HKAL Exercise : Part 4 Electricity and Electromagnetism

HKAL Exercise : Part 4 Electricity and Electromagnetism Chapter 16 Electromagnetism

1. Which of the following properties is NOT common to both electric and magnetic fields ? A. Both can exert attractive and repulsive forces. B. Both can be ‘shielded’ using suitable materials. C. Both can be represented by field lines of closed loops. D. Both can store energy.

16.1 Moving Charged Particles

v is perpendicular to B-field

B 8 cm o 1 cm centre of charged particles screen

The above figure shows an electron entering a uniform field which may be A beam of charged particles passes electric or magnetic. Which of the through a vacuum chamber and strikes the following descriptions about the centre of the fluorescent screen at the end subsequent motion of the electron is of the chamber. When a magnetic field B correct ? is applied in the direction shown, two A. Whether the field is electric or spots appear on the screen, one 1 cm magnetic, the speed of the above the centre, and one 8 cm above the electron will increase. centre. B. Whether the field is electric or Which of the following can be possible magnetic, the electron can be constituents of the beam? deflected by more than 90∘. A. protons and alpha particles, traveling C. Whether the field is electric or at the same speed magnetic, the force depends on B. protons traveling with speed v and the magnitude of the charge on alpha particles traveling with speed the electron. 4v D. Only in an electric field can the C. electrons and protons, traveling at the magnitude and direction of the same speed force acting on the electron are D. electrons and alpha particles, constant. traveling at the same speed

HKAL Exercise Chapter 16 Electromagnetism 1/28 4. A free electron traveling horizontally with 6. speed v enters a uniform vertical magnetic field B. Which of the following statements B out of is/are correct ? paper (1) The kinetic energy of the electron increases. A particle, of mass 9.6 × 10-26 kg and (2) The path of the electron is a vertical charge –1.6 × 10-19 C, enters a uniform circle. magnetic field of flux density 0.48 T at a (3) The radius of curvature of the path is speed of 6 × 105 m/s, as shown. It will inversely proportional to B. A. be deflected upward in a circular A. (1) only arc of radius 0.75 m. B. (3) only B. be deflected upward in a circular C. (1) and (2) only arc of radius 1.50 m. D. (2) and (3) only C. be deflected downward in a circular arc of radius 0.75 m. 5. D. be deflected downward in a circular arc of radius 1.50 m. ion source

P B Q A X Y Two particles P and Q of the same

quantity of speed and mass but moving uniform magnetic with different charges qP and qQ field (into paper) respectively enter a region of uniform magnetic field directed into the plane of Particles A and B moving at the same the paper. The subsequent circular paths speed enter a square region of uniform are as shown. Which of the following magnetic field as shown. Particle A leaves statements is/are correct ? at X while particle B leaves at Y. If the (1) The period of circular motion of P is charge to mass ratio of particle A is k, what longer than that of Q. is that of particle B ? (2) Both P and Q are negatively charged. A. 2k

(3) qP is larger than qQ. B. 4k A. (1) only C. k/2 B. (3) only D. k/4 C. (1) and (2) only D. (2) and (3) only

HKAL Exercise Chapter 16 Electromagnetism 2/28 8. In a Bainbridge mass spectrometer, an ion 10. of mass m and charge Q travels in a circular path of radius r. The path of an ion of mass 3m and charge 4Q has radius A. r/12. B. 3 r/4. The figure shows a charged particle C. 4 r/3. moving in a circle with constant speed v D. 12 r. on a plane perpendicular to a uniform magnetic field. Which of the following 9. A particle of mass m and charge q moves graphs represents the relation between the in a circular orbit in a magnetic field B. time T for the particle to complete a circle The time taken to complete a single orbit and its mass m ? is A. B. A. 2πm/(Bq). T T B. 2mq/(Bπ). C. 2π/(mBq) D. Bm/(2πq). 0 m 0 m

0 m 0 m

Moving Charged Particles in Crossed E and B Fields

11. In Thomson’s experiment, an electron is accelerated from rest through a p.d. V (not shown) and then passes without any deflection through a region with mutually perpendicular electric and magnetic fields. - Y1

The electric field is provided by the deflecting plates Y1, Y2 with p.d. V and separation d. The applied uniform magnetic field is B. The charge to mass ratio (e/m) of an electron is given by V 2V B2d 2 2B2d 2 A. . B. . C. . D. . 2B 2d 2 B 2 d 2 2V V 3

HKAL Exercise Chapter 16 Electromagnetism 3/28 12. A. (1) only B. (3) only V1 B C. (1) and (2) only e- e- V2 D. (2) and (3) only

14. cathode anode

In Thomson’s method of measuring e/m, P Q S1 S2 electrons are accelerated by a potential

difference V1, then passed undeviated A mixed stream of ions (of different through a region with a magnetic flux charges, polarities and speeds) travels density B and an electric field E. E is along PQ and passes through a narrow slit

provided by a potential difference V2 S1. In the region between S1 and S2, an

between the two plates. If V1 is increased electric field E and a magnetic field of

to 25 V1, in order for the electron beam to flux density B are directed normally to

remain undeviated, V2 must be changed to each other. The E-field acts vertically

A. 5 V2. downward and the B-field acts out of the

B. 25 V2. plane of the paper. Ions that are

C. 125 V2. undeflected and emerge from slit S2 must

D. 625 V2. have the same A. charge to mass ratio. 13. An electron travelling with velocity v B. polarity. enters a region with a uniform electric C. speed. field E and a uniform magnetic flux D. sign of charge density B. E, B and v are mutually perpendicular, as shown in the diagram. 15. A beam of charged particles passes undeflected through a region of crossed E uniform electric and magnetic fields. B into the paper Which of the following must be common to the particles making up this beam ? A. magnitude of charge v B. polarity Which of the following statements is/are C. velocity correct? D. mass (1) When E = 0, the path of the electron is circular. (2) When B = 0, the path of the electron is circular. (3) The curvature of the electron’s path is independent of v.

HKAL Exercise Chapter 16 Electromagnetism 4/28 16.2 Hall Effect C. (2) and (3) only 16. D. (1), (2) and (3) constant Hall Probe 17. In a Hall probe, the slice of semiconductor current N Q -3 24 P with thickness 1.4 × 10 m inside has 10 charge-carriers per cubic metre. When a S steady current of 0.3 A passes through the slice and a uniform magnetic field B The figure shows the essential parts of an applies perpendicularly to it, a Hall apparatus to demonstrate the Hall effect. Which voltage of 30μV is set up. Find the of the following statements is/are correct ? magnitude of B. (1) The magnitude of the Hall potential is (Given : electronic charge = 1.6 × 10-19 C) smaller if the applied magnetic flux A. 0.002 T density is increased. B. 0.007 T (2) The magnitude of the electric field due to C. 0.02 T the Hall effect is greater if the width PQ of D. 0.07 T the specimen is decreased. (3) In the arrangement above, the Hall p.d. is developed across PQ. A. (1) only B. (1) and (2) only

16.3 Magnetic Fields Magnetic Effect on a Current-carrying Conductor 18. A horizontal wire 0.3 m long carries a current of 7 A in a magnetic field of flux density 10-3 T, which dips at an angle of 50∘to the vertical. The force on the wire is A. 8.7 × 10-4 N B. 1.6 × 10-3 N C. 1.3 × 10-3 N D. 1.2 × 10-3 N Turning Effect of a Coil in a B-Field 19.

p q y I r s x

A circular loop carrying a current I is placed in a uniform magnetic field B in the xy plane as shown. If the loop is free to move, the magnetic forces will cause it to A. rotate about the y-axis as indicated by q. B. rotate about the x-axis as indicated by r. C. rotate about the x-axis as indicated by s. D. remain stationary. 20.

HKAL Exercise Chapter 16 Electromagnetism 5/28 B  I S A N X Y C D The above diagram shows a rectangular B current-carrying coil ABCD in a uniform A square coil of N turns and area A carries magnetic field between two pole pieces. a current I. The coil is free to rotate about The magnetic field is perpendicular to the the axis XY which is normal to a uniform plane of the coil. Which of the following magnetic field B. When the field makes an statements is/are correct ? angleθwith the plane of the coil, what are (1) The coil will continue to move when the magnitude and direction of the torque it is disturbed slightly. acting on the coil as detected by an (2) There is no magnetic force acting on observed by X ? the side BC of the coil. Magnitude Direction (3) The magnetic forces acting on the A. BANI cosθ clockwise coil tend to increase its area. B. BANI cosθ anticlockwise A. (1) only C. BANI sinθ anticlockwise B. (3) only D. none of the above C. (1) and (2) only D. (2) and (3) only 21.

Moving Coil Galvanometer 22. It is desired to re-design a moving coil B. (3) only galvanometer so as to make it nine times C. (1) and (2) only as sensitive. Which of the following would D. (2) and (3) only alone achieve the desired result ?

(1) Increasing the magnetic flux density 23. A ballistic galvanometer of resistance R1 is of the permanent magnet to three connected in series with a search coil of

times its value and tripling the cross- resistance R2 (the resistance of the sectional area of the coil. connecting wires is negligible). When the (2) Changing the suspension search coil is removed from a magnetic characteristics so that only one-ninth field, the charge which passes through the as great a couple is needed to cause ballistic galvanometer is proportional to

one radian twist. A. 1/R2.

(3) Providing the coil with a shunt so B. R2.

that only a one-ninth of the input C. 1/(R1 + R2).

current flows through the coil itself. D. (R1 + R2). A. (1) only

HKAL Exercise Chapter 16 Electromagnetism 6/28 24. Which of the following descriptions about sensitivity of 25 divisions per milliampere, a moving-coil meter is/are correct ? and a resistance of 5.0 ohms. What is its (1) It has curved magnetic poles to assist voltage sensitivity, in divisions per in producing linear scale. millivolt ? (2) It has weak hair springs to increase A. 0.2 B. 5 the sensitivity. C. 8 D. 40 (3) It has a massive soft iron core to provide damping. 26. A moving-coil galvanometer with a coil of A. (1) only area A and N turns has a full-scale B. (3) only deflection for a current i. If the coil were C. (1) and (2) only of area 3 A and 4 N turns, the current D. (2) and (3) only which would give full scale deflection would be 25. A galvanometer has a scale divided into A. i. B. 12i. 200 equal divisions. It has a current C. 4i/3. D. i/12.

16.4 Production of B-Field A Solenoid

27. Which of the following graphs best represents the variation of the magnetic flux density B along the axis of a long current-carrying solenoid, with the distance x from the centre of the solenoid along the axis? A. B. C. D.

B B B B

x x x x 0 0 0 0

28. Which of the following graphs correctly shows the variation of the magnetic flux density B along the axis of a long solenoid carrying a steady current with its length l ? A. B. C. D.

B B B B

0 0 0 0 l l l l

HKAL Exercise Chapter 16 Electromagnetism 7/28 29. A very long solenoid with a metallic core end of the first so as to extend it to as far has a radius r and n turns per unit length. as Y, and the same current as before is It carries a current I. The magnetic flux passed through the complete solenoid, the density B on its axis is magnetic field at Y will then be (1) independent of n. A. 5 × 10-3 T (2) independent of r. B. 9 × 10-3 T (3) independent of I. C. 14 × 10-3 T A. (1) only B. (2) only D. 16 × 10-3 T C. (1) and (2) only 32. D. (2) and (3) only magnetic  30. 500 turns of wire are wound on a solenoid north of length 0.25 m and area of cross-section 2.6 × 10-4 m2. When the solenoid carries a magnetic current of 0.4 A, the magnetic flux through Coil needle the solenoid is A tangent galvanometer has a narrow A. 6.6 × 10-8 Wb. circular coil of radius r, with N turns. B. 2.6 × 10-7 Wb. When a current I passes through the coil, C. 1.3 × 10-4 Wb. the magnetic needle, constrained to move D. 1.0 × 10-3 Wb. in a horizontal plane, sets at an angle θ to -6 (μ0 = 1.26 × 10 H/m.) magnetic north, as shown. If the flux 31. The magnetic field due to a steady current density of the earth’s magnetic field has in the long air-core solenoid (uniformly magnitude B, and the horizontal -3 wound) shown below is 2 × 10 T at X and component is Bh, then tanθ is equal to -3 7 × 10 T at Y. 2rB 0 NI A. B. 2 0 NI 2r Bh X Y  NI  NI L L C. 0 D. 0 2rBh 2rB If an identical solenoid is connected to the A Long Straight Wire 33. 1 A X 0.01 m 1 A The above figure shows two long parallel straight wires separated by a distance of 0.01 m, carrying currents of 1 A in the same direction. The magnetic field at a point X mid-way -7 -1 between the wires is (Given : permeability constant μ0 = 4π × 10 TmA ) A. 0 T. B. 4 × 10-5 T into paper. C. 4 × 10-5 T out of paper. D. 8 × 10-5 T out of paper. 34.

HKAL Exercise Chapter 16 Electromagnetism 8/28 y distance of 0.3a, as shown in the figure Q above. Each of them carries a current I flowing into or out of the plane of the x 0.3 a 0.4 a 0 paper. The y-component of magnetic density at the point R is 0.5 a R P  I A. zero. B. 0  0.50. P and Q represent two long, straight, 2a parallel, conducting wires separated by a  I  I C. 0  1.50. D. 0  4.00. distance of 0.3a, as shown in the figure 2a 2a above. Each of them carries a current I 36. flowing into the plane of the paper. The x-

component of magnetic density at the P point R is r r  I A. zero. B. 0  1.50. 2a current I out of paper current I into paper  I  I r C. 0  2.00. D. 0  4.00. 2a 2a Two long, straight parallel conducting 35. wires, each carrying a current I, are y separated by a distance r as shown. What Q is the magnetic field at a point P at the

same distance r from both wires ? (μo = x 0.3 a 0.4 a 0 permeability of free space)

o I 3o I P 0.5 a R A. upward B. upward 2r 2r P and Q represent two long, straight,  I 3 I C. o downward D. o downward parallel, conducting wires separated by a 2r 2r

Forces between Currents 37.

I2 H K I1 y

In the figure shown, MN is a fixed long conductor, carrying a current I1. HK is another

conductor perpendicular to MN. When a current I2 is allowed to pass through HK in the direction shown, the force on HK A. is zero. B. acts in the +y direction. C. acts in the -y direction. D. acts in the +x direction. 38. Two long vertical wires X and Y are at a short distance apart, and the vertical plane containing

HKAL Exercise Chapter 16 Electromagnetism 9/28 them is at right angles to the earth’s magnetic field. When each wire carries the same current I,   the force on X due to the earth’s field is Fe and force on X due to the current in Y is Fc . If the

current is now tripled in both wires, the resultant force on X is         A. Fe + Fc B. 3 Fe + 3 Fc C. 3 Fe + 9 Fc D. 9 Fe + 9 Fc

39. Two parallel wires repel each other with a force F when the same current passes through them. If the current is doubled and the distance between the wires is also tripled, the force of repulsion will then be A. 2F/9. B. 2F/3. C. 4F/3. D. F.

40. Two parallel straight conductors separated by a distance r carry currents in the same direction. Which of the following statements is/are INCORRECT ? (1) The two wires repel each other. (2) The wires produce a magnetic field with maximum flux density midway between them. (3) The force acting on each wire is inversely proportional to r2. A. (1) only B. (1) and (2) only C. (2) and (3) only D. (1), (2) and (3)

41. For two long, straight parallel conducting wires carrying the same current, the magnitude of the force acting on a section of the wires depends on (1) the magnitude of the current. (2) the distance between the wires (3) the directions of current flow in the wires A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

42. For which of the following does the force between two objects vary inversely as the square of the distance between their centres ? (1) The sun and the earth. (2) Two equal masses joined by a rubber band under tension. (3) Two long straight parallel conducting wires carrying steady electric currents. A. (1) only B. (3) only C. (2) and (3) only D. (1), (2) and (3)

HKAL Exercise Chapter 16 Electromagnetism 10/28 16.5 Electromagnetic Induction Magnetic Flux 43. Magnetic flux is measured in weber. Which of the following is/are equivalent to weber ? (1) henry-ampere (2) tesla-metre2 (3) volt-second A. (1) only B. (3) only C. (1) and (2) only D. (1), (2) and (3) 44. A length of wire is bent to form a circular coil of one turn. The coil is placed in a uniform magnetic field with its plane normal to the direction of the field. The flux linkage through the coil is ψ. The same length of wire is now bent to form a fourth loop of smaller radius. The flux linkage is now A. ψ/4. B. ψ/16. C. 4ψ. D. 16ψ. Laws of Electromagnetic Induction 45. 46. wire frame y

field A out of paper O B

A rectangular wire frame surrounds a magnetic field magnetic field out of paper into paper uniform magnetic field which is confined to a square region as shown in the Two uniform magnetic fields of equal diagram. The magnetic field is situated at magnitude but with one into paper and the the centre of the frame and is other out of paper, are separated on the two perpendicular to the plane of the paper. If sides of the y-axis as shown. A wire is bent into the frame moves to the right with a a closed loop OABO, which is shaped as a uniform velocity, which of the graphs quarter of a circle. It is rotated uniformly in a below best represents the variation of the clockwise direction about O on the plane of the induced current i with time t ? paper. Which of the following graphs best (The clockwise direction of the current is shows the variation of current, I, in the loop taken as positive.) with time, t, in one revolution ? A. B. A. B. i i I I t 0 0 t 0 t 0 t C. D. C. D. i i I I 0 t 0 t 0 t 0 t

HKAL Exercise Chapter 16 Electromagnetism 11/28 47. A rectangular coil PQRS is driven with 49. constant velocity in a direction L 2 L2 perpendicular to a uniform magnetic field S as shown. S

Q R L1 L1

S is a long, current-carrying solenoid. L1 is

a wire loop just inside the solenoid, and L2 P S is a wire loop just outside the solenoid. Which of the following statements is The current in the solenoid is increased at correct? a steady rate, such that the e.m.f. induced

A. An induced current is flowing in the in L1 is 1.4 V. The e.m.f. induced in L2 is coil in the clockwise direction. approximately B. An induced current is flowing in the A. 0.7 V. B. 1.4 V. coil in the anticlockwise direction. C. 2.8 V. D. larger than 2.8 V. C. There is no induced current flowing 50.

in the coil. loop D. The magnitude of the magnetic flux through the coil changes with time. B A 48. field uniform magnetic field The uniform magnetic field shown pointing into, and acting perpendicular to, the plane of the paper is confined to a cylindrical volume of radius 7 cm. The magnetic flux density now A circular frame and a square frame, made decreases at a constant rate of 0.02 T/s. A from the same type of insulated metal circular loop of radius 9 cm is placed so that its wires, are placed in a uniform magnetic plane is perpendicular to the magnetic field, as field as shown. When the flux density of shown. What will be the magnitude and the field is increased at a steady rate, the direction of the induced e.m.f. in the loop ? ratio of the induced current in the circular Magnitude Direction frame to that in the square frame is A. 5.09 × 10-4 V from A to B via the A. 1 : 1. loop B. 1 : π. B. 5.09 × 10-4 V from B to A via the C. 2 : π. loop D. π : 4. C. 3.08 × 10-4 V from A to B via the loop D. 3.08 × 10-4 V from B to A via the loop

HKAL Exercise Chapter 16 Electromagnetism 12/28 51. 53.

P Q N2 turns area A2 n1 turns per metre area A1

Two coaxial solenoids P and Q are arranged as A solenoid of n1 turns per metre and cross- shown. The cross-sectional areas of P and Q sectional area A1 carries a current I. It is are A1 and A2 respectively. P contains N1 turns inserted into the core of another larger while Q contains N2 turns. Q is now solenoid of N2 turns and cross-sectional connected to a power supply so that the current area A2. If the current in the smaller through it rises at a uniform rate S. The solenoid drops uniformly to zero in time t, maximum e.m.f. induced in P is what is the e.m.f. induced in the larger A. zero. solenoid ?

B. μ0N1N2A1S. A. μ0n1IA1A2/t

C. μ0N1N2A2S. B. μ0n1IA2N2/t

D. μ0N1N2A2S/L. C. μ0n1IA1N2/t

D. 2μ0n1IA2N2/t 52. A secondary coil of N turns and resistance 50 ohms is wound round the middle of a 54. long solenoid of cross-sectional area A m2 with n turns per metre carrying a current I primary coil secondary coil amperes. A ballistic galvanometer of soft iron resistance 10 ohms and sensitivity k bar divisions per coulomb is connected in Ip series with the secondary coil. Neglecting current A B source damping, how many divisions is the deflection of the galvanometer when the Two coils are linked by a soft iron bar as current in the solenoid is switched off ? shown. A current source is connected to

(μ0 = the permeability of free space in the primary coil. The primary current Ip henry per metre.) varies with time as shown by the graph  nNAIk below : A. 0 40 Ip  nNAI B. 0 40k 0 t t time  nNAIk 1 2 C. 0 60 Which of the following sketches  nNAI represents the variation of the voltage D. 0 60k across the secondary coil VAB with time ? A. B.

HKAL Exercise Chapter 16 Electromagnetism 13/28 VAB VAB VAB VAB

time time time time 0 t1 t2 0 t1 t2 0 t1 t2 0 t1 t2 C. D.

Understanding Faraday’s Law (Induced E.M.F. and Induced Current) 55. following statements is correct ? A. No current flows through R because P and Q are at the same horizontal level. A B B. An alternating current flows through R. C. A steady current flows from P to Q D C through R. D. A steady current flows from Q to P A light rectangular wire frame ABCD moves through R. with a uniform speed to the left across a region of uniform magnetic field acting out of the 57. paper. Which of the following is/are true at the P instant shown in the figure ? (1) A current is flowing in the anticlockwise direction. Q (2) The electric potential at B is lower than that at C. In the above figure, when the metal rod PQ (3) The side AD experiences a magnetic force moves with constant velocity across a uniform acting to the right. magnetic field, a p.d. is induced across the rod. A. (1) only B. (3) only Which of the following statements is/are C. (1) and (2) only D. (2) and (3) only correct ? (1) P is at a higher potential than Q. 56. (2) The magnitude of the p.d. depends on the magnetic field strength. R (3) The net force acting on the rod is zero. A. (1) only B. (3) only Z P Q C. (1) and (2) only D. (2) and (3) only uniform magnetic field into paper 58. In the above figure, a copper disc rotates P Q uniformly between the pole-pieces of a 30o powerful magnet (not shown in figure) in an v anti-clockwise direction. P and Q are metallic l brushes making contact with the axle and the R S edge of the disc respectively. Which of the

HKAL Exercise Chapter 16 Electromagnetism 14/28 A metal rod of length l is inclined at D. doubled halved 60∘to rail PQ as shown. It is moved Search Coil across a uniform magnetic field along the 60.

direction of the two horizontal rails PQ search long straight coil and RS. If the rod moves with a uniform wire carrying 3 cm 12 cm To an a.c. current CRO velocity v and the flux density of the field A B is B, the e.m.f. induced in the rod is The figure shows a long straight wire Blv Blv carrying an a.c. current which lies on the A. . B. . 2 4 plane of the paper. When a small search 4Blv 3Blv coil is placed at B such that the plane of C. . D. . 3 2 the coil is on the paper, the length of the A.C. Generator trace on the CRO is 1 cm (with the time 59. A sinusoidal voltage is generated by an base of the CRO switched off). If the a.c. dynamo. If the speed of rotation of the search coil is moved to A, the length of the dynamo is halved, what will happen to the trace would be frequency and the amplitude of the voltage A. 5 cm. B. 1 cm. formed? C. 0.5 cm. D. 0.2 cm. frequency amplitude A. halved halved B. no change no change C. doubled no change

Transformer 61.

10 cm 10 cm

Figure (a) Figure (b) A step-down transformer of turns-ratio 25 : 1 has its primary winding connected to the mains (100 Hz) and its secondary winding connected across the Y plates of an oscilloscope, with the time-base freely running. The trace observed on the screen is as shown in Figure (a). The transformer is now disconnected from the oscilloscope. With the same time base setting, a signal of unknown frequency f is connected across the Y plates, and the trace is as shown in Figure (b). The value of f is A. 80 Hz. B. 200 Hz. C. 1 250 Hz. D. 5 000 Hz. 62.

HKAL Exercise Chapter 16 Electromagnetism 15/28 primary secondary coil coil magnetic flux S

soft iron core The above diagram shows a step-down voltage transformer. Which of the The diagram shows the circuit of an ideal following is/are correct ? transformer with a load connected to the (1) The dotted line indicates the path of secondary. Which of the following is/are the magnetic field. correct at the moment when switch S is (2) The number of turns in the primary is closed ? lower than that of the secondary. (1) The primary current will increase. (3) If the terminals of the secondary coil (2) The magnetic flux in the soft iron are shortened, the primary voltage core will be increased. will increase. (3) The back e.m.f. in the primary will A. (1) only raise. B. (3) only A. (1) only C. (1) and (2) only B. (3) only D. (2) and (3) only C. (1) and (2) only D. (1), (2) and (3) only 63. Eddy Currents 64. C. D.

A large aluminium disc mounted on a 65. A magnet is moved along a perpendicular horizontal axle is spun in the clockwise direction towards a sheet of copper. Which direction between the poles of a powerful of the following statements is/are correct ? horseshoe magnet. Which of the following (1) attractive force is experienced by the diagrams shows how the eddy currents magnet. flow in the disc? (2) Eddy current flows in the sheet. A. B. (3) Temperature of the sheet increases. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

HKAL Exercise Chapter 16 Electromagnetism 16/28 D.C. Motors

66. Each of the following three students states a conclusion after learning the formulae P = IV, P = V 2 / R and P = I 2 R in electricity. Which of these conclusions is/are correct ? (1) The power dissipated by any electric appliance can be calculated from P = I 2 R. (2) The power consumed by a running motor can be calculated from P = V 2 / R. (3) The power dissipated by a kettle is independent to its resistance as P = IV. A. (1) only B. (3) only C. (1) and (2) only D. (1), (2) and (3)

67. A d.c. motor is connected to a 20 V battery. Which of the following statements is/are correct? (1) As the motor gathers speed, the torque acting on the rotating coil increases. (2) As the motor gathers speed, the current through the motor decreases. (3) If the efficiency is 25% at steady state, the back e.m.f. is then 5 V. A. (1) only B. (3) only C. (2) and (3) only D. (1), (2) and (3)

68. The armature of a d.c. electric motor has resistance 10 Ω. When the applied potential difference is 100 V, a current of 2 A flows. The back e.m.f. is A. 20 V. B. 80 V. C. 100 V. D. 120 V.

69. The mechanical power output of a d.c. motor is always less than the electrical power input. Which of the following can be an explanation of this ? (1) heat loss in the coil of the motor (2) back e.m.f. is less than the applied e.m.f. (3) work done against the back e.m.f. generated by the rotating coil A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

70. A d.c. motor is connected to a source of constant voltage V. When rotating at a steady speed, the motor draws a current I and the back e.m.f. developed in its armature coil isε. which of the following is/are correct ? (1) The mechanical power developed is Iε. (2) The resistance of the armature coil is ε/I. (3) The back e.m.f.εdecreases with the speed of rotation. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

71. An ammeter is connected in series with an electric motor which is running freely, and the reading noted. When the motor raises a load at a steady speed, the reading of the ammeter will A. increase to a higher value. B. decrease to a lower value. C. increase to a maximum value and then decrease.

HKAL Exercise Chapter 16 Electromagnetism 17/28 D. decrease to a minimum value and then increase. 72. Which of the following graphs best shows the change of current I with time t when an electric motor connected to a d.c. source is switched on? (The magnetic field is supplied by a permanent magnet.) A. B. C. D.

I I I I

0 t 0 t 0 t 0 t

73. Which of the following statements about a d.c. motor is FALSE ? A. The back e.m.f. changes the input energy into mechanical energy. B. If the motor is stopped by some obstruction, the current through the coil will increase. C. An ideal d.c. motor develops a back e.m.f. equal to the applied e.m.f. D. A single-coil motor will not start when it is switched on, if the plane of the coil is parallel to the magnetic field.

74. An additional mechanical load is applied to a rotating motor. Which of the following is/are true ? (1) The motor will decrease in speed. (2) More power will be drawn from the power supply. (3) The e.m.f. induced in the rotating coil will increase. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

75. When a simple motor rotating at a steady speed is suddenly jammed and comes to a stop, which of the following statements is/are correct ? (1) The rate of change of magnetic flux through the coil of the motor will be very small. (2) A large current will flow through the coil of the motor. (3) A large e.m.f. will be induced in the coil of the motor. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

(Structural question)

76. A simple electric motor has rectangular coil of 150 turns, each of area 0.004 m2, and of total resistance 0.5 Ω. It is connected to a 8 V d.c. supply of negligible internal resistance. The strength of the uniform magnetic field in the region of the coil is 0.4 T. Figure 76.1 shows the variation of current I with time t when the motor is switched on.

HKAL Exercise Chapter 16 Electromagnetism 18/28 I P Imax Not to scale

Figure 76. 1 Q 4.0 A C

0 t1 t

(a) (i) Estimate the maximum value of the current Imax. (2 marks)

(ii) When the motor is switched on, the current is so large that it may burn out the coil. Explain how this can be avoided. (2 marks)

(b) Explain why the current (i) does not rise immediately to its maximum value; (ii) drops gradually from P to Q and becomes steady along QC. (3 marks)

(c) (i) What is the maximum torque acting on the coil due to the current when it is rotating at constant speed ? (2 marks)

(ii) For the motor running at constant speed, calculate (I) the back e.m.f. developed across the coil; (II) its efficiency in converting electrical power to mechanical power. (4 marks)

16.6 Self Inductance 77. Which of the following combinations of physical quantities take(s) the unit of time ? (1) capacitance times resistance (2) capacitance times inductance (3) inductance times resistance A. (1) only B. (3) only C. (1) and (3) only D. (2) and (3) only

HKAL Exercise Chapter 16 Electromagnetism 19/28 78. X and Y are two long solenoids having the same length and the same cross-sectional area. They are wound on the same type of core material. X has 1 000 turns and Y has 500 turns. If the self- inductance of X is 2.0 H, the self-inductance of Y is A. 0.5 H. B. 1.0 H. C. 2.0 H. D. 4.0 H. 79. The current in a coil changes steadily from 3 A to 8 A in 30 ms so that a back e.m.f. of 4 V is induced in the coil. The self-inductance of the coil is A. 0.005 H. B. 0.024 H. C. 42 H. D. 200 H.

80. The self-inductance of an air-core solenoid can be increased by (1) placing a ferro-magnetic material inside the solenoid. (2) compressing it to a shorter length. (3) decreasing the current through it. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

LR Circuit 81. I

t A constant p.d. is applied to a solenoid. The variation of current I with time t is as shown. Which of the following can be deduced from the shape of the graph ? A. The solenoid has resistance as well as inductance. B. The e.m.f. induced in the solenoid is proportional to the current. C. The inductance of the solenoid decreases as time increases. D. The inductance of the solenoid increases as time increases. 82. coil L, R S + - V A steady potential difference V is applied across a coil with a piece of soft iron inside of inductance L and resistance R, connected to a switch S, as shown. After closing the switch S, the current increases and takes time t to reach half its steady maximum value. The time t can be shortened by (1) applying a lower potential difference to the circuit. (2) removing the piece of soft iron from the solenoid. (3) adding a resistor in series with the coil. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

HKAL Exercise Chapter 16 Electromagnetism 20/28 83. 85. R 9 V i X

Y 2 H 3  L is a pure inductor, in series with a When the switch in the circuit is closed, resistor R. The current i in the circuit is (1) the final energy stored in the inductor initially zero at time t = 0 and afterwards it is 9 J. rises linearly to reach a maximum at t = T; (2) the current will rise initially at the it then falls linearly to zero in the same rate of 3 A/s, time. Which of the following waveforms (3) the final value of the current is 4.5 A, represents the variation of the potential V A. (1) only B. (3) only at point X with respect to time t? C. (1) and (2) only A. B. D. (2) and (3) only V V 86.

i S 0 t 0 t y C. D. V V 0 t

0 t 0 t When the switch S in the above circuit is closed, the variation of quantity y with 84. A cell, a switch, a resistor and an inductor time t is plotted as shown. The quantity y are connected in series to form a circuit. could be

At time t = 0 the switch is closed. Which (1) the voltage V1 across the resistor. of the following best represents the (2) the current i in the circuit.

variation of the current I in the circuit with (3) the voltage V2 across the inductor. time t ? A. (1) only B. (3) only A. B. C. (1) and (2) only I I D. (2) and (3) only 87.

t t 0 0 C. D. I I

t t 0 0

HKAL Exercise Chapter 16 Electromagnetism 21/28 are of resistances 2 Ω and 5 Ω respectively. 4.0 V What will the current drawn from the cell be (I) at the moment when switch S is closed ? (II) when the steady state is reached after S 0.4 H closing switch S ? (I) (II) (I) (II) A. 0 A 7 A B. 2 A 0 A 2.0  C. 2 A 7 A D. 7 A 7 A A coil of inductance 0.4 H is connected in 90. series with a switch S and a cell of e.m.f. 4 V S 4.0 V. The total resistance of the circuit is 2.0 Ω. What is the initial rate of growth of L B the current when the switch is closed ? A. 1 A s-1 B. 5 A s-1 C. 10 A s-1 D. 20 A s-1 neon lamp 88. In the above circuit, a coil L of large B1 inductance, a 4 V light bulb B, a switch S B2 and a 4 V battery are connected in series. A neon lamp is connected across L. Which 12 V of the following statements is/are correct r.m.s. a.c. upon the opening of switch S ?

Bulbs B1, B2 are connected to an a.c. (1) A large e.m.f. is induced across coil L. supply and both bulbs are lit. If the a.c. (2) Light bulb B lights up again after the neon supply is replaced by a 12 V d.c. supply lamp dies out. with negligible internal resistance, what (3) The neon lamp dies out momentarily. will happen to the brightness of each bulb? A. (1) only B. (3) only

B1 B2 C. (1) and (2) only A decreases decreases D. (2) and (3) only B increases unchanged 91. C unchanged increases L D unchanged decreases B 89. A

S E R2 L R1 In the above circuit, A and B are identical In the above circuit, both the cell E and the light bulbs and L is a pure iron-cored inductor L have negligible resistance. The inductor. Which of the following e.m.f. of E is 14 V, and the resistors R1 and R2 statements is/are correct ?

HKAL Exercise Chapter 16 Electromagnetism 22/28 (1) After switch S is closed for some (3) When switch S is open, bulb B will time, A and B are equally bright. go out first. (2) When switch S is closed, bulb B will A. (1) only B. (3) only light up first. C. (1) and (2) only D. (1) and (3) only Magnetic Energy 92. Which of the following devices is/are used to store energy ? (1) a capacitor (2) a photocell (3) a resistor A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only

93. A long solenoid uniformly wound with N turns is of length l, cross-sectional area A and carries a current I. The total energy stored in the magnetic field inside the solenoid is given approximately by  AI 2 N 2  AIN 2  AIN 2  AI 2 N 2 A. 0 B. 0 C. 0 D. 0 2l 2 2l 2 l 2 2l

LRC Circuit 94.

20 V 2 

2 F 2 

When a steady state is reached, the current delivered by the battery is A. 3.3 A. B. 5.0 A. C. 6.7 A. D. 30.0 A. (Structural question) 95. An iron-cored inductor L, a milliammeter A and a 12 V d.c. supply of negligible internal resistance are connected as shown in Figure 95.1. The graph shows the variation of current with time during the first few milliseconds, OA, and a few seconds later, BC, after closing switch S.

HKAL Exercise Chapter 16 Electromagnetism 23/28 current/mA B C 400 L

A S 20 A 12 V 0 1 3000 3500 time/ms

Figure 95.1 (a) What is meant by the inductance of an inductor ? (1 marks) (b) (i) Explain why the current rise instantaneously to the final steady value. (2 marks)

(ii) Find the inductance of L. (2 marks)

(iii) Calculate the resistance of the circuit. (2 marks)

(iv) If the soft iron core of inductor L is removed, sketch on the same graph the parts corresponding to OA and BC. (2 marks)

(c) When the circuit is broken by opening switch S, sparking occurs at the contacts of the switch. (i) Where does the energy for the sparks come from ? (1 marks)

(ii) In order to prevent sparking, a capacitor is now connected in parallel with the switch. It is known that sparking occurs when the voltage across the contacts of the switch exceeds 250 V. Assuming that the energy loss due to the resistance of the circuit is negligible, calculate the minimum capacitance required to prevent sparking(3 marks)

96. Figure 96.1 shows a solenoid of diameter 10.0 cm and length 150 cm. The solenoid has 500

HKAL Exercise Chapter 16 Electromagnetism 24/28 turns and it carries a current of 15 mA. (given: permeability of free space = 4π × 108 H m-1 ) 150 cm

O Figure 96.1 15 mA solenoid

(a) (i) Calculate the magnetic field strength at the centre O of the solenoid. Justify the major assumption you made in the calculation. (3 marks)

(ii) Calculate the magnetic flux linkage through the solenoid. Hence or otherwise find the inductance of the solenoid. (Assume that the flux leakage of the solenoid is negligible.) (4 marks)

(b) The solenoid is now connected with a resistor R0 and a 4 V battery as shown in Figure

96.2. When switch S is opened the variation of the current I through R0 with time t for the first 20μs is as shown.

I / mA R0 A B 15

solenoid 11 D C Figure 96.2

4 V S 0 20 t / s

Rt According to textbooks, the current would decrease exponentially as L , where R I  I oe and L are the resistance and inductance of the solenoid respectively. Assume that the  x resistance of R0 is much smaller than R. (Given: e can be approximated to 1 – x for small x) (i) Explain why the graph in Figure 96.2 appears to be a straight line. (2 marks)

(ii) Find the experimental values of R and L. (4 marks)

HKAL Exercise Chapter 16 Electromagnetism 25/28 (iii) Account for the difference between the experimental value of L in (b) (ii) and its theoretical value in (a) (ii). (1 mark)

HKAL Exercise Chapter 16 Electromagnetism 26/28 HKAL Exercise (key) : Part 4 Electricity and Electromagnetism Chapter 16 Electromagnetism

1 – 10 : CCBBD, ACBAC, 11 – 20 : AAACC, CCCCB, 21 – 30 : BCCCB, DCABB,

31 – 40 : BCABA, ACCCD, 41 – 50 : CADAB, CAABC, 51 – 60 : DCCCA, CDAAA,

61 – 70 : AADCD, ACBCA, 71 – 75 : ABDCC,

8 76. (a) (i) Imax = 1 0.5 = 16 A 1 2 (ii) Connect a ‘starting, resistance in series with the motor and gradually reducing 1 it as the motor speeds up. 1 2 (b) (i) The coil of the motor has inductance, therefore the rise in current will generate dI an e.m.f. (  L ) which opposes its rise at the initial stage. 1 1 dt

(ii) The back e.m.f. εb is proportional to the speed of rotation of the armature.1 When the motor is first switched on, the back e.m.f. is zero; it increases as the motor speeds up and at the same time the current decreases accordingly.

Eventually the rotating speed and thus the back e.m.f. become steady, the current reaches the working value. 1 2 (c) (i) T = NBAI = (150) (0.4) (0.004) (4) 1 = 0.96 N m 1 2

(ii) (I) ε – εb = IR 1

8 – εb = (4) (0.5)

εb = 6 V 1 I  I 2 R  (II) Efficiency = × 100 % (or b × 100 %) 1 I  (4)(8)  (4)2 (0.5) = × 100 % (4)(8) = 75 % 1 4

77 – 80 : AABC, 81 – 90 : ADCDA, CCCCC, 91 – 94 : AADB,

HKAL Exercise Chapter 16 Electromagnetism 27/28 95. (a) The back e.m.f. induced in the inductor per unit area of change of current 1 1 dI (b) (i) When there is a change of current, back e.m.f. εb = - L is produced by the 1 dt inductor, therefore only part of the applied p.d. is used for driving the current. 1 2 dI (V  IR  L ) dt dI (ii) At t = 0 s, V = L dt 20103 12 = L 1 1103 L = 0.6 H 1 2 (iii) At steady state, V = IR 12 = 400 × 10-3 R 1 R = 30 Ω 1 2 (iv) 2 2

current/mA B C 400 B' C'

A' A 20

0 1 3000 3500 time/ms

(c) (i) The energy stored in the magnetic field of the inductor. 1 1 1 2 1 2 (ii) 2 LI = 2 CV 1 0.6 (400 × 10-3)2 = C (250)2 1 C = 1.54μF 1 3

 NI 96. (a) (i) B = 0 l (4 107 )(500)(15103 ) = 1 1.5 = 6.28 × 10-6 T 1 Assumption : solenoid is long since 10.0 cm diameter << 150 cm length. 1 3 (ii) Φ = NBA 1

2   0.1  -6   = (500) (6.28 × 10 )       2   = 2.47 × 10-5 Wb 1 Total flux linkage Φ = Nψ = LI 1

HKAL Exercise Chapter 16 Electromagnetism 28/28 (2.47 × 10-5) = L (15 × 10-3) L = 1.65 × 10-3 H 1 4

Rt  (b) (i) I = I0 e L R Rt As is constant, for small t, I  I0 (1 – ) is approximately linear. 2 2 L L V (ii) R = I 0 4V = 1 15mA = 267 Ω 1  R slope of the graph = I0 1 L 4103 267 R =  (15 × 10-3) (i.e. = 1.33 × 104 Ω H-1) 20106 L L L = 0.0200 H 1 4 (iii) Stray inductance / flux leakage/ there exists inductance, say, in the connecting wires. 1 1

HKAL Exercise Chapter 16 Electromagnetism 29/28