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3.7.5.4 Electromagnetic Induction
Q1. (a) Figure 1 shows two coils, P and Q , linked by an iron bar. Coil P is connected to a battery through a variable resistor and a switch S. Coil Q is connected to a centre- zero ammeter. Figure 1 (i) Initially the variable resistor is set to its minimum resistance and S is open. Describe and explain what is observed on the ammeter when S is closed. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... (3) (ii) With S still closed, the resistance of the variable resistor is suddenly increased. Compare what is now observed on the ammeter with what was observed in part (i). Explain why this differs from what was observed in part (i). ............................................................................................................... ............................................................................................................... ............................................................................................................... ...............................................................................................................
(2) (b) Figure 2 shows a 40-turn coil of cross-sectional area 3.6 × 10–3^ m^2 with its plane set at right angles to a uniform magnetic field of flux density 0.42 T. Figure 2 (i) Calculate the magnitude of the magnetic flux linkage for the coil. State an appropriate unit for your answer. flux linkage ....................................................... unit ..................... (2) (ii) The coil is rotated through 90° in a time of 0.50 s. Determine the mean emf in the coil. mean emf ................................................. V (2) (Total 9 marks)
(b) Explain how the initial emf induced in the coil of the geophone would be affected: if the stiffness of the springs were to be increased ........................................................................................................................ ........................................................................................................................ if the number of turns on the coil were to be increased. ........................................................................................................................ ........................................................................................................................ (2) (c) (i) The geophone’s magnet has a mass of 8.0 × 10–3^ kg and the spring stiffness of the system is 2.6 N m–1. Show that the natural period of oscillation of the mass−spring system is approximately 0.35 s. (2) (ii) At the instant that the Earth stops moving after one earthquake, the emf in the coil is at its maximum value of +8 V. The magnet continues to oscillate. On the grid below, sketch a graph showing the variation of emf with time as the magnet’s oscillation decays. Show at least three oscillations.
(3) (Total 10 marks) Q3.Figure 1 shows an arrangement for investigating electromagnetic induction. Figure 1
When the switch is closed there is a current in the coil in circuit X. The current is in a
The mean diameter of the turns on the coil is 35 cm. Figure 4 shows the output
recorded for the variation of potential difference V with time t when the coil is rotated
at 1.5 revolutions per second. Figure 4
(b) Determine the flux density, B H, of the horizontal component of the Earth’s magnetic
field. horizontal component of flux density = _____________T (3) (Total 7 marks)
Q4. A vertical conducting rod of length l is moved at a constant velocity v through a uniform
horizontal magnetic field of flux density B.
Which of the rows gives a correct expression for the induced emf between the ends of the rod for the stated direction of the motion of the rod? Direction of motion Induced emf A Vertical B Horizontal at right angles to
the field Blv
C Vertical Blv
D
Horizontal at right angles to the field (Total 1 mark)
Q5. The graph shows how the flux linkage, NΦ , through a coil changes when the coil is moved
into a magnetic field. The emf induced in the coil
(Total 1 mark) Q8. A vertical conducting rod of length l is moved at a constant velocity v through a uniform horizontal magnetic field of flux density B. Which line, A to D , in the table gives a correct expression for the induced emf for the stated direction of the motion of the rod? direction of motion induced emf A vertical B horizontal at right angles to the field Blv C vertical Blv
D horizontal at right angles to the field (Total 1 mark) Q9. A transformer, which is not perfectly efficient, is connected to a 230 V rms mains supply and is used to operate a 12 V rms, 60 W lamp at normal brightness. The secondary coil of the transformer has 24 turns. Which line, A to D , in the table is correct? number of turns on primary coil rms current in primary coil A 92 less than 0.26 A B 92 more than 0.26 A C 460 less than 0.26 A D 460 more than 0.26 A (Total 1 mark) Q10. A rectangular coil is rotating anticlockwise at constant angular speed with its axle at right angles to a uniform magnetic field. Figure 1 shows an end-on view of the coil at a particular instant. Figure 1 (a) At the instant shown in Figure 1 , the angle between the normal to the plane of the coil and the direction of the magnetic field is 30°.
Figure 3 (iii) Calculate the peak value of the emf generated. peak emf ......................................... V (3) (c) Sketch a graph on the axes shown in Figure 3 above to show how the induced emf varies with time over the time interval shown in Figure 2. (2)
(d) The coil has 550 turns and a cross-sectional area of 4.0 × 10–3m^2. Calculate the flux density of the uniform magnetic field. flux density .......................................... T (2) (Total 13 marks) Q11. A rectangular coil is rotated in a uniform magnetic field. When the coil is rotated at a constant rate, an alternating emf ε is induced in it. The variation of emf ε , in volts, with time t , in seconds, is given by ε = 20 sin (100 π t ) Which line, A to D , in the table gives the peak value ε 0 and the frequency f of the induced emf? ε 0 / V f / Hz A 10 50
(i) The dimensions of P and Q are identical but Q has a greater mass than P. Explain what material property is responsible for this difference. ............................................................................................................... ............................................................................................................... ............................................................................................................... (1) (ii) When P and Q are released from rest and allowed to fall freely through a vertical distance of 1.0 m, they each take 0.45 s to do so. Justify this time value and explain why the times are the same. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... (2) (c) The steel cylinder Q is a strong permanent magnet. P and Q are released separately from the top of a long, vertical copper tube so that they pass down the centre of the tube, as shown in Figure 2. Figure 2
The time taken for Q to pass through the tube is much longer than that taken by P. (i) Explain why you would expect an emf to be induced in the tube as Q passes through it. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... (2) (ii) State the consequences of this induced emf, and hence explain why Q takes longer than P to pass through the tube. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... (3) (d) The copper tube is replaced by a tube of the same dimensions made from brass.
emerges first emerges second emerges third A P Q R B R P Q C P R Q D R Q P (Total 1 mark) Q15. The graph shows how the magnetic flux, Φ , passing through a coil changes with time, t. Which one of the following graphs could show how the magnitude of the emf, V , induced in the coil varies with t? (Total 1 mark) Q16. Using the circuit shown, and with the switch closed, a small current was passed through the coil X. The current was slowly increased using the variable resistor. The current reached a maximum value and was then switched off.
The maximum reading on the microammeter occurred when A the small current flowed at the start. B the current was being increased. C the current was being switched off. D the current in X was zero. (Total 1 mark) Q17. When a mobile phone is being recharged, the charger heats up. The efficiency of the transformer in the charger can be as low as 15% when drawing a current of 50 mA from a 230 V mains supply. If the charging current required is 350 mA, what is the approximate output voltage at this efficiency? A 4.9 V B 11 V C 28 V D 33 V (Total 1 mark) Q18. The output electromotive force (emf) of a simple ac generator can be increased by any of the four factors listed. Which one of these factors should not be changed if the frequency of the output is to remain unaffected when the emf is increased? A the area of the coil B the number of turns on the coil C the speed of rotation D the strength of the magnetic field (Total 1 mark)
