Cambridge A Level Physics 9702 — 2014 May/June Paper 5 · Variant 2

1 Two identical coils are connected together and arranged as shown in Fig. 1.1. coil coil r X Fig. 1.1 The coils are in the vertical plane and are parallel to each other. When the coils are connected to a power supply, there is a magnetic field between them. It is suggested that the magnetic flux density B of the field at the point X is related to the radius r of the coils by the relationship 0.72μ0NI B = r where N is the number of turns on each coil, I is the current in the coils and is the μ0 permeability of free space. Design a laboratory experiment that uses a Hall probe to test the relationship between B and r and determine a value for μ0. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. 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Defining the Methods of data Method of Safety Additional problem collection analysis considerations detail

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P r is the independent variable, B is the dependent variable or vary r and measure B. [1] P Keep the number of turns on the coil(s) constant. [1] Do not accept “same coil”. P Keep the current in the coil constant. [1] Methods of data collection (5 marks) M Diagram showing flat coils and labelled Hall probe positioned at X. Minimum two labels needed. Solenoids will not be credited. [1] M Workable circuit diagram for coil connected to a (d.c.) power supply and ammeter. Do not allow a.c. power supply or incorrect circuit diagrams. [1] M Connect Hall probe to voltmeter / c.r.o. Allow galvanometer but do not allow ammeter. [1] M Measure diameter (radius) with a ruler / vernier calipers. Do not allow micrometer. [1] M Calibrate Hall probe with a known magnetic flux density. [1] Method of analysis (2 marks) A Plot a graph of B against 1 / r [allow lg B against lg r or other valid graph] [1] gradient A µ 0 = [1] 0.72 N I Safety considerations (1 mark) S Precaution linked to (large) heating of coil, e.g. switch off when not in use to avoid overheating coil; do not touch coil because it is hot. [1] GCE AS/A LEVEL – May/June 2014 9702 52 Additional detail (4 marks) D Relevant points might include [4] 1 Use large current / large number of turns to create a large magnetic field 2 Use rheostat (to adjust current in circuit) (with ammeter) to keep the current constant 3 Hall probe at right angles to direction of magnetic field / parallel to coils. Allow adjust to obtain maximum reading 4 Reasoned method to keep Hall probe perpendicular to direction of magnetic field or at X (e.g. use of set square, fix to rule, optical bench or equivalent) 5 Method to check coils are correctly aligned in parallel 6 Repeat experiment with Hall probe reversed and average 7 Repeat measurement for d (or r) and average 8 Relationship is valid if the graph is a straight line passing through the origin for appropriate graph [if lg–lg then straight line with gradient = –1 (ignore reference to y-intercept)] Do not allow vague computer methods. [Total: 15]

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2 A student investigates the oscillations of a simple pendulum attached to a pole on the side of a building, as shown in Fig. 2.1. pole building pendulum bob d Fig. 2.1 The student records the distance d from the ground to the centre of the pendulum bob and the time t for the pendulum to complete 10 oscillations. It is suggested that the period T of the oscillations and the distance d are related by the equation 2 4π2 T = (k − d) g where g is the acceleration of free fall and k is a constant. (a) A graph is plotted of T 2 on the y-axis against d on the x-axis. Determine expressions for the gradient and the y-intercept in terms of g and k. gradient = ...................................................... y-intercept = ...................................................... [1] (b) For each value of d the measurement of t is repeated. Values of d and t are given in Fig. 2.2. d / m t / s t / s 0.45 ± 0.05 56.4 56.4 0.70 ± 0.05 55.4 55.6 1.00 ± 0.05 54.6 54.2 1.20 ± 0.05 53.4 53.8 1.45 ± 0.05 52.9 52.5 1.65 ± 0.05 51.6 52.0 Fig. 2.2 Calculate and record values of mean t / s, T / s and T 2 / s2 in Fig. 2.2. [2] (c) (i) Plot a graph of T 2 / s2 against d / m. Include error bars for d. [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 uncertainty in your answer. gradient = ................................................. [2] 32.0 31.5 T 2 / s2 31.0 30.5 30.0 29.5 29.0 28.5 28.0 27.5 27.0 26.5 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 d / m

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 2 − 4π Gradient must be negative. gradient = g 2 Allow y-intercept = –gradient × k 4π y-intercept = k g (b) T1 (mean) t / s, T / s and T 2 / s2 All column headings to be correct. T2 Check all values of T 2. 31.8 or 31.81 Allow a mixture of significant figures. 30.8 or 30.80 29.6 or 29.59 28.7 or 28.73 27.8 or 27.77 26.8 or 26.83 (c) (i) G1 Six points plotted correctly Must be within half a small square. Penalise “blobs” Ecf allowed from table. U1 Error bars in d plotted All error bars to be plotted. Must be accurate to less correctly than half a small square. (c) (ii) G2 Line of best fit Lower end of line should pass between (1.60, 27.0) and (1.64,27.0) and upper end of line should pass between (0.44,31.8) and (0.48,31.8). GCE AS/A LEVEL – May/June 2014 9702 52 G3 Worst acceptable straight Line should be clearly labelled or dashed. line. Examiner judgement on worst acceptable line. Steepest or shallowest Lines must cross. Mark scored only if all error bars possible line that passes are plotted. through all the error bars. (c) (iii) C1 Gradient of best fit line Must be negative. The triangle used should be at least half the length of the drawn line. Check the read offs. Work to half a small square. Do not penalise POT. (Should be about –4.) U2 Uncertainty in gradient Method of determining absolute uncertainty: difference in worst gradient and gradient. (c) (iv) C2 y-intercept FOX does not score. Check substitution into y = mx + c Allow ecf from (c)(iii). (Should be about 33.7.) U3 Uncertainty in y-intercept Uses worst gradient and point on WAL. Do not check calculation. FOX does not score. (d) (i) C3 g between 9.20 and 9.90 2 4π given to 2 or 3 s.f. and g = − ; allow N kg–1 correct unit (m s–2) having m used gradient. C4 k determined correctly with g c k = c = (k must be positive.) correct unit (m) 2 − m 4π (d) (ii) U4 Percentage uncertainty in g U5 Percentage uncertainty in k Percentage uncertainty in k must be larger than the percentage uncertainty in g. [Total: 15] Uncertainties in Question 2 (c) (iii) Gradient [U2] Uncertainty = gradient of line of best fit – gradient of worst acceptable line Uncertainty = 1 (steepest worst line gradient – shallowest worst line gradient) 2 (c) (iv) [U3] Uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line Uncertainty = 1 (steepest y-intercept – shallowest y-intercept) 2 GCE AS/A LEVEL – May/June 2014 9702 52 (d) (ii) [U4] ∆ m ∆ g Percentage uncertainty in g = × 100 = × 100 m g [U5] ∆ k ∆ g ∆ c Percentage uncertainty in k = × 100 = × 100 + × 100 k g c max g × max y-intercept max y − intercept max k = 2 = 4 π min gradient min g × min -intercept min y − intercept min k = 2 = 4 π max gradient

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