Cambridge A Level Physics 9702 — 2020 Feb/March Paper 5 · Variant 2

1 Fig. 1.1 shows a bar magnet attached to a spring. spring N bar magnet S Fig. 1.1 The bar magnet is displaced a distance x from its equilibrium position and released. It then oscillates vertically. A student investigates how the maximum induced electromotive force (e.m.f.) E in a coil placed below the magnet depends on x. It is suggested that the relationship between E and x is k E = αBNx m where B is the magnetic flux density at one of the poles of the bar magnet, N is the number of turns on the coil, k is the spring constant, m is the mass of the magnet and α is a constant. Design a laboratory experiment to test the relationship between E and x. Explain how your results could be used to determine a value for α. 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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Mark scheme: 1 Defining the problem x is the independent variable and E is the dependent variable, or vary x and measure E. 1 Keep B or m constant and keep k or N constant. 1 Methods of data collection Labelled diagram of workable experiment including: • labelled spring supported by stand and clamp • labelled magnet • labelled coil positioned so that magnet is vertically above the coil by eye in the correct orientation. 1 Circuit diagram showing voltmeter / multimeter set to p.d. range / oscilloscope connected to the ends of the coil. Do not accept other electrical components. 1 Method to measure x, e.g. labelled ruler drawn parallel to spring/magnet and equilibrium position and displaced position indicated and x indicated or difference determined or description of use of ruler to measure equilibrium position and displaced position and difference determined. 1 Method to measure mass of magnet e.g. use balance or use newton-meter to measure weight and divide by g. 1 Method of Analysis Plots a graph of E against x or equivalent. Allow lg E against lg x. 1 Relationship valid if a straight line passing through the origin is produced. (for lg E against lg x: relationship valid if a straight line with gradient = 1). 1 α = gradient m BN k (for lg E against lg x: α = -intercept 10 y m BN k ) 1 Question Answer Marks 1 Additional detail including safety considerations Max 6 6 Use safety goggles / safety screen to prevent injury (to eyes) from (detached) spring/magnet; do not accept from D1 oscillating magnet or use cushion / sand box in case magnet falls or use g clamp / weights on stand to prevent toppling. Keep distance between equilibrium position and coil constant. D2 Check that the unstretched length of the spring has not changed or is not permanently deformed (after removing D3 load / magnet). Expression to determine k from relevant experiment, e.g. k = mg / extension or gradient of F – extension graph. D4 Weight / force must be defined. Measure B using a (calibrated) Hall probe. D5 Additional detail on use of Hall probe, e.g. D6 adjust probe until maximum value or measure B using Hall probe first in one direction and then in the opposite direction and average. Method to maximise E, e.g. position magnet so that equilibrium position is at the centre of the coil or use D7 a large number of turns. Explanation to determine max E e.g. use of video and slow-motion playback. D8 Repeat experiment for each x and average E. D9 Method to ensure clamped rule to measure x is vertical, e.g. correctly positioned set square indicated at D10 right angles between the rule and the horizontal surface or plumb line supported on a surface shown in appropriate position.

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2 A student investigates the discharge of a capacitor through a resistor as shown in Fig. 2.1. E C R A Fig. 2.1 The student initially closes the switch and charges the capacitor. The switch is then opened and a stop-watch is started. The capacitor discharges through the resistor. At different times t the current I is measured. It is suggested that I and t are related by the equation E – t I = e e RC o R where E is the e.m.f. of the power supply, C is the capacitance of the capacitor and R is the resistance of the resistor. (a) A graph is plotted of ln I on the y-axis against t on the x-axis. Determine expressions for the gradient and the y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of t and I are given in Table 2.1. Table 2.1 t / s I / μA ln (I / μA) 0 46 ± 2 12 40 ± 2 24 34 ± 2 36 28 ± 2 48 24 ± 2 60 20 ± 2 Calculate and record values of ln (I / μA) in Table 2.1. Include the absolute uncertainties in ln (I / μA). [2] (c) (i) Plot a graph of ln (I / μA) against t / s. Include error bars for ln (I / μA). [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 = −1 CR y-intercept = ln E R 2(b) 3.83 or 3.829 3.69 or 3.689 3.53 or 3.526 3.33 or 3.332 3.18 or 3.178 3.00 or 2.996 1 Absolute uncertainties in ln I from ± 0.04 to ± 0.1 1 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 ln I plotted correctly. All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Line of best fit drawn. Points must be balanced. Line must pass between (5.5, 3.75) and (8.0, 3.75) and between (56, 3.05) and (58, 3.05) 1 Worst acceptable line drawn. Steepest or shallowest possible line that passes through all the error bars. Mark scored only if all error bars are plotted. 1 Question Answer Marks 2(c)(iii) Negative gradient determined with clear substitution of data points into Δy / Δx; distance between data points must be at least half the length of the drawn line. 1 Gradient determined of WAL 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(c)(iv) y-intercept read from y-axis to less than half a small square, or y-intercept determined from substitution into y = m x + c. 1 2(d)(i) C determined using gradient and C given to two or three significant figures Correct substitution of numbers must be seen, − − = = × × × × 3 3 1 1 150 10 gradient 150 10 (c)(iii) C 1 E determined using y-intercept Correct substitution of numbers must be seen, ( ) − = × = × × × -intercept 3 (c)(iv) 6 150 10 e 10 y E R e Or = + ln ln -intercept E R y 1 C determined using gradient and E determined using y-intercept and dimensionally correct SI unit for C: F or s Ω–1 or C V–1 or A s V–1 and E: V or A Ω. 1 Question Answer Marks 2(d)(ii) Absolute uncertainty in C.   Δ Δ = + ×     gradient 0.05 gradient C C OR Correct substitution for max/min methods − = × × 3 1 max 142.5 10 minnumericalgradient C − = × × 3 1 min 157.5 10 max numerical gradient C 1 2(e) I determined from (d)(i) OR (c)(iii) and (c)(iv) with correct substitution and correct power of ten(s). Do not accept ecf for POT from (c)(iii), (iv) or (d). − = × 120 CR E e R I OR ( ) × − = × × gradient 120 -intercept 6 10 y e e I OR = × + ln 120 gradient -intercept y I × + − = × 120 gradient -intercept 6 10 y e I 1

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