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Transcript
HKAL Extra Exercise : Part 4 Electricity and Electromagnetism Chapter 13 Electrostatics 13.1 Electric Charges : Charging Object 1. Two uncharged metal spheres, A and B, supported by insulating stands are placed side by side but not touching each other. A student places a positively-charged rod near sphere A and he touches sphere B with his finger. After the rod is removed, he moves his finger away from the sphere. What are the signs of the charges induced on the spheres ? Sphere A Sphere B A. positive neutral B. negative neutral C. neutral positive D. neutral neutral (1) The ball always carries negative charges. (2) If the separation of the metal plates decreases, the frequency of oscillation of the ball decreases. (3) The galvanometer shows a current, sometimes positive, and sometimes negative. A. (1) only B. (3) only C. (1) and (2) only D. (1), (2) and (3) 3. 2. insulating thread A conducting ball is suspended between two metal plates connected through a sensitive centre-zero galvanometer to a source of high p.d. The ball shuttles back A light conducting sphere is hanged from a long insulating thread between oppositely charged metal plates connected to a high voltage supply. If the sphere is given a positive charge, it will A. oscillate, touching each plate in turn, beginning with the negative plate. B. oscillate, touching each plate in turn, beginning with the positive plate. C. move to the positive plate and and forth between the plates, making alternate contacts with each plate. Which of the following statements is/are stick to it. D. move to the negative plate and stick to it. source of high voltage G + INCORRECT? HKAL Extra Exercise Chapter 13 Electrostatics 1/10 13.2 Electric Fields Electric Field Strength 4. Two parallel metal plates are placed horizontally with a separation of 0.20 m. A p.d. V is connected across the plates. An oil drop with a charge of –1.6 × 10-19 C and mass 8.0 × 10-17 kg is observed to remain at rest between the plates. (Assume g = 10 m/s2.) The p.d. V is A. 10 V. B. 100 V. C. 1 kV. D. 5 kV. 5. A stationary charged particle is accelerated across the gap between two parallel metal plates maintained at a certain potential difference in a vacuum. Assuming there is no gravitational force, the speed acquired by the charged particle in crossing the gap depends on (1) the mass of the charged particle. (2) the potential difference between the plates. (3) the charge of the charged particle. A. (1) only B. (1) and (2) only C. (2) and (3) only D. (1), (2) and (3) Motion of a charge in a uniform E-field 6. 7. 4 3 IV v X III II 1 2 The diagram shows an electron in a uniform, vertical electric field E. At the instant shown, the electron is traveling in the direction of the arrow v. Which of the arrows 1 to 4 gives the direction of the acceleration of the electron at this instant? A. 1 B. 2 C. 3 D. 4 HKAL Extra Exercise Chapter 13 Electrostatics I E Y E A particle carrying a positive charge is free to move in a uniform electric field E. If the particle starts with a certain velocity from point X, which of the paths shown could represent the route which the particle would follow from X to Y? A. B. C. D. II only I and II only III and IV only I, II, III and IV 2/10 8. The straight lines in the diagram represent electric field lines. Which of the following 9. Y statements about this electric field is/are INCORRECT ? P X Q R (1) A stationary positive charge placed at Q tends to move to P. (2) Work has to be done in moving a positive charge from P to R. (3) The electric field strength at P is stronger than that at Q. A. (1) only B. (3) only C. (1) and (2) only D. (1), (2) and (3) 13.3 Coulomb’s Law E due to a Point Charge 10. +Q q W In the above figure the solid lines represent part of an electric field due to a fixed point charge Q ( not shown in the figure). A charged particle q, subjected only to electric force in the field, travels along the dotted curve shown. Which of the following conclusions can be drawn ? A. B. C. q is travelling from Y to X. q has a greater speed at Y than at X. The electric potential at X due to Q is higher than that at Y. The charge of q has different sign as that of Q. D. E due to a Circle of Charge 11. P2 4b X Z +Q Y -Q Three charges +Q, -Q and +Q are fixed at the corners W, Y and Z respectively of a square as shown. A fourth charge, q, is fixed at X, after which the charge at X experiences a NET electrostatic force indicated by the arrow. q is equal to A. -Q. B. -2Q. C. D. - 2 Q. -2 2 Q. P1 b b b A uniformly charged wire has the form of a circular loop of radius b. P1 and P2 are two points on the axis of the loop. P1 is at a distance b from the loop centre and P2 is at a distance 5b from the loop centre. At P1, P2, the potentials are V1, V2 respectively. V1 / V2 is equal to A. C. HKAL Extra Exercise Chapter 13 Electrostatics 13 . 3. B. D. 17 / 2 . 5. 3/10 12. Six identical point charges, each of charge Q, are fixed evenly on a circle of radius r. How much work has to be done to bring another point charge Q from infinity to the centre of the circle ? (ε0 = permittivity of free space) A. zero B. 3Q 20 r C. 3Q 2 20 r D. 3Q 2 20 r 2 E on the surface of a Uniform Conductor 13. An uncharged metal sphere is placed in a uniform electric field. Which of the following best represents the electric field pattern around the metal sphere ? A. B. C. D. 13.4 Electric Potential Potential 14. Which of the following pairs of physical quantities is/are both vectors ? (1) electric force and electric field intensity (2) pressure and force (3) mass and gravitational potential A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only 15. Two insulated uncharged metal spheres X and Y are in contact with each other. A positively charged rod is brought near X without any contact while sphere X is earthed as shown. X Y At steady state, which of the following descriptions is/are correct ? (1) (2) (3) (4) Sphere X gains electrons. Sphere Y loses electrons. Sphere X acquires a positive electric potential. Sphere Y acquires a positive electric potential. A. (1) only B. (1) and (2) only C. (1) and (3) only D. (1), (2), (3) and (4). HKAL Extra Exercise Chapter 13 Electrostatics 4/10 Potential Difference 16. The specific charge (charge per unit mass) of a Zn+2 ion is 5.1 × 106 C/kg. A dry cell with a zine anode has an e.m.f. of 2.17 V. When the cell drives a current round a circuit, zinc is removed from the anode. Assuming that the system is a perfectly efficient converter of energy, what is the electrical energy produced per kg of zinc ? A. 0.43 J B. 1.1 MJ C. 2.43 MJ D. 11 MJ A. (1) only B. C. D. (3) only (1) and (2) only (2) and (3) only 18. H Y vertical X A potential difference V is maintained 17. Which of the following statements about the coulomb is/are correct? (1) When one coulomb of charge flows across a potential difference of one volt, 103 joule of energy is released. (2) 1 coulomb is the charge on 1 mole of electrons. (3) The force exerted on a charge of 1 coulomb in an electrostatic field of 1 volt/metre is 1 newton. between plates X and Y, separated by a distance h. A particle of mass m and negative charge -q enters the region between X and Y through the hole H with negligible velocity. If it makes no collisions on the way, it will strike X with kinetic energy. A. mgh. B. qV + mgh. C. qV - mgh. D. mgh – qV. Potential due to a Point Charge 19. Which of these statements concerning electric potential is correct? A. Potential is a scalar quantity. B. The potential at a point is proportional to the gradient of the strength of the electric field at that point. C. D. The potential due to a point charge varies as 1/r2, where r is the distance from the point charge. The potential is zero whether the electric field is zero. 20. How do the two physical quantities below change along the direction indicated by an electric field line from a point positive charge ? (1) electric field intensity E (2) potential V A. Only E will increase B. C. D. 21. A HKAL Extra Exercise Chapter 13 Electrostatics Both E and V will increase Both E and V will decrease Both E and V will remain constant B C D 5/10 A, B, C and D are four points on a straight line as shown. A point charge –Q is fixed following statements is/are correct ? (1) The two charges +q are at the same at A. When another point charge +Q is moved from B to C, which of the following quantities will increase ? (1) The magnitude of the electric field strength at the point D. (2) The electric potential energy of the system of charges. (3) The electric potential at the point D. A. (1) only B. (3) only C. (2) and (3) only potential. (2) The work done in bringing the two charges +q from infinity to their respective positions is the same. (3) The potential energy of the system would increase if d decreases. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only D. (1), (2) and (3) 24. a -q +2 q 22. a -particle electron The above diagram shows a α-particle and an electron moving directly away from each other with the same speed. Which of the following statements is/are correct ? (1) The two particles repel one another. (2) The total momentum of the two particles remains constant in the subsequent motion. (3) The electric potential energy of the two particles is decreasing at the instant shown. A. (1) only B. (2) only C. (1) and (3) only D. (1), (2) and (3) 23. +q +q d a +Q d In the above arrangement, two small test charges +q are brought from infinity to the positions shown. The two charges are collinear with another charge +Q and their mutual separation is d. Which of the HKAL Extra Exercise Chapter 13 Electrostatics +2 q a -q Four particles carrying charges +2q, +2q, -q and -q are placed at the vertices of a square of side a. The electric potential at the center of the square is A. 2q 2 0 a B. 2q 0 a C. 2q 2 0 a D. 2q 0 a 25. The electric potential energy of a system of charges at infinitely large distances from one another is taken to be zero. What is the electric potential energy stored in a system of three charges, each of +1 C, placed at the vertices of a equilateral triangle with length of side 1 m ? ( o = permittivity of vacuum) A. C. 3 1 2 B. D. 1 1 2 o 2 3 4 6/10 Potential due to a Metal Sphere 26. Permittivity of free space = 8.85 × 10-12 29. F/m. A conducting sphere of radius 0.15 m carries a positive charge of 10-6 C. A particle P of mass 4 × 10-5 kg carrying a a negative charge of 10-8 C is released from rest at a distance of 0.5 m from the center of the sphere. If the force due to gravity is neglected, the velocity of P when it strikes the surface of the sphere will be A. 3.3 m/s. B. 4.6 m/s. C. D. A. C. 28. Which of the graphs below best represents the variation of electrical field intensity E with distance r from the centre of a charged hollow metal sphere of external radius a ? A. B. 0 E a r C. 0 a r D. E 0 A negatively-charged metal sphere A of radius a is joined by a conducting wire to an uncharged metal sphere B of radius b placed far away from the first sphere. The ratio of the total surface charge on sphere A to that on sphere B is 8.1 × 10-9 C m-2 9.8 × 10-9 C m-2 E E a r B A 13.5 m/s. 21.0 m/s. 27. A metal sphere is charged to a potential of 300 V. If the radius of the sphere is 0.27 m, find the charge density on its surface. (Given : permittivity of free space = 8.85 × 10-12 F m-1) A. 1.1 × 10-9 C m-2 B. 4.9 × 10-9 C m-2 C. D. b 0 a HKAL Extra Exercise Chapter 13 Electrostatics r b/a . b/a. B. D. a/b. a2/b2. 30. small hole +Q The arrangement above shows two concentric hollow metal spheres of inner radius b and outer radius a. A charge +Q is given to the outer sphere and the inner sphere is earthed. What is the work done in bringing a small positive charge q from infinity to the surface of the inner sphere? A. qQ(1/a – 1/b)/(4πε0) B. C. D. qQ(1/b – 1/a)/(4πε0) qQ/(4πε0a) qQ/(4πε0b) 31. An isolated spherical conductor of radius r is charged to a total charge of Q. The total electrical energy stored is A. Q2 / (8πε0r). B. Q2 / (4πε0r). C. Q2 × 2πε0r. D.Q2 × 4πε0r. 7/10 32. Which of the following graphs shows correctly the relationship between the energy E stored in an isolated conducting sphere and the potential V at the surface of it ? A. B. E 0 C. E V 0 E V 0 Electric Field and Potential 33. X Y D. Z The diagram shows a pattern of electric field lines in which X, Y and Z are points marked on one of the field lines. It would be correct to say that (1) a positive charge placed at Z would accelerate to the right along the tangent to the field line at Z. (2) X is at a higher potential than Z. (3) the force exerted on a charge at Z would be greater than if the charge were placed at X. A. (1) only B. (1) and (2) only C. (2) and (3) only D. (1), (2) and (3) 34. E V V 0 lines in which X, Y and Z are points marked on one of the field lines with XY = YZ. If the potential at X is -400 V, which of the following can give the possible potentials at Y and at Z ? Potential at Y Potential at Z A. - 150 V 0V B. - 250 V 0V C. - 550 V - 750 V D. - 600 V - 750 V 35. X, Y are two different points in an electric field. A small charged object is released from rest at X. Which of the following conditions would ensure that the charged object will NOT pass through Y ? A. The electric potential at X is stronger than that at Y. B. The electric field at Y is stronger than that at X. C. The electric potentials at X and Y are equal. D. The electric potential at Y is zero. X Y Z The figure shows a pattern of electric field HKAL Extra Exercise Chapter 13 Electrostatics 8/10 36. Two insulated parallel metal plates are connected to the terminals of an EHT. 37. Two parallel plates are connected to an E.H.T. of 2.0 kV. Electric breakdown When a charged aluminium foil strip is placed between the plates, deflection of the foil is observed as shown. occurs when the separation of the plates is reduced to 1.2 mm. Estimate the maximum acceleration of an electron between the plates.(Given : charge of an electron = 1.6 × 10-19 C; mass of an electron = 9.1 × 10-31 kg) A. 2.0 × 109 m s-2 B. 4.2 × 1011 m s-2 C. 3.7 × 1015 m s-2 D. 2.9 × 1017 m s-2 polystyrene rod metal plate metal plate aluminium foil strip + EHT - Which of the following statements is/are true ? (1) Deflection of the foil increases if the separation between the plates increases. (2) The charge on the foil is negative. (3) When moving the foil towards the negative plate, the deflection of the foil remains unchanged. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only Equipotential Surface 38. - 100 V X Y Z - 200 V - 300 V - 400 V The diagram shows points of equal potential joined as equipotential lines. Which of the following statements is/are correct ? (1) The electric field at Z is in a direction tangential to the line passing through Z. (2) The electric field at point Y is greater than that at X. (3) Work has to be done in moving an electron from point X to point Z. A. (1) only B. (3) only C. (1) and (2) only D. (1), (2) and (3) HKAL Extra Exercise Chapter 13 Electrostatics 9/10 39. Which of the following statements about equipotential lines is incorrect ? A. They are closest where the field is strongest. B. C. D. They are always perpendicular to electric field lines. The electric field strength is the same at the same equipotential line. Work has to be done in moving a proton from a low potential line to a high potential line. Ice-pail Experiment (Gold-leaf Electroscope) 40. A gold-leaf electroscope is negatively charged. Which of the following objects when placed near the cap, will cause the leaf of the electroscope to raise ? (1) a negatively charged rod (2) a lighted match (3) an earthed metal plate A. (1) only B. (3) only C. (2) and (3) only D. (1), (2) and (3) KEY : 1 – 10 : DDACD, BCDDD, 11 – 20 : ACDCC, DBBAC, 21 – 30 : DBBCD, BDDBA, 31 – 40 : ADBDC, BDBCA. HKAL Extra Exercise Chapter 13 Electrostatics 10/10