Cambridge A Level Physics 9702 — 2018 May/June Paper 5 · Variant 1

1 A student is investigating the force between two charged metal spheres S and T, as shown in Fig. 1.1. T r S Fig. 1.1 Each sphere may be charged by connecting the positive lead from a power supply to the sphere and then removing the lead. The electromotive force (e.m.f.) of the power supply used to charge sphere T is V. The force F between the two charged spheres may be determined by attaching sphere S to a top pan balance. For a constant charge on sphere S, it is suggested that the relationship between F and V is αV F = r 2 where r is the distance between the centres of the spheres and α is a constant. Design a laboratory experiment to test the relationship between F and V. 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 V is the independent variable and F is the dependent variable or vary V and measure F. 1 keep r constant 1 Methods of data collection labelled diagram of workable experiment including: • T suspended (clamp or ceiling) • S on top-pan balance vertically below T • T and S labelled and at least one other label. 1 F = difference/change in balance readings when sphere(s) (S) is uncharged and charged. 1 voltmeter across a power supply (with flying lead) or read V from high voltage power supply/EHT power supply 1 measure r with a rule 1 Method of analysis plot a graph of F against V (allow valid log-log graphs) 1 relationship valid if a straight line passing through the origin is produced 1 α = gradient × r2 (consistent with graph) 1 Question Answer Marks Additional detail including safety considerations Max. 6 D1 safety precaution linked to avoiding shock/high voltages, e.g. insulating gloves to hold flying lead/to charge sphere/to avoid electrocution or use shrouded leads/ensure that there no bare connections/avoid touching metal parts D2 use of insulator between sphere S and balance or between sphere T and stand D3 discharge sphere(s) by earthing or connecting to the negative of the power supply D4 additional detail to determine r e.g. determine radius of each sphere and add distance between spheres or measure from top of S to top of T etc. D5 use of calipers/micrometer to measure diameter of spheres (and halve) to determine r or use of calipers/micrometer to measure diameter of spheres to check that spheres are the same diameter to determine r or use of fiducial mark and ruler from top of spheres etc. D6 use of ∆mg to determine F D7 repeat experiment for each value of V and average F D8 take reading of balance quickly to avoid discharge/keep other charged objects away D9 method to ensure charge on S is constant, e.g. re-charge S periodically/regularly (with initial value of p.d.)/keep S connected to a separate positive terminal D10 avoid draughts to prevent T moving

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2 A student is investigating monochromatic light passing through a diffraction grating. A series of maxima are produced on a screen, as shown in Fig. 2.1. second order central second order maximum maximum maximum s Fig. 2.1 The student measures the distance s between the central maximum and the second order maximum on the screen. The experiment is repeated for different wavelengths of light. It is suggested that s and the wavelength λ are related by the equation s 2 = 4N 2λ2 s 2 + D 2 where D is the distance between the diffraction grating and the screen and N is the number of lines per unit length of the diffraction grating. 1 1 (a) A graph is plotted of on the y-axis against on the x-axis. s 2 λ2 Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of λ and s are given in Fig. 2.2. 1 1 λ/ 10−7 m s / m 2 / 1012 m−2 2 / m−2 λ s 4.3 0.62 ± 0.02 4.8 0.72 ± 0.02 5.3 0.82 ± 0.02 5.8 0.92 ± 0.02 6.2 1.02 ± 0.02 6.6 1.10 ± 0.02 Fig. 2.2 1 1 Calculate and record values of / 1012 m−2 and / m−2 in Fig. 2.2. 2 2 λ s 1 Include the absolute uncertainties in . [2] s 2 1 1(c) (i) Plot a graph of / m−2 against / 1012 m−2. s 2 λ2 1 Include error bars for . [2] s 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 1 4N D and y-intercept = 2 1 D − 1 2(b) 5.4 or 5.41 2.6 or 2.60 4.3 or 4.34 1.9 or 1.93 3.6 or 3.56 1.5 or 1.49 3.0 or 2.97 1.2 or 1.18 2.6 or 2.60 0.961 or 0.9612 2.3 or 2.30 0.826 or 0.8264 1 Uncertainties in 1 / s2 from ± 0.16 or ± 0.17 or ± 0.18 or ± 0.2 to ± 0.02 or ± 0.03. 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 1 / s2 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 does not pass through bottom point and line must pass between (4.70, 2.2) and (4.85, 2.2). 1 Worst acceptable line drawn (steepest or shallowest possible line). All error bars must be plotted. 1 2(c)(iii) Gradient determined with clear substitution of points from the line of best fit into ∆y / ∆x. Distance between points must be at least half the length of the drawn line. 1 Gradient of worst acceptable line determined. uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 Question Answer Marks 2(c)(iv) y-intercept determined by substitution into y = mx + c. 1 y-intercept determined using gradient from worst acceptable line. uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) 1 2(d)(i) D determined using y-intercept and N determined using gradient. D and N given to 2 or 3 significant figures. 1 D determined using y-intercept. 1 -intercept D y = − 1 N determined using gradient with correct power of ten and units. Correct substitution of numbers must be seen. 2 1 -intercept 4 gradient 4 gradient y N D − = × × × or 1 2(d)(ii) Percentage uncertainty in N determined. Correct substitution of numbers must be seen. % uncertainty in N = ½ (% uncertainty in gradient + 2 × % uncertainty in D) or % uncertainty in N = ½ (% uncertainty in gradient + % uncertainty in y-intercept) 1

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