ö æ eö bç ÷ + (3 - b) ç - ÷ = 0 è3ø è 3ø 16. It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted 2 by u) of charge + æç ö÷ e and the ‘down’ quark (denoted è3ø 1 æ by d) of charge ç - ö÷ e, together with electrons build è 3ø up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter). Suggest a possible quark composition of a proton and neutron. NCERT Sol. For the protons, the charge on it is +e. Let the number of up quarks are a, then the number of down quarks are (3 - a) as the total number of quarks are 3. So, (a ´ up quark charge + (3 - a) down quark charge) = + e æ2 ö æ eö a ´ ç e ÷ + (3 - a) ç - ÷ = e è3 ø è 3ø 2 ae (3 - a) e =e Þ 3 3 Þ 2a - 3 + a = 3 Þ 3a = 6 Þ a =2 Thus, in the proton, there are two up quarks and one down quark. \Possible quark composition for proton = uud Value Based Questions 1. Þ 2b - 3 + b = 0 Þ 3b = 3 Þ b =1 Thus, in neutron, there are one up quark and two down quarks. \ Possible quark composition for neutrons = udd. [1] 17. A balloon gets negatively charged by rubbing HOTS ceilings of a wall. Does this mean that the wall is positively charged? Why does the balloon eventually fall? Sol. No, this does not imply that the wall is positively charged. The balloon induces a charge of opposite sign in the ceiling of the wall, causing the balloon and the ceiling to be attracted to each other. The balloon eventually falls because its charge slowly diminishes as it leaks to ground. Some of the charge on the balloon could also be lost due to the presence of positive ions in the surrounding atmosphere, which would tend to neutralize the negative charges on the balloon. [1+1] [4 Marks] Geeta has dry hair. A comb ran through her dry hair attracts small bits of paper. She observes that Neeta with oily hair combs her hair, the comb could not attract small bits of paper. She consults her teacher for this and gets the answer. She then goes to the junior classes and shows this phenomenon as Physics experiment to them. All the juniors feel very happy and tell her that they will also look for such interesting things in nature and try to find the answers. She succeeds in forming a Science club in her school. Read the above passage and answer the following questions. (i) What according to you are the values displayed by Geeta? (ii) Explain the phenomenon involved. Sol. (i) The values displayed by Geeta are curiosity, leadership and compassion. [2] (ii) Frictional electricity. Frictional electricity is the electricity produced by rubbing two suitable bodies and transfer of electrons from one body to other. [1+1] Further, if the hair are oily or wet, then the friction between the hair and comb reduces and the comb will not attract small bits of paper. ll 8 2. ne Physics Class 12th As it is known, that all matter is made up of atoms/ molecules. Every atom consists of a central core, called the atomic nucleus, around which negatively charged electrons revolve in circular orbits. Every atom is electrically neutral containing as many electrons as the number of protons in the nucleus. All the materials are electrically neutral, they contain charges, but their charges are exactly balanced. An object contains equal amounts of positive charge and negative charge with such an equality or balance of charges, the object is said to be electrically neutral or uncharged. To electrify or charge a neutral body, we need to add or remove one kind of charge. The body which gains electrons becomes negatively charged and the body which loses electrons becomes positively charged. Further, like charges repel and unlike charges attract. Read the above passage and answer the following questions. (i) Every body whether a conductor or an insulator is electrically neutral. Is it true? (ii) Charging lies in charge imbalance, i.e. excess charge or deficit charge, comment. (iii) How do you visualize this principle being applied in our daily life? Sol. (i) Yes, it is true. Every conductor/insulator is electrically neutral, as it contains equal amounts of positive charge and negative charge. [1] (ii) This statement is true. Charging lies in charge imbalance. When a body loses some electrons, it becomes positively charged because it has excess of protons over electrons. The reverse is also true. [1] (iii) Nature/God has created the universe. In original, all bodies are neutral with no forces of attraction/repulsion. When interests of any two persons clash (i.e. two bodies are rubbed against each other), they become charged. From the charging, arises the forces of attraction/repulsion, i.e. pulls and pressures of life. [1] Nature/God wants us to live in peace without stress and tensions in life. We get charged over petty things in life and invite all sorts of pulls, pressures and tensions. [1] Q.1 Is the mass of an amber rod after charging with fur (a) less than, (b) greater than or (c) same as its mass before charging? Explain. Q.2 Predict and explain: An electrically neutral sphere is given a negative charge. (i) In principle, does the object’s mass increase, decrease or remain the same after being charged? (ii) Choose the best appropriate explanation from the following: (a) To give the sphere a negative charge, we must give it more electrons and this will increase its mass. (b) A positive charge increases the sphere’s mass, a negative charge decreases its mass. (c) Charge is conserved therefore the mass of the object will remain the same. Q.3 Two objects P and Q carry charges -3.00 mC and -0.44 mC. What is the number of electrons transferred from P to Q, so that they acquire equal charges? Q.4 Explain the following: (i) Would life be different, if the electron were positively charged and the proton were negatively charged? (ii) Does the choice of signs have any bearing on physical and chemical interactions? (iii) When a person chews a winter green life saver in a dark room, a faint flash of blue light is seen from his mouth. How? Q.5 A copper sphere of mass 2 g contains nearly 2 ´ 1022 atoms. If charge on the nucleus of each atom is 29 e, what will be the fraction of electrons that must be removed from the sphere to give it a charge of +2 mC ? [Ans. 2.16 ´ 10- 11] ll TOPIC ne 9 Electric Charges and Fields 2 Coulomb’s Law and Electrostatic Field Coulomb’s Law The force of interaction (attraction or repulsion) between two stationary point charges in vacuum is directly proportional to the product of the charges and inversely proportional to the square of distance between them. Mathematically, electrostatic force between two stationary charges is given by q2 q1 r F = 2 Also, r21 \ where, e 0 = 8.85 ´ 10 -12 C 2 N -1m -2 and is called the permittivity of free space. q 1q 2 i.e. F = 9 ´ 10 9 r2 The coulomb force acts along the straight line connecting the points of location of the charges. It is central and spherically symmetric. If q1 = q 2 = 1 C and r = 1m 1´ 1 Then, F = 9 ´ 10 9 2 (1) F = 9 ´ 10 9 N i.e. one coulomb is the charge that when placed at distance of 1m from another charge of same magnitude in vacuum, experiences an electric force of repulsion of magnitude 9 ´ 10 9 N. Coulomb is a big unit, in practice we use smaller units like mC or mC. Coulomb’s Law in Vector Form Consider two like charges q1 and q 2 present at points A and B respectively in vacuum at a distance r apart. r r12 q1 [Q F12 is along the direction of unit vector r21 ] be the unit vector pointing from charge q 2 to q1 . 1 q 1q 2 …(iii) × F21 = r$12 4pe 0 r 2 [Q F21 is along the direction of unit vector r21 ] = 9 ´ 10 9 Nm 2C -2 F12 Let r12 be the unit vector pointing from charge q1 to q 2 . 1 q 1q 2 …(ii) F12 = r$21 × 4pe 0 r 2 k | q 1q 2 | r where, k is a proportionality constant. In SI unit, k is given by 1 k= 4pe 0 A According to Coulomb’s law, the magnitude of force on charge q1 due to q 2 (or on charge q 2 due to q1 ) is given by 1 q 1q 2 …(i) × | F12 | = | F21 | = 4pe 0 r 2 B r21 F21 q2 Coulomb force between two charges $r21 = - r$12 \ Eq. (ii) becomes - 1 q 1q 2 F12 = r$12 × 4pe 0 r 2 …(iv) On comparing Eq. (iii) with Eq. (iv), we get F12 = - F21 i.e., Coulomb’s law agrees with Newton’s third law. Comparison of Coulomb’s Law with Gravitational Law Both the Coulomb’s and Newton’s laws are inverse square law. Gm1m 2 [Newton’s gravitational law] F = r2 kq q [Coulomb’s law] F = 12 2 r The electric force is much stronger than the gravitational force between two electrons, F E = 10 39 FG Electric force can be attractive or repulsive. But the gravitational force is always attractive. Electric force depends on the nature of the medium between the charges but gravitational force does not. Coulomb force and gravitational force, both are central forces. ll ne 15 Electric Charges and Fields EXAM Practice Very Short Answer Type Questions 1. Two equal balls having equal positive charge q coulombs are suspended by two insulating strings of equal length. What would be the effect on the force when a plastic sheet is inserted between the two? All India 2014 Sol. From Coulomb’s law, electric force between the two charged bodies, in a medium, 1 |q1 q2| F= 4 pe 0 K r 2 where, K = dielectric constant of the medium For vacuum K =1 For plastic, K >1 Therefore, after insertion of plastic sheet, the force [1] between the two balls will reduce. 2. The test charge used to measure electric field at a point should be vanishingly small. Why? Sol. In case, test charge is not vanishingly small, it will produce its own electric field and the measured value of electric field will be different from the actual value of an electric field at that point. [1 Mark] 7. Force experienced by an electron in an electric field is F newton. What will be the force experienced by a proton in the same field? Take mass of proton 1836 times the mass of an electron. Sol. The proton will experience the same force, F newton, but in the opposite direction. 8. Two point charges of + 3 mC each are 100 cm apart. At what point on the line joining the charges will the electric field intensity be zero? Sol. At the centre, since the electric field due to two charges is equal and opposite at this point. 9. A proton is placed in a uniform electric field directed along a positive x-axis. In which direction will it tend to move? Delhi 2011C Sol. Proton will tend to move along the x-axis in the direction of uniform electric field. 10. 3. A point charge q is placed at the origin. How does the electric field due to the charge vary with the distance r from the origin? Sol. The electric field varies inversely as the square of the distance from the point charge. 4. Why electrostatic field be normal to the surface at every point of a charged conductor? Delhi 2012 Sol. For the condition of electrostatics, the electric field lines must be normal to the surface of the conductor, otherwise there would be a non-zero component of electric field along the surface of conductor and charges could not be at rest. 5. An electrostatic field line is continuous curve. That is, a field line cannot have sudden breaks. Why not? Sol. An electrostatic field line cannot be a discontinuous curve, i.e. it cannot have breaks.If it has breaks, then it will indicate absence of electric field at the break points. But the electric field vanishes only at infinity. 6. Does the Coulomb force that one charge exerts on another charge, if other charge is brought nearby? Sol. Yes, it changes as the distance becomes less. Two point charges having equal charges separated by 1 m distance experience a force of 8 N. What will be the force experienced by them, if they are held in water, at the same distance? (Given, K water = 80 ) All India 2011C Two point charges system is taken from air to water keeping other variable (e.g. distance, magnitude of charge) uncharged. So, the only factor which may affect the interacting force is dielectric constant of medium. Sol. Force acting between two point charges, F= Þ Fair 1 1 q1 q2 or F µ Þ =K 2 Fmedium 4 pe 0 K r K 8 1 8 N = 80 Þ Fwater = = 80 10 Fwater 11. Why should electrostatic field be zero inside a conductor? Delhi 2012 Sol. Electric field lines do not pass through a conductor. Hence, the interior of the conductor is free from the influence of the electric field. 12. Why the electric field lines do not form closed loops? All India 2014 Sol. Because it is always directed from positive charge to negative charge. ll 16 13. The dimensions of an atom are of the order of an Angstrom. Thus there must be large electric fields between the protons and electrons. Why, then is the electrostatic field inside a conductor zero? NCERT Exemplar Sol. The electric fields find the atoms to neutral entity. As it is known that, electrostatic fields are caused by excess charges. However, there is no excess charge on the inner surface of an isolated conductor. Therefore, electrostatic field inside a conductor is zero. 14. 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 surface charge density on (i) the inner surface and (ii) the outer surface? NCERT Exemplar An uncharged, metallic ball is suspended in the region between two vertical metal plates. If the two plates are charged, one positively and one negatively, describe the motion of the ball after it is brought into contact with one of the plates. 2. The sum of two point charges is 7 mC. They repel each other with a force of 1 N when kept 30 cm apart in free space. Calculate the value of each charge. Foreign 2009 +Q of spherical cavity, as shown in the figure. Then, charge induced on the inner surface of a shell is - Q and charge induced on the outer surface of a shell is + Q. Therefore, surface charge density on -Q inner surface of shell is and on 4 pR12 +Q outer surface of shell is = . 4 pR22 R2 –Q +Q R1 16. In a fair weather condition, there is an electic field at the HOTS surface of the earth, pointing down into the ground. What is the electric charge on the ground in the situation? Sol. Electric field lines start from positive charges and end on negative charges. Thus, if the fair weather field is directed down into the ground, the ground must possess a negative charge. [2 Marks] Sol. Let one of two charges be x mC. Therefore, other charge be will be (7 - x)mC. By Coulomb’s law, F = 1 qq × 1 22 4 pe 0 r 1 = 9 ´ 10 9 ´ Sol. The two charged plates create a region with a uniform electric field between them, directed from the positive toward the negative plate. Once the ball is disturbed so as to touch one plate (say, the negative one), some negative charge will be transferred to the ball and an electric force will act on the ball, that will accelerate it to the positive plate. Once the ball touches the positive plate, it will release its negative charge, acquire a positive charge and accelerate back to the negative plate. The metallic ball will continue to move back and forth between the plates until it has transferred all their net charge, thereby making both the plates neutral. [2] Physics Class 12th Sol. When a charge +Q is placed at the centre Short Answer Type I Questions 1. ne (x ´ 10 -6) ( 7 - x) ´ 10 -6 (0.3)2 9 ´ 10 -2 = 9 ´ 10 9 - 12 x (7 - x) Þ [1] 10 = x (7 - x) \ x 2 - 7 x + 10 = 0 Þ (x - 2) (x - 5) = 0 x = 2 mC or 5mC Therefore, charges are 2mC and 5mC. [1] 3. A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 ´ 103 N/C and points radially inwards, what is the net charge on the sphere? NCERT Sol. Let the value of unknown charge be q. Electric field at 20 cm away, E = 1 .5 ´ 10 3 N/C From the formula, electric field 9 ´ 10 9 ´ q 1 q . 2 Þ 1.5 ´ 103 = E= 4 pe 0 r (20 ´ 10 - 2)2 20 cm q P E 1.5 ´ 10 3 ´ 20 ´ 20 ´ 10 -4 = 6 .67 ´ 10 -9 C 9 ´ 10 9 As, the electric field is radially inwards which shows that the nature of unknown charge q is negative. [2] q= ll ne 45 Electric Charges and Fields Miscellaneous Questions A set of questions based on the concepts of the chapter mingled with some other concepts of Physics, to assess student’s approach to Multi-disciplinary Questions 1. There are great similarities between electric and gravitational fields. A room can be electrically shielded, so that there are no electric fields in the room by surrounding it with a conductor. Can a room be gravitationally shielded? Why or why not? æ 1 ö ÷÷ = 9 ´ 10 9 N- m 2 /C2 The value of k = çç 4 pe 0 ø è The value of e (charge of an electron) = 1.6 ´ 10 -19 C The value of G (universal gravitational constant) = 6.67 ´10 -11 N-m 2 / kg 2 There are two kinds of charge in nature, but only one kind of mass. The value of me (mass of electron) = 9.1 ´ 10 -31 kg The value of mp (mass proton) = 1.67 ´ 10 -27 kg Sol. No, the electric shielding effect of conductors depends on the fact that there are two kind of charges : positive and negative. Therefore, charges can move within the conductor, so that the combination of positive and negative charges establishes an electric field which exactly cancel out the external field within the conductor and any cavities inside the conductor. There is only one type of gravitational charge, however, because there is no negative mass. As a result, gravitational shielding is not possible. The value of = where, G =gravitational constant me = mass of an electron, m = mass of a proton qq From Coulomb’s law, F = k 1 2 2 r 2 Fr Fr 2 or k = 2 Þ k= q1 q2 q æ 1 ö [MLT -2 ][L2 ] ÷÷ = The dimensions of k = çç [AT] [AT] è 4 pe 0 ø = [ML3 T -4 A -2 ] The dimensions of e (electronic charge) =[ AT ] The dimensions of G (universal gravitational [MLT -2 ] [L2 ] constant) = = [M -1L3 T -2 ] [M 2 ] The dimensions of me or mp (mass of electron or mass of proton) =[M] ke 2 [ML3 T -4 A -2 ] [A 2 T 2 ] The dimensions of = G me mp [M -1L3 T -2 ] [M 2 ] =[M 0L0 T 0 A 0 ] Thus, the given ratio is dimensionless. 9 ´ 10 9 ´ (1.6 ´ 10 -19)2 6.67 ´ 10 -11 ´ 9.1 ´ 10 -31 ´ 1.67 ´ 10 -27 = 2.29 ´ 10 39 The ratio signifies that the ratio of electrostatic force to the gravitational force is 2.29 ´ 10 39 . This means the electrostatic force between an electron and a proton is 2.29 ´ 10 39 times the gravitational force between an electron and a proton. 2. Check that the ratio ke 2 / G m e m p is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify? NCERT 2 ke Sol. In the ratio , k = 4 pe 0 (constant) Gme mp ke 2 G me mp 3. An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 ´ 104 N/C in Millikan’s oil drop experiment. The density of the oil is 1.26 g/cm 3. Estimate the radius of the drop. NCERT (g = 9.81m/s 2 ; e = 1.60 ´ 10- 19 C). Here, oil drop is held stationary under electric field that means the weight of the drop is balanced by the electrostatic force applied on it. Sol. Given, the number of excess electrons, n =12 E = 2.55 ´ 10 4 N/C r =1.26 g/cm 3 = 1.26 ´ 10 3 kg/m 3 Electronic charge, e = 1.6 ´ 10 -19 C Electric field, Density of oil, g = 9.81m/s 2 E mg Let the radius of drop be r. The electrostatic force on drop = qE = neE [Q q = ne] The gravitational force on the drop = mg [where, m = mass of the drop] = volume × density × g [QMass = Volume × Density] 4 3 = pr ´ r ´ g 3 As the drop is held stationary. So, the net force on the drop is zero. REVISION MAP Electric Charges and Fields Coulomb’s Law and Electrostatic Field Electric Charge The property of protons and electrons, which gives rise to electric force between them is called electric charge. Conductors and Insulators Conductors are those substances which conduct the electricity, whereas insulators are those substances which cannot conduct the electricity. Charging by Induction The process of charging a neutral body by bringing a charged body nearby it without making contact between the two bodies is called charging by induction. Quantisation of Electric Charge The charge on any body can be expressed as an integral multiple of basic unit of charge, i.e. charge on one electron. It can be written as q = ± ne, where n = 1, 2,... Properties of Electric Field Lines ŸElectric lines of forces start from positive charges and end at negative charges. ŸTwo field lines never intersect each other. ŸThese are perpendicular to the surface of charged conductor. ŸThese do not pass through a conductor. Coulomb’s Law The force of interaction (attraction or repulsion) between two stationary point charges in vacuum is directly proportional to the product of the charges and inversely proportional to the square of distances between them. kq q i.e. F = 1 2 r 2 Electric Flux Electric Dipole It is a pair of point charges with equal magnitude and opposite in sign separated by a very small distance. Dipole Moment It is the product of the charge and separation between the charges. i.e. p = 2aq Superposition Principle Force on any charge due to number of charges is the vector sum of all the forces on that charge due to other charges, taken one at a time. Electric Field Intensity due to an Electric Dipole [ At a point on axial line. 2kpx E = ——— (x2–l 2)2 Electrostatic Force due to Continuous Charge Distribution q l q s= A q = r v l= ; where l is a linear charge density. ; where s is a surface charge density. ; where r is a volume charge density. Electric Field It is the space around the given charge in which another charge experience an electrostatic force of repulsion or attraction. Electric Field Intensity It is the force experienced per unit positive test charge placed at that point without disturbing source charge. i.e. E = (F/q0) Electric Field Lines It is a path traversed by a test charge around the given charge. [ Gauss Theorem The surface integral of the electric field intensity over any closed surface in free space is 1 times the net charge equal to — e0 enclosed with in the surface. q fE = Šs E×d s = — e Application of Gauss Theorem ŸField due to an infinitely long [ [ kp E = ——— (x 2+l 2)3/2 straight charged wire: l E = ——— 2pe0r ŸField due to thin infinite sheet of charge: s E = ——— 2e0 [ Electric Field Intensity at Any Point due to Short Electric Dipole Electric field intensity at any point due to short electric dipole is [ Area Vector The vector associated with area element of a closed surface is taken to be in the direction of outward normal. 0 At a point on equitorial line. [ It is defined as the total number of electric lines of force passing normally through the surface. [ P Ö3cos2q+1 |E | = —————— 4pe0r 3 Dipole in a Uniform Electric Field Work done on Dipole in a Uniform Electric Field Total work done in rotating the dipole from orientation q 1 to q2 is W = PE (cos q1 – cos q2) [ [ ŸField due to a uniformly charged thin spherical shell: sR 2 Outside the shell, E = —— e0r 2 s ŸOn the surface of shell,E = — e0 Inside the shell, E = 0 Torque on an Electric Dipole in a Uniform Electric Field It is given by, t = pE sin q ŸIf q = 0°, then t = 0. The dipole is in stable equilibrium. ŸIf q = 90°, then t = PE. The torque will be maximum. ŸIf q = 180°, then t = 0. The dipole is in unstable equilibrium. Self Assessment Sheet 8 A point charge causes an electric flux Very Short Answer Type 1 The electric field induced in a dielectric when placed in an external field is 1/10 times the electric field. Calculate relative permittivity of the dielectric. [Ans. 10 times] 2 “Electrostatic forces are much stronger than the gravitational forces”. Give one example to justify this statement? 3 Give one difference between the conductors and insulators? 4 Electric charge is additive in nature. Explain? 5 A metallic solid sphere is placed in a uniform electric field as shown below. 10 Two identical metallic spherical shells 1 1 2 2 3 3 4 4 (a) + + + + + – – – – – of - 3 ´ 10 4 N-m 2 /C to pass through a spherical Gaussian surface. (i) Find the value of the point charge. [Ans. 2 .6 ´ 10 -7 C] (ii) If the radius of the Gaussian surface is doubled, how much flux would pass through the surface? 9 Two charged conducting spheres of radii r1 and r2 connected to each other by a wire. Find the ratio of electric fields at the surfaces of the two spheres. E A and B having charges + 4 Q and - 10Q are kept a certain distance apart. A third identical uncharged sphere C is first placed in contact with sphere A and then with sphere B, then spheres A and B are brought in contact and then separated. Find the charge on the spheres A and B. 11 What is the use of Gaussian surface? 4 4 Also, mention the importance of Gauss theorem 12 Deduce the expression for the electric (b) Which path is followed by electric field lines? 6 Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge (q) and the other an equal negative charge by friction. Is three masses after charging equal? field E due to a system of two charges q1 and q 2 with position vectors r1 and r2 at a point r with respect to a common origin. 13 S1 and S 2 are two parallel concentric spheres enclosing charges Q and 2Q as shown. Short Answer Type I S2 7 Two small identical dipoles AB and CD, each of dipole moment p are kept at an 2Q S1 Q D P 120° P A B C angle of 120° as shown in the figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field (E) directed along + X-direction, what will be the magnitude and direction of the torque acting on this? (i) What is the ratio of the electric flux through S1 and S 2 ? [Ans. 1/3] (ii) How will the electric flux through the sphere S1 change, if a medium of dielectric constant 5E0 is introduced in the space inside S1 in place of air? [Ans. Q /5e ] 0 18 An early model for an atom considered it to Short Answer Type II have a positively charged point nucleus of charge Ze, surrounding by a uniform density of negative charge upto a radius R. The atom as a whole is neutral. For this model, what is the electric field at a distance r from the nucleus? Assuming, r > R. 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. (i) What is the surface charge density on the (a) inner surface, (b) outer surface of the shell? (ii) Write the expression for the electric field at a point X > R2 from the centre of the shell. é Ze æ 1 1 öù ç 2 - 2 ÷ú ê Ans. 4pe 0 è r R øû ë 19 Total charge – Q is uniformly spread along length of a ring of radius R. A small test charge + q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring. (a) Show that the particle executes a simple harmonic oscillation. (b) Obtain its time period. 15 A large plane sheet of charge having surface charge density 5 ´ 10 -6 C/m 2 lies in XY -plane. Find the electric flux through a circular area of radius 0.1 m, if the normal to the circular area makes an angle of 60° with Z-axis. (Take, e 0 = 8.85 ´ 10 -12 C 2 /Nm 2 ) [Ans. 4.44 ´ 103 Nm 2 /C] 20 The electric field components in figure are EX = ax1/ 2 , EY = EZ = 0, in which a = 800 N/C m 1/ 2 . Calculate (a) the flux through the cube and (b) the charge within the cube. Assume that a = 01 . m. 16 Consider a region bounded by conical Y surface as shown in the figure. a E Ù nR Ù nL a a X q a l Z Long Answer Type r In this region, E is in vertical upward direction, then find the electric field when electric flux is passing through curved surface? [Ans. E ´ pr 2 ] 17 What is meant by continuous charge distribution? How do you apply superposition principle to obtain total force on a point charge due to n discrete charges and three continuous charge distribution? 21 (i) Define electric flux and write its SI unit. (ii) Using Gauss’ law, prove that electric current at a point due to a uniformly charged infinite plane sheet is independent of the distance from it. (iii) How is the field directed if, (a) the sheet is positively charged (b) negatively charged? 22 Find the electric field intensity at a point due to thin uniformly charged sheet having charge density s using Gauss’ theorem. CBSE Examinations Archive Collection of Questions Asked in CBSE Examinations held in Last 3 Years from 2014-2012 Very Short Answer Type Questions [1 Mark] Short Answer Type II Questions [3 Marks] 1 Two equal balls having equal positive charge q coulombs are 12 A hollow cylindrical box of length 1 m and area of suspended by two insulating strings of equal length. What would be the effect on the force when a plastic sheet is inserted between the two? All India 2014 cross-section 25 cm 2 is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by E = 50x $i , where E is in NC -1 and x is in metre. Find Refer to Q.no. 1 on page 15. 2 Why do the electrostatic field lines not form closed loop? Refer to text on page 13. All India 2014 (i) Net flux through the cylinder. (ii) Charge enclosed by the cylinder. Refer to text on page 13. All India 2014 4 Two charges of magnitudes -2 Q and +Q are located at points (a, 0) and (4 a, 0) respectively. What is the electric flux due to these charges through a sphere of radius 3a with its centre at the origin? Refer to Q.no. 9 on page 36. 5 Distinguish between a dielectric and a conductor. Refer to text on page 2. Delhi 2012 6 Define dipole moment of an electric dipole. Is it a scalar or vector? Foreign 2012 Refer to text on page 23. 7 A charge q is placed at the centre of a cube. What is the electric flux passing through a single face to the cube? Refer to Q.no. 11 on page. 37. All India 2012 8 Why most electrostatic field be normal to the surface at every point of a charged conductor? Foreign 2012 Refer to Q.no. 4 on page 15. 9 An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of 4 3 Nm. Calculate the potential energy of the dipole, if it has charge ± 8 nC. Delhi 2014 Refer to Q.no. 5 on page 29. 10 An electric dipole is held in a uniform electric field. (i) Show that the net force facing on it is zero. (ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180°. All India 2012 11 Calculate the amount of work done in rotating a dipole, of dipole moment 3 ´ 10-8 cm, from its position of stable equilibrium to the position of unstable equilibrium, in a uniform electric field of intensity 103 N / C. Foreign 2011 Refer to text on page 27. O X 1m Z Refer to Q.no. 4 on page 42. 13 State Gauss’ law in Y electrostatics. A cube with each side A is kept in an electric field given X by E = Cx $i , (as in a a shown in the figure) where C is a positive Z dimensional constant. Find out (i) the electric flux through the cube and (ii) the net charge inside the cube. Foreign 2012 Refer to Q.no. 3 on page 41. Long Answer Type Questions [5 Marks] Short Answer Type Questions [2 Marks] Refer to text on page 26 and 27. Delhi 2014 Y 3 Why do the electric field lines never cross each other? 14 Using Gauss’ law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point (i) outside and (ii) inside the shell. Plot a graph showing variation of electric field as a function of r > R and r < R. (r being the distance from the centre of the shell). All India 2013 Refer to text on page 35. 15 (i) Define electric flux. Write its SI units. (ii) Using Gauss’ law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it. (iii) How is the field directed if (a) the sheet is positively charged, (b) negatively charged? (i) Refer to text on page 32. (ii) and (iii) Refer to text on page 34. Delhi 2012 Sample Question Paper 1 (Fully Solved) Physics A Sample Question Paper for CBSE Class XII Summative Examination Time : 3 hrs Max. Marks : 70 General Instructions 1. All questions are compulsory. There are 26 questions in all. 2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E. 3. Section A contains five questions of one mark each, Section B contains five questions of two marks each, Section C contains twelve questions of three marks each, Section D contains one value based question of four marks and Section E contains three questions of five marks each. 4. There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all the three questions of five marks weightage. You have to attempt only one of the choices in such questions. 5. You may use the following values of physical constants wherever necessary. c = 3 ´ 108 m/s; h = 6 .63 ´ 10-34 Js; e = 1.6 ´ 10-19 C; m0 = 4p ´ 10-7 TmA-1; e 0 = 8 .854 ´ 10-12 C 2N-1m-2 ; 1 = 9 ´ 109 Nm2C-2 ; me = 9 .1 ´ 10-31 kg; mass of neutron = 1.675 ´ 10-27 kg; 4pe0 mass of proton = 1.673 ´ 10-27 kg; Avogadro’s number = 6023 . ´ 1023 per gram mole; Boltzmann constant = 1.38 ´ 10-23 JK -1 1. If an oil drop of weight 3.2 ´ 10 -13N is stationary in an electric field of 5 ´ 105 V/m, then find the charge on oil drop. 2. A carbon resistor is marked in coloured bands of red, black, orange and silver. What is the resistance and the tolerance value of the resistor? 3. What is the resistance offered by the capacitance to DC? 4. A concave mirror is held in water. What should be the change in focal length of the mirror? 5. Identify the parts X and Y in the following block diagram of a generalised communication system X Transmitter Y Receiver Sample Question Papers Section A ll 542 ne Physics Class 12th Section C Section B 6. Apply Kirchhoff’s laws to the loops ACBPA and 11. (i) An electrostatic field line is a continuous curve, ACBQA to write the expressions for the currents I1, I 2 and I 3 in the network. i.e. a field line cannot have sudden breaks. Why not? + (ii) Explain why two field lines never cross each other at any point? 6V – P (iii) A proton is placed in a uniform electric field directed along the positive X-axis. In which direction will it tend to move? 0.5 W I1 A B 12. (i) A current is set up in a long copper pipe. Is there I2 I3 Q + – 10 V a magnetic field (a) inside, (b) outside the pipe? 1W (ii) Figure shown below shows a bar magnet M falling under the gravity through an air cored coil C. C 12 W M Circuit diagram of loops S N 7. The frequency of oscillation of the electric field vector of a certain electromagnetic wave is 5 ´ 10 4 Hz. What is the frequency of oscillation of the corresponding magnetic field vector and to which part of the electromagnetic spectrum does it belong? or Show that linear magnification of an image formed by a curved mirror may be expressed as, m= f f-v = f-u f where, letters have their usual meanings. 8. Draw suitable graphs to show the variation of photoelectric potential for current with collector plate Sample Question Papers (i) a fixed frequency but different intensities I1 > I 2 > I3 of radiation. (ii) a fixed intensity but different frequencies f1 > f2 > f3 of radiation. 9. For what kinetic energy of a neutron, will be associated by the de-Broglie wavelength be 1.32 ´ 10 -10 m? Given that mass of a neutron = 1675 . ´ 10 -27 kg. C V (a) Plot a graph showing variation of induced emf (E ) with time ( t ). (b) What does the area enclosed by the E-t curve depict? or On a smooth plane inclined at 30°° with the horizontal, a thin current carrying metallic rod is placed parallel to the horizontal ground. The plane is located in a uniform magnetic field of 0.15 T in the vertical direction. For what value of current can the rod stationary? The mass per unit length of the rod is 0.03 kg m -1. 13. Does the current in an AC circuit lag, lead or remain in phase with the voltage of frequency ( f ) applied to the circuit, when (ii ) f < fr (iii) f > fr , (i ) f = fr where fr is the resonant frequency? 14. (i ) Two slits are made 1 mm apart and the screen is 10. A carrier wave of peak voltage 12 V is used to placed 1 m away. What is the fringe separation, when blue-green light of wavelength 500 nm is used. transmit a message signal. What should be the peak voltage of the modulating signal, in order to have a modulation index 75%? (ii ) What should the width of each slit be to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern? ll ne Sample Question Paper 1 15. Three light rays, A red (R), green (G ) and B blue (B ) are incident G R on a right angled 45° prism ABC at face AB. B C The refractive indices Light rays are of the material of the incident on a prism for red, green right angled and blue wavelengths prism ABC are 1.39, 1.44 and 1.47 respectively. Out of the three, which colour of ray will emerge out of face AC? Justify your answer. Trace the path of these rays after passing through face AB. 16. A beam of light, consisting of two wavelengths 560 nm and 420 nm, is used to obtain interference fringes in a Young’s double-slit experiment. Find the least distance from the central maximum, where the bright fringes due to both the wavelengths coincide. The distance between the two slits is 4.0 mm and the screen is at a distance of 1.0 m from the slits. 17. Calculate the binding energy per nucleon 543 20. Sketch the graph, showing the variation of stopping potential with frequency of incident radiation for two photosensitive material A and B having threshold frequencies v 0 ¢ and n 0 respectively ( v 0 ¢ > v 0 ). (i) Which of the two metals, A or B has higher work function? (ii) What information do you get from the slope of the graphs? (iii) What does the value of the intercept of graph it on the potential axis represent? 21. The diagram given below represents the block diagram of a generalised communication system. Identify the elements labelled as X, Y and Z in this diagram. Explain the function of each of these elements. Information Message source signal X Y Z Message User signal 22. Give the circuit diagram of a common emitter amplifier, using an n-p-n transistor. Draw the input and output waveforms of the signal. Write the expression for its voltage gain? Section D 40 nucleus given 20 Ca 40 m( 20 Ca ) = 39.962589 u 23. Physics teacher Mr. Sharma conducts viva-voice for mn = 1.008665 u, mp = 1.007825 u (take, 1 amu = 931 MeV). 18. The electron in a given Bohr orbit has a total energy of -1.5 eV. Find (i) its kinetic energy (ii) potential energy (iii) wavelength of light emitted, when the electron makes a transition to the ground state. (take, E g = - 13.6 eV) board practical and asks the following two questions from every student. (i) Why a potentiometer be preferred over a voltmeter for measurement of emf of a cell? (ii) Why should a six wire potentiometer be preferred over a three wire potentiometer? The student A who could not answer many questions was teacher ward. However another student B answered following questions correctly do not belong to teacher ward. Mr. Sharma award full marks to student B. 19. In the figure given below, circuit symbol of Answer the following questions on the basis of given informations. a logic gate and two input waveforms A and B are shown. (ii) Write the answer of the questions asked by Mr. Sharma. (i) Which values are displayed by Mr. Sharma? A Y B Circuit symbol Section E 24. Find an expression for the torque acting on an electric A B Input waveform (i) Name the logic gate. (ii) Write its truth table. (iii) Give the output waveform. dipole placed in uniform electric field. A system of two charges, qA = 2.5 ´ 10 -7 C and qB = 2.5 ´ 10 -7 C located at points A(0, 0, - 15 cm) and B(0, 0, + 15 cm) respectively. Find the electric dipole moment of the system and the magnitude of the torque acting on it, when it is placed in a uniform electric field 5 ´ 10 4 NC -1, making an angle 30°. or Sample Question Papers of ll 544 A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, what will happen to (i) (ii) (iii) (iv ) (v) (ii) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency. (iii) Determine the rms potential drop across the three elements of the circuit. 26. Show that the refractive index of the material 25. Explain with the help of a neat and labelled diagram, the principle, construction and working of a transformer. or ( A + dm ) 2 æAö sinç ÷ è2ø sin of a prism is given by m = where the symbols have their usual meanings. The given circuit diagram shows a series L-C-R circuit connected to a variable frequency 230 V source. 80 mF Physics Class 12th (iv ) How do you explain the observation that the algebraic sum of the voltage across the three elements in (C ) is greater than the supplied voltage? charge stored by the capacitor? potential difference across it? field strength between the plates? energy stored by the capacitor? capacitance of the capacitor? 5.0 H ne 40 W or Define the term resolving power of an astronomical telescope. How does, it get affected on (i) increasing the aperture of the objective lens? (ii) increasing the wavelength of light used? 230 V (i) Determine the source frequency which derives the circuit in resonance. (iii) increasing the focal length of the objective lens? SOLUTIONS 1. Weight of drop, W = 3.2 ´ 10 -13 N Electric field, 5 E = 5 ´ 10 V/m W 3.2 ´ 10 -13 = E 5 ´ 10 5 = 6.4 ´ 10 -19 C \ Charge on oil drop, q = Sample Question Papers 2. According to colour code of carbon resistor, a carbon resistance of bands red and black having figures 2 and 0. The third band of orange having multiplier 10 3 . \ The value of resistance is given by R = 20 ´ 103 W But the fourth band having silver colour, which represents a tolerance of ±10% . Hence, the value of carbon resistor R = 20 ´ 103 W ´ 10% 3. We know that, capacitive reactance is XC = 1 2pf C For DC, frequency, f C = 0 i.e. XC = ¥ Therefore, resistance offered by capacitance to DC is infinite. 4. No change in focal length as focal length of mirror ( f ) is independent of medium and depends only on radius of curvature (R). R f= Q 2 5. X part is information and Y part is medium or channel. 6. Apply Kirchhoff’s Ist law, I3 = I1 + I 2 Applying Kirchhoff’s IInd law to loop ACBPA -12 I3 - 0 .5 I1 + 6 = 0 0 .5 I1 + 12 I3 = 6 Applying Kirchhoff’s IInd law to loop ACBQA -12 I3 - 1I 2 + 10 = 0 I 2 + 12 I3 = 10 7. For electromagnetic waves, frequency of electric field vector and magnetic field vector is same. \ Frequency, v = 5 ´ 104 Hz CBSE Examination Paper 2015 (Delhi) Physics Max. Marks : 70 Time : 3 hrs General Instructions 1. All questions are compulsory. There are 26 questions in all. 2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E. 3. Section A contains five questions of one mark each, Section B contains five questions of two marks each, Section C contains twelve questions of three marks each, Section D contains one value based question of four marks and Section E contains three questions of five marks each. 4. There is no overall choice. However, an internal choice has been provided in one question of two marks, one question of three marks and all the three questions of five marks weightage. You have to attempt only one of the choices in such questions. 5. You may use the following values of physical constants wherever necessary. c = 3 ´ 108 m/s; h = 6 .63 ´ 10-34 Js; e = 1.6 ´ 10-19 C; m 0 = 4p ´ 10-7 TmA-1; e 0 = 8 .854 ´ 10-12 C 2N-1m-2 ; 1 = 9 ´ 109 Nm2C-2 ; me = 9 .1 ´ 10-31 kg; mass of neutron = 1.675 ´ 10-27 kg; 4pe0 mass of proton = 1.673 ´ 10-27 kg; Avogadro’s number = 6023 . ´ 1023 per gram mole; -23 -1 Boltzmann constant = 1.38 ´ 10 JK Section A 1. Define the term ‘Self-inductance’ of a coil. Write its SI unit? Sol. Self Inductance is the property of a coil by virtue of which, the coil opposes any change in the strength of the current flowing through it by inducing an emf in itself. (1/2) The SI unit of self-inductance is henry. (1/2) Since, the blue colour has shorter wavelength than red. So, it is scattered much more strongly. Hence, sky looks (1) blue. 3. I-V graph for a metallic wire at two different temperatures, T1 and T2 is as shown in the figure. Which of the two temperature is lower and why? T1 2. Why does bluish colour predominate in a clear sky? T2 I Sol. Blue colour of the sky is due to scattering of light from atmosphere’s particles. Light of shorter wavelength is scattered more than the light of longer wavelength. V ll 592 Sol. Consider the figure, ne Physics Class 12th Sol. (i) Size of the antenna T1 1 T2 2 I V Since, slope of 1>slope of 2. R1 < R2 (1/2) Þ Also, we know that resistance is directly proportional (1/2) to the temperature. therefore, T2 >T1 4. Which basic mode of communication is used for telephonic communication? Sol. Point to point is a basic mode of communication. Which is used for telephonic conversation. In this mode of communication, communication takes place over a link between a single transmitter and a receiver. (1) 5. Why do the electrostatic field lines not form the closed loops? Sol. Electrostatic field lines are discontinuous curves. They start from a positively charged body and end at a negatively charged body. No electric lines of force exist inside the charged body. Thus, electrostatic field lines do (1) not form any closed loops. 8. Use Kirchhoff’s rules to determine the potential difference between the points A and D. When no current flows in the arm BE of the electric network shown in the figure. 3W F E 1V Section B D R1 R 6. Which an electron in hydrogen atom jumps from the third excited state to the ground state, how would the de-Broglie wavelength associated with the electron change? Justify your answer. h h = p mv h hr nh or mvr = = or, mv = l l 2l 2p 2pr or, l= ´ hr = n nh 2 As, r µn 1 Þ l µ (n 2 ) = n n l l 3 Thus we can say that 3 = or l1 = 3 3 l1 1 Since, an antenna is needed both for transmission and reception. Each antenna should have a size comparable to the wavelength of the signal. for an EM wave of frequency 20 kHz, wavelength is 15 km. 15 \ length of antenna = km = 3.75 km. 4 It is an obvious that such a long antenna is not possible. Hence, antenna length can be made reasonable, if the frequency is high. So, there is a need to convert low frequency signal in to high (1/2) frequency signal before transmission. (ii) Effective power radiated by an Antenna Power P radiated from linear antenna of length l is 2 1 proportional to æç ö÷ . èlø Hence, antenna length can be made reasonable, if the frequency is high. So, there is a need to convert low frequency signal in to high frequency signal before transmission. (1) 2W 3V A 6V C B 4V Sol. Consider the given figure, Sol. We know that l = F I 3W 1V I E D R1 R 2W (1/2) Thus wavelength decreases 3 times as an electron jumps from third excited state to the ground state. (1/2) 7. Write two factors which justify the need of modulating a low frequency signal in to high frequencies before transmission? I 3V I A 6V B I C 4V Applying Kirchhoff’s IInd law in AFEBA 2 I -1+3 I - 6 = 0 [Since, no current flows in the arm BE of the circuit] 7 …(i) 5I =7 Þ I = A 5 Applying Kirchhoff’s IInd law in mesh AFDCA 3 I +RI - 4 - 6 +2 I -1= 0 …(ii) 5 I + RI = 11 ll ne CBSE Examination Paper 2015 (Delhi) Now, substitute the vales of I from equation (i) to (ii), we get 7R 7 7 = 11 5 ´ + R ´ = 11 Þ 7 + 5 5 5 7R 20 Þ = 4 Þ R = W. (1) 5 7 For PD across A and D, along AFD 7 7 VA - ´ 2 + 1 - 3 ´ = VD 5 5 21 14 VA - - 1 - = VD 5 5 14 21 Þ VA - VD = + - 1 5 5 (1) (VA - VD ) = 7 - 1 = 6 V 9. You are given two converging lenses of focal length 1.25 cm and 5 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and eyepiece. or A small telescope has on objective lens of focal length 150 cm and eyepiece of focal length 5 cm. What is the magnifying power of the telescope for viewing distance objects in normal adjustments. If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the tower formed by the objective lens. Sol. Given, F 0 = 1 . 25 cm, Fe = - 5 cm Magnification, M = 30, D= 25 cm Q If the objective is very close to the principal focus of the objective and the image formed by the objective is very close to eyepiece, then Magnifying power of a microscope is given by, 1 D 1 25 (1) Þ 30 = M= - × × f 0 fe 1 .25 5 1.25 ´ 30 ´ 5 25 ´ 30 Þ L= Þ L= 25 ´ 100 100 30 Þ L= Þ L= 7.5 cm 4 This is a required separation between the objective and (1) the eye piece. or When final image is at D, f æ f ö then magnifying power, M = 0 ç1 + e ÷ fe è Dø In normal adjustment, M = - f0 fe 593 For telescope, Focal length of objective lens, f 0 = 150 cm focal length of eye lens, f e = 5 cm when final image forms at D = 25 cm -f æ f ö \ Magnification, M = 0 ç1 + e ÷ fe è Dø 5ö -150 æ ç1 + ÷ 5 è 25 ø -150 6 = ´ 5 5 Þ M = - 36 Let height of final image be h cm. h tanb = Þ 25 b = Visual angle formed by final image at eye. a = Visual angle subtended by object at objective. 100m 1 tana = = 3000m 30 tanb But, M= tana æhö ç ÷ è 25 ø h Þ -36 = Þ -36 = ´ 30 1 25 æ ö ç ÷ è 30 ø 6h -36 ´ 5 -36 = Þ h= Þ 5 6 h = - 30 cm = (1) (1) 10. Calculate the shortest wavelength in the Balmer series of hydrogen atom. In which region (infra-red, visible, ultraviolet) of hydrogen spectrum does this wavelength lie? Sol. Since, we know that for Balmer series, æ1 1 1ö = R ç 2 - 2 ÷ , n 2 = 3, 4, 5, ..... l è2 n2 ø (1) for shortest wavelength in Balmer series, the spectral series is given by, n1 = 2 ,n 2 = ¥ 1 1 ö æ1 Þ =Rç 2 - 2 ÷ è2 l ¥ ø 1 1 1 R 4 =R´ Þ = Þ l= Þ l 4 l 4 R 4 [Q R = 1. 097 ´ 10 -7 m -1 ] l= 7 1097 . ´ 10 Þ l = 3.64 ´ 10 -7 m. The lines of Balmer series are found in the visible part of the spectrum. (1) ll 594 relaxation time of charge carriers in a conductor. A conductor of length L is connected to a d.c. source of emf ‘E’. If the length of the conductor is tripled by stretching it, keeping ‘E’ constant, explain how its drift velocity would be affected. 11. Calculate the potential difference and the energy stored in the capacitor C 2 in the circuit shown in the figure. Given potential at A is 90 V. C1 = 20 mF, C 2 = 30 mF, C 3 = 15 mF. A C2 Physics Class 12th 12. Find the relation between drift velocity and Section C C1 ne Sol. + C2 E F = –eE h – Sol. Consider the given figure, 20 mF 30 mF 15 mF V A C1 C2 C3 Let V be the potential difference applied across the ends of a conductor of length (l), then the magnitude of electric field is V E= (1) l Given, C1 = 20 mF, C 2 = 30 mF, C3 = 15 mF Potential at A = 90 V As, we can see that capacitor C3 is earthed, therefore, potential across C3 will be zero. Since, capacitor C1 , C 2 and C3 are connected in series, 1 1 1 1 therefore, = + + C eq C1 C 2 C3 1 1 1 1 = + + C eq 20 30 15 3+2+ 4 1 = Þ C eq 60 The direction of electric field is from positive to negative end of conductor as shown in the above figure. Since, the charge on an electron is -e and each free electron in the conductor experiences a force (F). F = - eE Acceleration of each electron is given by, - eE F [Qfrom Newton’s second law, a = ] a= m m 60 1 9 = Þ C eq = 9 C eq 60 20 mF 3 Since, charge remains same in series combination, 20 So, Q = C eq V Þ Q = ´ 90 3 Þ Q = 600 mC Þ Q = 600 ´ 10 -6 C Þ C eq = Þ Q = 6 ´ 10 -4 C \Potential difference across C 2 = Q C2 Þ V2 = Þ V2 = Þ V2 = 0 .2 ´ 10 2 Q V2 6 ´ 10 -4 30 ´ 10 -6 Þ V2 = 20 V Also, energy stored in capacitor l 2 is given by 1 E = C 2V22 2 1 E = ´ 30 ´ (20) 2 ´ 10 -6 Þ 2 1 Þ E = ´ 30 ´ 400 ´ 10 -6 2 Þ E = 6000 ´ 10 -6 Þ E = 6 ´ 10 -3 J (1) (1) At any instant of time, the velocity acquired by electron having thermal velocity (V1 ) is givne by V1 = u1 + at1 where, t1 is the time elapsed. Similarly, V2 = u 2 + at 2 , ...Vn = u n + at n \ Average velocity, Vd = V1 + V2 + ... + Vn (u + at1 ) + (u 2 + at 2 ) + ... + (u n + at n ) = 1 n (u1 + u 2 + ... + u n ) a (t1 + t 2 + ... + t n ) = + n n (u1 + u 2 + ... + u n ) We know that, =0 n t + t 2 + ... + t n is called the average relaxation and 1 n time. It’s value is of the order of 10 -14 second. V d = 0 + at eE V d = at Þ V d = - t m Negative sign shows that Vd is opposite to the direction of E . eE \ Average drift velocity, V d = t m (1) This is a required relation between drift velocity and relaxation time of the charge carriers in a conductor. (1) ll ne CBSE Examination Paper 2015 (Delhi) The conductor connected to d.c. source of emf E is shown in the figure alongside. Conductor E Suppose initial length of the conductor, l 2 = l 0 . New length l f = 3l 0 We know that drift velocity Vd µ E 0 (Electric field) (V d ) f (E 0 ) f E/ lf Thus, = = (V d )i (E 0 ) i E/ li = Thus (V d ) f = li l 0 1 = = lf 3l 0 3 (V d )i 3 Thus drift velocity decreases three times. (1) 13. State clearly how an unpolarised light get linearly polarised, when passed through a polaroid. (i) Unpolarised light of intensity I 0 is incident on a polaroid P1 which is kept near polaroid P2 whose pass axis is parallel to that of P1. How will the intensities of light, I1 and I 2 transmitted by the polaroids P1 and P2 respectively, change on rotating P1 without disturbing P2? (ii) Write the relation between the intensities I1 and I 2. Sol. (i) Angle with planes of transmission = q Unpolarised light Polarised light 595 When polarizer and analyzer are perpendicular to each other other, q = 90° Þ cos q = cos 90° = 0 (1) Þ I=0 In unpolarised light, vibrations are probable in all the direction in a plane perpendicular to the direction of propagation. Therefore, q can have any value from 0 and 2p. 1 2p \ [cos 2 q] av = ò cos 2 q dq 2p 0 1 2p (1 + cos 2q) dq = ò 2p 0 2 2p sin2 q ù 1 é = + 0 2 úû 0 2p ´ 2 êë 1 Þ [cos 2 q] av = 2 using law of Malus, I = I 0 cos 2 q 1 1 I = I0 ´ = I0 Þ (1) 2 2 As, per the question, I 0 is the intensity of incident unpolarised light and I1 and I 2 are the intensities of polaroids P1 , and P2 respectively, then we can say that when unpolarised light of intensity I o get polarised on passing through a polaroid P1 its I (1) intensity become half i.e. I1 = 0 2 (ii) and when this polarised light of intensity I1 passes through polaroid P2 , then its intensity will be given by, I 2 = I1 cos 2 q This is a required relation between intensities I1 and (1) I 2. 14. Define modulation index. Why is its value kept, in Intensity = I0 Polariser P1 Intensity I0 I1= — 2 Polorised E cos2 q Intensity = I0 — P2 2 I2= I1 cos2 q According to law of Malus, when a beam of completely plane polarised light is incident on an analyser, the resultant intensity of light (I ) transmitted from the analyzer varies directly as the square of the cosine of angle q between the plane of transmission of analyzer and polarizer. i.e. I µ cos 2 q Þ I = I 0 cos 2 q When polarizer and analyzer are parallel, q = 0° or 180°. So that cosq = ± 1 Þ I = I0 practice, less than one? A carrier wave of frequency 1.5 mHz and amplitude 50 V is modulated by a sinusoidal wave of frequency 10 kHz producing 50% amplitude modulation. Calculate the amplitude of the AM wave and frequencies of side bands produced. Sol. Amplitude modulation index is the ratio of the modulating signal to the maximum amplitude of carrier wave. Am It is given by, m = Ac Since, the amplitude modulation index (m) determines the quality of the transmitted signal. When modulation index is small, variation in carrier amplitude will be small. Therefore, audio signal being transmitted will be weak. ll 596 As the modulation index increases, the audio signal on reception becomes clearer. (1) Given, frequency of carrier wave, n c = 1.5 mHz = 1500 kHz frequency of sinusoidal (modulated) wave, n m = 10 kHz Amplitude of carrier wave, Ac = 50 V. 50 1 = 100 2 Modulation Index (m) = 50% Þ QModulation index, m = Am Ac 1 Am = 2 50 A m = 25 V Þ Þ (1) So, the amplitude of AMwave, A m = 25 V. As, we know, the side bands are USB = n c + n m = 1500 + 10 = 1510 kHz LSB = n c - n m = 1500 - 10 = 1490 kHz Physics Class 12th mV^2 = qV^ B r from equation (i) and (ii), we get V^2 m V m = qV^ B Þ ^ = r r qB 2pV^ m T= Þ qB × V^ 2pm T= Bq …(ii) and (1) Distance moved by the particle along the magnetic field in one rotation (pitch of the helix path) = VII ´ T [QVII = Vparallel ] 2pm = Vcos q ´ Bq 2pmV cos q (1) P= qB 16. (i) Determine the value of phase difference between the current and the voltage in the given series L-C-R circuit These are the required frequencies of the side bands (1) produced. 15. A Uniform magnetic field B is set up along the positive x-axis. A particle of charge ‘q’ and mass ‘m’ moving with a velocity v enters the field at the origin in X-Y plane such that it has velocity components both along and perpendicular to the magnetic field B. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation. Sol. ne R=400 W C=2 mF V=V sin(1000t+f) ° L=100 mH (ii) Calculate the value of additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity. Sol. (i) Consider the given figure, R=400 W y B V^=V sin q L=100 mH V x VII=Vcosq z The path of the charged particle will be helix. As, the charge moves linearly in the direction of the magnetic field with velocity V cosq and also describe the circular path due to velocity V sinq. Time taken by the charge to complete one circular 2pr rotation, T= (1) V^ f = qV^ B C=2 mF V=V sin(1000t+f) ° …(i) Since, the alternating emf in the above L-C-R series circuit would be represented by V = V0 sin(1000 t + f) Þ w = 1000 Hz Given, R = 400 W, C = 2mF, L= 100 mH 1 Q Capacitive reactance, X C = wC 1 XC = Þ 1000 ´ 2 ´ 10 -6 103 2 Þ X C = 500 W Q Inductive reactance, X L = wL Þ XC = (1) ll ne Þ CBSE Examination Paper 2015 (Delhi) X L = 1000 ´ 100 ´ 10 -3 Þ X L = 100 W So, we can see that X C > X L Þ tan f is negative Hence, the voltage lags behind the current by a phase angle f. The A.C. circuit is capacitance dominated circuit. X - XC Q phase difference, tan f = L R 100 - 500 -400 Þ tan f = tan f = 400 400 æpö tan f = - 1 Þ tan f = - tanç ÷ è 4ø -p Þ f= 4 This is the required value of the phase difference between the current and the voltage in the given (1) series L-C-R circuit. As, cos f < 1 (ii) Suppose new capacitance of the circuits is C¢ . Thus, to have power factor unity R cos f¢ = 1 = 2 R + (X L - X C¢ ) 2 R2 = R2 + (X L - X C¢ ) 2 1 1 or, or, w L = X L = X C¢ = wC ¢ w C¢ 1 1 or, (1000) 2 = or, w2 = [Q w = 1000] LC¢ LC¢ 1 1 or, C¢ = = 6 L ´ 10 100 ´ 10 -3 ´ 10 6 10 1 = 6 = 5 = 10 -5 10 10 or, C¢ = 10 -5 F = 10 ´ 10 -6 F = 10mF As, C¢ > C. Hence we have to add an additional capacitor of capacitance 8 mF (10mF- 2mF) in parallel with previous capacitor. (1) or, 597 While dealing with the charging of a parallel plate capacitor with varying current. It was found that ampere’s circuital law is not logically consistent, because òB × d l has not the same value on the two sides of a plate of charged capacitor. The inconsistency of ampere’s circuital law was removed by Maxwell by predicting the presence of displacement current in the region between the plates of capacitor, when the charge on the capacitor is changing with time. So, displacement current is the missing term (which is related with the changing electic field which passes through the surface (1) between the plates of capacitor). In this way, Maxwell pointed out that for consistency of ampere’s circuital law, there must be displacement current I D along with the conduction current in the closed loop as (I + I D ) has the property of continuity. (1) 18. Use Huygen’s principle to show how a plane wave front propagates from a denser to rarer medium. Hence, verify Snell's law of refraction. Sol. According to Huygen’s principle (i) Each point on the given wave front (called primary wave front) is the source of a secondary disturbance (called secondary wavelets) and the wavelets emanating from these point spread out in all the (1) directions with the speed of the wave. (ii) A surface touching these secondary wavelets, tangentially in the forward direction at any instant gives the new wavefront at that instant. This is called secondary wave front. A1 A A2 A2 A A1 1 1 S æ d fE ö ÷ dt ø (1) Propagation of 3 light wave New 4 wavefront New wavefront (Spherical) B B B plane 2 1 (a) (b) N¢ N 3 in wa cid ve en fro t nt 2 1 X Medium 1 Medium 2 B Rarer Medium V1, m1 E i i F Y r Denser Medium V2, m2 r G ed ct nt fra fro Re ave w òB × d l = m 0 (I + I D ) = m 0 çè1 + e 0 3 Propogation of wavefront ampere’s circuital law. Discuss its significance and describe briefly how the concept of displacement current is explained through charging/discharging of a capacitor in an electric circuit. by Maxwell states that 2 B2 4 B B1 17. Write the expression for the generalised for of Sol. The generalised form of ampere’s circuital law, modified 2 1¢ 3¢ 2¢ ll 598 If V1 , V2 are the speed of light in to two mediums and t is the time taken by light to go from B to C or A to D or E to EF FG G through F, then t = + V1 V2 EF In DAFE, sini = AF AF sini FC sinr FG In DFGC, sinr = + Þ t= V1 V2 FC amplifier. Briefly explain its working and write the expression for (i) current gain, (ii) voltage gain of the amplifier. Sol. Circuit diagram of a C.E. transistor amplifier IC C IB p-n-p VCE IE So, t should not depend on F. This is possible only, if sini sinr sini V1 = 0 or = =m V1 V2 sinr V2 Now, if C represents the speed of light in vacuum, then C C are known as the refractive index m1 = and m 2 = V1 V2 of medium and medium 2 respectively. m1 sini = m 2 sinr Þ m = sini sinr This is known as Snell’s law of refraction. (1) 19. Identify the gates P and Q shown in the figure. Write the truth table for the combination of gates shown. A P B Q X Y Name the equivalent gate representing this circuit and write its logic symbol. Sol. Consider the given figure, A P B Q X Y P is AND gate and Q is a NOT gate. Truth Table B X X=Y 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 B VCC + – + VBE Output AC signal IB IC (1) Working The emitter-base circuit is forward biased by a low voltage battery VBE , that means the resistance of input circuit is small. The collector-emitter circuit is reversed biased by a high voltage battery VCC , that means the resistance of the output circuit is high. RL is a load resistance connected in collector-emitter circuit. The weak input AC signal is applied across the base-emitter circuit and the amplified output is obtained across the collector emitter circuit. When no AC voltage is supplied to the input circuit, we have …(i) IE = IB + IC Due to collector current I C , the voltage drop across the load resistance (RL) is I C RL. Therefore, the collector emitter voltage VCE is given by, …(ii) VCE = VCC - I C RL when the input AC voltage signal is applied across the base-emitter circuit, it changes base-emitter voltage and hence, emitter-current I E changes which in turn changes the collector current I C . So, the collector-emitter voltage VCE varies in the accordance with equation (ii). (1) Current gain and Voltage gain of amplifier I (i) D.C. Current gain, b DC = C IB æDI ö AC current gain, b AC = ç C ÷VCE è DIB ø (1) The equivalent gate representing this circuit is NAND gate. Its logic symbol is A Input AC signal IC – This variation in VCE appears as an amplified output. (1) A R2 E For rays of light from the different parts on the incident wave front, the values of AF are different. But light from different points of the incident wave front should take the same time to reach the corresponding points on the refracted wave front. Then, Physics Class 12th 20. Draw a circuit diagram of a C.E. transistor æ sini sinr ö AC sinr t= + AF ç ÷ è V1 V2 V2 ø Þ ne Y=A.B (1) D I c ´ Rout D I b ´ Rin D I c Rout = ´ DIb Rin (ii) AC voltage gain, AV = (1) ll CBSE Examination Paper 2015 (Delhi) ne 21. (i) Write three characteristic properties of nuclear force. (ii) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the graph. Sol. (i) Characteristics properties of nuclear force (a) Nuclear forces act between a pair of neutrons, a pair of protons and also between a neutron-proton pair, with the same strength. This, shows that nuclear forces are independent of charge. (b) The nuclear forces are dependent on spin or angular momentum of nuclei. (c) Nuclear forces are non-central forces. This shows that the distribution of nucleons in a nucleus is not spherically symmetric. (1) Potential energy (Mev) (ii) 100 0 –100 r01 2 r (fm) 3 (Potential energy versus distance) (1) From the plot, it is concluded that (i) The potential energy is minimum at a distance r0 (» 0.8 f m) which means that the force is attractive for distances larger than 0.8 Fm and repulsive for the distance less than 0.8 Fm between the nucleons. (ii) Nuclear forces are negligible, when the distances between the nucleons is more than 10 Fm. (1) 22. (i) Describe briefly three experimentally observed features in the phenomenon of photoelectric effect. (ii) Discuss briefly how wave theory of light cannot explain these features. or (i) Write the important properties of photons which are used to establish Einstein’s photoelectric equation. 599 (ii) Use this equation to explain the concept of (a) threshold frequency and (b) stopping potential. Sol. (i) Three experimentally observed features in the phenomenon of photoelectric effect. (a) Intensity When intensity of incident light increases as one photon ejects one electron, the increase in intensity will increase the number of ejected electrons. Frequency has no effect on photoelectron. (b) Frequency when the frequency of incident photon increases, the kinetic energy of the emitted electrons increases. Intensity has no effect on kinetic energy of photoelectron. (c) No time lag When energy incident photon is greater than the work function, the photoelectron is immediately ejected. Thus, there is no time lag between the incidence of light and emission of photoelectron. (½ ´ 3) (ii) These features cannot be explained on the wave number of light because wave nature of radiation cannot explain the following. (a) The instantaneous ejection of the photoelectrons. (b) The existence of threshold frequency for a metal surface. (c) The fact that kinetic energy of the emitted electrons is independent of the intensity of light and depends upon its frequency. (½ ´ 3) or (i) Important properties of photon’s which are used to establish Einstein’s photoelectric equations. (a) In interaction of radiation with matter, radiation behaves as, if it is made up of particles called photons. hc ö æ (b) Each photon has energy E ç = hv = ÷ and è lø æ hv hc ö momentum p ç = = ÷ , where c is the è c lø speed of light h is planck’s constant, v and l are frequency and wavelength of radiation respectively. (c) All photons of light of a particular frequency v or wavelength l have the same energy hc ö æ æ hv h ö E ç = hv = ÷ and momentum p ç = - ÷ è è c lø ø l whatever the intensity of radiation may be. (½ ´ 3) (ii) Since, Einstein’s photoelectric equation is given by, 1 2 K × E max = mv max = hv - hf0 2 ll 600 (a) For a given material, there exist a certain minimum frequency of the incident radiation below, which no emission of photoelectron takes place. This frequency is called threshold frequency. Above threshold frequency, the maximum kinetic energy of the emitted photoelectron or equivalent stopping potential is independent of the intensity of the incident light but depends only upon the frequency of the incident light. (1½) (b) If the collecting plate in the photoelectric apparatus is made at high negative potential, then most of the high energetic electrons get repelled back along the same path and the photoelectric current in the circuit becomes zero. So, for a particular frequency of incident radiation, the minimum negative potential for which the electric current becomes zero, is called cutoff or stopping potential. (1½) Section D 23. One morning an old man walked bare-foot to replace the fuse wire in kit kat fitted with the power supply mains for his house. Suddenly he screamed and collapsed on the floor. His wife cried loudly for help. His neighbour’s son Anil heard the cries and rushed to the place with shoes on. He took a wooden baton and used it to switch off the main supply. Answer the following questions (i) What is the voltage and frequency of mains supply in India? (ii) These days most of the electrical devices we use require AC voltage. Why? (iii) Can a transformer be used to step up DC voltage? (iv) Write two qualities displayed by Anil by his action. Sol. (i) In India, the voltage and frequency mains supply is (1) 220 V and 60 Hz respectively. (ii) Since, the power loss at 220 V supply is less that at 110 V. So due to this reason, most of the electrical (1) devices require AC voltage. (iii) Since, the transformer requires an alternating magnetic flux to operate correctly, transformers cannot therefore be used to transform or supply DC voltages or currents. Also, the magnetic field must be changing to induce a voltage in the secondary winding. ne Physics Class 12th Even if in case, the transformers primary winding is connected to a DC supply, the inductive reactance of the winding. Would be zero as DC has no frequency. So, the effective impedance of the winding will therefore be very low and equal only to the resistance of the copper used. Thus, the winding will draw a very high current from the DC supply causing it to overheat and eventually burnout, V (1) because as we know I = . R (iv) Anil is very helpful and has a great presence of mind as in such condition, he used the wooden baton to (1) switch off the main supply. Section E 24. (i) Define electric flux. Write its SI unit. “Gauss’s law in electrostatics is true for any closed surface, no matter what its shape or size is.” Justify this statement with the help of a suitable example. (ii) Use Gauss’s law to prove that the electric field inside a uniformly charged spherical shell is zero. or (i) Derive the expression for the energy stored in parallel plate capacitor. Hence obtain the expression for the energy density of the electric field. (ii) A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than stored initially in the single capacitor. Sol. (i) Electric flux over an area in an electric field represents the total number of electric field lines crossing the area. The SI unit of electric flux is Nm 2C -1 . According to Gauss’s law in electrostatics, “The surface integral of electrostatic field E produced by any sources over any closed surface S enclosing a volume V in vacuum, i.e. total electric flux over the closed surface S in vacuum, is 1/ e 0 times the total charge (q) contained inside S, i.e. q f E = ò E .ds = e0 S ‘‘Gauss’s law in electrostatics is true for an closed surface, no matter what its shape or size is.’’ So, In order to justify the above statement, suppose in isolated positive charge q is situated at the centre O of a sphere of radius r.