Cambridge A Level Physics 9702 — 2017 Oct/Nov Paper 5 · Variant 2

1 A flat circular coil P carrying a current produces a magnetic field. When a second coil Q is placed with its centre a distance x from the centre of coil P, as shown in Fig. 1.1, an e.m.f. V may be induced in coil Q. coil P coil Q x centre of coil Q centre of coil P Fig. 1.1 It is suggested that V is related to x by the relationship V = V0 e–kx where V0 and k are constants. Design a laboratory experiment to test the relationship between V and x. Explain how your results could be used to determine a value for k. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed, • the measurements to be taken, • the control of variables, • the analysis of the data, • any safety precautions to be taken. 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[Total: 15]

Mark scheme: 1 Defining the problem x is the independent variable and V is the dependent variable or vary x and measure V 1 keep current (in the coil P) constant 1 Methods of data collection labelled diagram showing both coils supported 1 two correct circuit diagrams for coil P and coil Q: power supply connected to one coil and voltmeter/c.r.o. connected to other coil 1 method to determine x, e.g. use a ruler or drawn labelled horizontal ruler adjacent to coils with x indicated 1 method to measure x from centre of coil P to centre of coil Q, e.g. measure width of (each) coil and divide by 2 and add to separation of coils 1 Method of analysis plots a graph of ln V against x [or log V against x etc.] 1 relationship valid if a straight line produced 1 k = –gradient 1 Question Answer Marks Additional detail including safety considerations Max. 6 D1 do not touch hot coil/use gloves to position hot coil/heat-proof gloves to position coil D2 use large current/number of turns/iron core (to produce large magnetic field/induced e.m.f.) D3 use high frequency (to produce larger induced e.m.f.) D4 use an a.c. power supply or signal generator (connected to coil P) D5 keep the number of turns (on each coil) constant/frequency constant D6 method described to check that current is constant, e.g. use an ammeter and variable resistor/variable power supply D7 repeat measurements of x for different parts of the coil and average D8 method to position ruler horizontally to measure x described e.g. use a spirit level or same height from bench at both ends D9 method to keep coils parallel/co-axial e.g. adjust coil Q until maximum reading or use set square to ensure that coils are at right angles to the axis D10 0 ln ln V kx V = − +

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2 A student is investigating stationary waves on a stretched elastic cord. A vibrator attached to the cord is connected to a signal generator. The apparatus is set up as shown in Fig. 2.1. elastic cord pulley vibrator M Fig. 2.1 The mass M attached to the cord is adjusted until resonance is obtained. The number n of antinodes on the stationary wave is recorded. The experiment is repeated with different masses to obtain different values of n. It is suggested that M and n are related by the equation n Mg f = 2 L n where f is the frequency of the vibrator, g is the acceleration of free fall, L is the length of the elastic cord and n is the mass per unit length of the elastic cord. 1 (a) A graph is plotted of M on the y-axis against 2 on the x-axis. n Determine an expression for the gradient. gradient = .......................................................... [1] (b) Values of n and M are given in Fig. 2.2. The percentage uncertainty in each value of M is ±10%. 1 n M / g 2 n 3 850 ± 4 500 ± 5 300 ± 6 200 ± 7 150 ± 8 100 ± Fig. 2.2 1 Calculate and record values of 2 in Fig. 2.2. n Determine the absolute uncertainties in M. [2] 1(c) (i) Plot a graph of M / g against 2. n Include error bars for M. [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ...........................................................[2]

Mark scheme: 2(a) gradient = 2 2 4 L f g µ 1 2(b) M / g 2 1 n 850 ± 85 (90) 0.1 or 0.11 or 0.111 or 0.1111 500 ± 50 0.06 or 0.063 or 0.0625 300 ± 30 0.04 or 0.040 or 0.0400 200 ± 20 0.03 or 0.028 or 0.0278 150 ± 15 (20) 0.02 or 0.020 or 0.0204 100 ± 10 0.02 or 0.016 or 0.0156 First mark for uncertainties in first column correct. Second mark for all second column correct. 2 2(c)(i) Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square. 1 Error bars in M plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Line of best fit drawn. Line must not pass through plotted point (0.11, 850) or (0.111, 850). If points are plotted correctly then lower end of line should pass between (0.032, 250) and (0.036, 250) and upper end of line should pass between (0.098, 800) and (0.104, 800). 1 Worst acceptable line drawn (steepest or shallowest possible line). All error bars must be plotted. 1 Question Answer Marks 2(c)(iii) Gradient determined with a triangle that is at least half the length of the drawn line. 1 uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(d)(i) µ determined correctly using gradient. 2 2 9.81 gradient 4 120 1.54 µ = × × × 5 7.18123 10 gradient µ − = × × 1 µ determined using gradient and given to 2 or 3 significant figures. 1 µ determined using gradient and correct unit g m–1 and in the range 0.560–0.630 (g m–1). 1 Question Answer Marks 2(d)(ii) Percentage uncertainty in µ. 0.01 5 gradient % uncertainty 2 2 100 1.54 120 gradient   ∆ = × + × + ×     gradient % uncertainty 9.63% 100 gradient ∆ = + × Maximum/minimum methods: 2 2 9.81 max gradient max 4 115 1.53 µ × = × × 2 2 9.81 min gradient min 4 125 1.55 µ × = × × Correct substitution of numbers must be seen. 1 Question Answer Marks 2(e) M determined correctly using µ from (d)(i). 2 2 180 1.54 7.833 9.81 1000 M × × = = × × (d)(i) (d)(i) Correct substitution of numbers must be seen. 1 Absolute uncertainty determined. 0.01 5 % uncertainty 2 2 100 6.9% 1.54 180   = × + × × + = +     (d)(ii) (d)(ii) Correct substitution of numbers must be seen. Maximum/minimum methods: ( ) ( ) 2 2 4 1 85 1.55 max max 8.382 max 4 9.81 1000 M × × × = = × × × (d)(i) (d)(i) ( ) ( ) 2 2 4 1 75 1.53 min min 7.308 min 4 9.81 1000 M × × × = = × × × (d)(i) (d)(i) 1

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