HKAL Extra Exercise : Part 4 Electricity and Electromagnetism

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, (1) The ball always carries negative supported by insulating stands are placed charges. side by side but not touching each other. A (2) If the separation of the metal plates student places a positively-charged rod decreases, the frequency of near sphere A and he touches sphere B oscillation of the ball decreases. with his finger. After the rod is removed, (3) The galvanometer shows a current, he moves his finger away from the sphere. sometimes positive, and sometimes What are the signs of the charges induced negative. on the spheres ? A. (1) only Sphere A Sphere B B. (3) only A. positive neutral C. (1) and (2) only B. negative neutral D. (1), (2) and (3) C. neutral positive D. neutral neutral 3.

2. insulating thread A light conducting sphere is hanged from a long insulating thread between - oppositely charged metal plates connected source of to a high voltage supply. If the sphere is high voltage G given a positive charge, it will + A. oscillate, touching each plate in A conducting ball is suspended between turn, beginning with the negative plate. two metal plates connected through a B. oscillate, touching each plate in sensitive centre-zero galvanometer to a turn, beginning with the positive plate. source of high p.d. The ball shuttles back C. move to the positive plate and and forth between the plates, making stick to it. alternate contacts with each plate. Which D. move to the negative plate and of the following statements is/are stick to it. 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

4 3 IV III v X Y 1 II I 2 E E A particle carrying a positive charge is The diagram shows an electron in a free to move in a uniform electric field E. uniform, vertical electric field E. At the If the particle starts with a certain velocity instant shown, the electron is traveling in from point X, which of the paths shown the direction of the arrow v. Which of the could represent the route which the arrows 1 to 4 gives the direction of the particle would follow from X to Y? acceleration of the electron at this instant? A. II only A. 1 B. I and II only B. 2 C. III and IV only C. 3 D. I, II, III and IV D. 4

HKAL Extra Exercise Chapter 13 Electrostatics 2/10 8. The straight lines in the diagram represent 9. electric field lines. Which of the following Y statements about this electric field is/are INCORRECT ? P Q X In the above figure the solid lines represent part R of an electric field due to a fixed point charge (1) A stationary positive charge placed at Q ( not shown in the figure). A charged particle Q tends to move to P. q, subjected only to electric force in the field, (2) Work has to be done in moving a travels along the dotted curve shown. Which of positive charge from P to R. the following conclusions can be drawn ? (3) The electric field strength at P is A. q is travelling from Y to X. stronger than that at Q. B. q has a greater speed at Y than at X. A. (1) only C. The electric potential at X due to Q is B. (3) only higher than that at Y. C. (1) and (2) only D. The charge of q has different sign as D. (1), (2) and (3) that of Q.

13.3 Coulomb’s Law E due to a Point Charge E due to a Circle of Charge 10. 11.

+Q q P2 W X 4b

Z Y +Q -Q

Three charges +Q, -Q and +Q are fixed at P1 the corners W, Y and Z respectively of a b b b square as shown. A fourth charge, q, is fixed at X, after which the charge at X A uniformly charged wire has the form of

experiences a NET electrostatic force a circular loop of radius b. P1 and P2 are

indicated by the arrow. q is equal to two points on the axis of the loop. P1 is at

A. -Q. a distance b from the loop centre and P2 is B. -2Q. at a distance 5b from the loop centre. At

C. - 2 Q. P1, P2, the potentials are V1, V2

D. -2 2 Q. respectively. V1 / V2 is equal to A. 13 . B. 17 / 2 . C. 3. D. 5.

HKAL Extra Exercise Chapter 13 Electrostatics 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) 3Q 3Q2 3Q2 A. zero B. C. D. 2 20 r 20 r 2 0 r

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.

At steady state, which of the following descriptions is/are correct ? (1) Sphere X gains electrons. (2) Sphere Y loses electrons. (3) Sphere X acquires a positive electric potential. (4) 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) A. (1) only of a Zn+2 ion is 5.1 × 106 C/kg. A dry cell B. (3) only with a zine anode has an e.m.f. of 2.17 V. C. (1) and (2) only When the cell drives a current round a D. (2) and (3) only circuit, zinc is removed from the anode. Assuming that the system is a perfectly 18. efficient converter of energy, what is the H electrical energy produced per kg of zinc ? Y vertical A. 0.43 J B. 1.1 MJ X C. 2.43 MJ D. 11 MJ A potential difference V is maintained 17. Which of the following statements about between plates X and Y, separated by a the coulomb is/are correct? distance h. A particle of mass m and (1) When one coulomb of charge flows negative charge -q enters the region across a potential difference of one between X and Y through the hole H with volt, 103 joule of energy is released. negligible velocity. If it makes no (2) 1 coulomb is the charge on 1 mole of collisions on the way, it will strike X with electrons. kinetic energy. (3) The force exerted on a charge of 1 A. mgh. B. qV + mgh. coulomb in an electrostatic field of 1 C. qV - mgh. D. mgh – qV. volt/metre is 1 newton.

Potential due to a Point Charge

19. Which of these statements concerning 20. How do the two physical quantities below electric potential is correct? change along the direction indicated by an A. Potential is a scalar quantity. electric field line from a point positive B. The potential at a point is charge ? proportional to the gradient of (1) electric field intensity E the strength of the electric field (2) potential V at that point. A. Only E will increase C. The potential due to a point B. Both E and V will increase charge varies as 1/r2, where r is C. Both E and V will decrease the distance from the point D. Both E and V will remain charge. constant D. The potential is zero whether the electric field is zero. 21.

A B C D

HKAL Extra Exercise Chapter 13 Electrostatics 5/10 A, B, C and D are four points on a straight following statements is/are correct ? line as shown. A point charge –Q is fixed (1) The two charges +q are at the same at A. When another point charge +Q is potential. moved from B to C, which of the (2) The work done in bringing the two following quantities will increase ? charges +q from infinity to their (1) The magnitude of the electric field respective positions is the same. strength at the point D. (3) The potential energy of the system (2) The electric potential energy of the would increase if d decreases. system of charges. A. (1) only B. (3) only (3) The electric potential at the point D. C. (1) and (2) only A. (1) only B. (3) only D. (2) and (3) only C. (2) and (3) only 24. D. (1), (2) and (3) - q a +2 q 22. a a -particle electron a The above diagram shows a α-particle +2 q - q and an electron moving directly away Four particles carrying charges +2q, +2q, from each other with the same speed. -q and -q are placed at the vertices of a Which of the following statements is/are square of side a. The electric potential at correct ? the center of the square is (1) The two particles repel one another.  2q  2q (2) The total momentum of the two A. B. 2 a  a particles remains constant in the 0 0 subsequent motion.  2q  2q (3) The electric potential energy of the C. D. 2 a  a two particles is decreasing at the 0 0 instant shown. A. (1) only B. (2) only 25. The electric potential energy of a system C. (1) and (3) only of charges at infinitely large distances D. (1), (2) and (3) from one another is taken to be zero. What 23. is the electric potential energy stored in a system of three charges, each of +1 C, + q + q + Q placed at the vertices of a equilateral d d triangle with length of side 1 m ? (  o = In the above arrangement, two small test permittivity of vacuum) charges +q are brought from infinity to the 3 1  1  A. B. 2   positions shown. The two charges are o  o  2  collinear with another charge +Q and their 1 3 C. D. mutual separation is d. Which of the 2o 4o

HKAL Extra Exercise Chapter 13 Electrostatics 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 -6 carries a positive charge of 10 C. A a b particle P of mass 4 × 10-5 kg carrying a negative charge of 10-8 C is released from B A rest at a distance of 0.5 m from the center of the sphere. If the force due to gravity is A negatively-charged metal sphere A of neglected, the velocity of P when it strikes radius a is joined by a conducting wire to the surface of the sphere will be an uncharged metal sphere B of radius b A. 3.3 m/s. placed far away from the first sphere. The B. 4.6 m/s. ratio of the total surface charge on sphere C. 13.5 m/s. A to that on sphere B is D. 21.0 m/s. A. b / a . B. a/b. C. b/a. D. a2/b2. 27. A metal sphere is charged to a potential of 30. 300 V. If the radius of the sphere is 0.27 small hole m, find the charge density on its surface. (Given : permittivity of free space = 8.85 × 10-12 F m-1) + Q A. 1.1 × 10-9 C m-2 B. 4.9 × 10-9 C m-2 C. 8.1 × 10-9 C m-2 D. 9.8 × 10-9 C m-2 The arrangement above shows two concentric hollow metal spheres of inner 28. Which of the graphs below best represents radius b and outer radius a. A charge +Q is the variation of electrical field intensity E given to the outer sphere and the inner with distance r from the centre of a sphere is earthed. charged hollow metal sphere of external What is the work done in bringing a small radius a ? positive charge q from infinity to the A. B. surface of the inner sphere?

E E A. qQ(1/a – 1/b)/(4πε0)

B. qQ(1/b – 1/a)/(4πε0)

C. qQ/(4πε0a) a a 0 r 0 r D. qQ/(4πε0b) C. D. 31. An isolated spherical conductor of radius r E E is charged to a total charge of Q. The total electrical energy stored is 2 2 A. Q / (8πε0r). B. Q / (4πε0r). a a 2 2 0 r 0 r C. Q × 2πε0r. D.Q × 4πε0r.

HKAL Extra Exercise Chapter 13 Electrostatics 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. C. D.

E E E E

0 V 0 V 0 V 0 V

Electric Field and Potential 33. 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 Y X Z potentials at Y and at Z ? Potential at Y Potential at Z A. - 150 V 0 V The diagram shows a pattern of electric B. - 250 V 0 V field lines in which X, Y and Z are points C. - 550 V - 750 V marked on one of the field lines. It would D. - 600 V - 750 V be correct to say that (1) a positive charge placed at Z would 35. X, Y are two different points in an electric accelerate to the right along the field. A small charged object is released tangent to the field line at Z. from rest at X. Which of the following (2) X is at a higher potential than Z. conditions would ensure that the charged (3) the force exerted on a charge at Z object will NOT pass through Y ? would be greater than if the charge A. The electric potential at X is were placed at X. stronger than that at Y. A. (1) only B. (1) and (2) only B. The electric field at Y is stronger C. (2) and (3) only than that at X. D. (1), (2) and (3) C. The electric potentials at X and Y are equal. 34. D. The electric potential at Y is zero.

The figure shows a pattern of electric field

HKAL Extra Exercise Chapter 13 Electrostatics 8/10 36. Two insulated parallel metal plates are D. (2) and (3) only connected to the terminals of an EHT. 37. Two parallel plates are connected to an When a charged aluminium foil strip is E.H.T. of 2.0 kV. Electric breakdown placed between the plates, deflection of occurs when the separation of the plates is the foil is observed as shown. reduced to 1.2 mm. Estimate the polystyrene maximum acceleration of an electron metal rod metal between the plates.(Given : charge of an plate plate electron = 1.6 × 10-19 C; mass of an -31 aluminium electron = 9.1 × 10 kg) 9 -2 foil strip A. 2.0 × 10 m s B. 4.2 × 1011 m s-2 EHT + - C. 3.7 × 1015 m s-2 Which of the following statements is/are D. 2.9 × 1017 m s-2 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

Equipotential Surface 38. - 100 V X Y - 200 V Z - 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) 39. Which of the following statements about equipotential lines is incorrect ?

HKAL Extra Exercise Chapter 13 Electrostatics 9/10 A. They are closest where the field is strongest. B. They are always perpendicular to electric field lines. C. The electric field strength is the same at the same equipotential line. D. 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