Cambridge A Level Physics 9702 — 2010 May/June Paper 5 · Variant 2

1 A current in a flat circular coil produces a magnetic field. For Examiner’s A student suggests that the strength B of the magnetic field is related to the distance x from Use the centre of the coil (see Fig. 1.1) by the equation B = B0e–px where B0 is the strength of the magnetic field for x = 0, and p is a constant. coil x centre of coil Fig. 1.1 Design a laboratory experiment that uses a Hall probe to investigate the relationship between B and x. You should draw a diagram 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 Method of Safety Additional For problem data collection analysis considerations detail Examiner’s Use

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P1 x is the independent variable, B is the dependent variable or vary x and measure B [1] P2 Keep the number of turns on the coil/radius of the coil constant [1] Do not accept same coil – ‘coil’ is not a variable P3 Keep the current (in the coil) constant [1] Methods of data collection (5 marks) M1 Diagram showing coil and Hall probe with a means of read out appropriately positioned along axis [1] M2 Coil connected to a power supply [1] M3 Measure x with a ruler [1] M4 Hall probe at right angles to direction of magnetic field or gives maximum output for each reading [1] M5 Method to determine axis of coil or to find x = 0 [1] Method of analysis (2 marks) A1 Plot a graph of ln B against x [1] A2 Relationship valid if a straight line is produced (ignore reference to y-intercept) [1] Safety considerations (1 mark) S1 Precaution linked to (large) current in coil/heating, e.g. switch off when not in use to avoid overheating coil; do not touch because it is hot [1] Additional detail (4 marks) D 1/2/3/4 Relevant points might include [4] 1. Method to create a large magnetic field, e.g. use large current or large number of turns. 2. Reasoned method to keep current constant. 3. Reasoned method to keep Hall probe in same orientation (e.g. use of set square, fix to rule, optical bench or equivalent). 4. B is proportional to voltage across Hall probe/calibrate Hall probe (in a known magnetic field). 5. Repeat experiment with Hall probe reversed or equivalent. 6. Identifies logarithmic equation i.e. ln B = –p x + ln B0 7. Avoid external magnetic fields. 8. Method to keep Hall probe along axis. Do not allow vague computer methods. [Total: 15] GCE AS/A LEVEL – May/June 2010 9702 52

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2 A student is investigating how the period T of a simple pendulum depends on its length l as For shown in Fig. 2.1. Examiner’s Use l Fig. 2.1 The time t for 10 oscillations is recorded for a pendulum of length l. The period T of the pendulum is determined. The procedure is then repeated for different lengths. Question 2 continues on the next page. It is suggested that T and l are related by the equation For Examiner’s l Use T = 2π g where g is the acceleration of free fall. (a) A graph is plotted of T 2 on the y-axis against l on the x-axis. Express the gradient in terms of g. gradient = ................................................. [1] (b) Values of l and t are given in Fig. 2.2. l / cm t / s 90.0 18.9 ± 0.1 80.0 17.9 ± 0.1 70.0 16.7 ± 0.1 60.0 15.5 ± 0.1 50.0 14.1 ± 0.1 40.0 12.6 ± 0.1 Fig. 2.2 Calculate and record values of T and T 2 in Fig. 2.2. Include the absolute uncertainties in T 2. [3] (c) (i) Plot a graph of T 2 / s2 against l / cm. Include error bars for T 2. [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] 3.7 For Examiner’s Use 3.5 T 2 / s2 3.3 3.1 2.9 2.7 2.5 2.3 2.1 1.9 1.7 1.5 30 40 50 60 70 80 90 100 l / cm

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 2 39.5 4π Allow g g (b) T1 Column headings: There must be a dividing mark between the quantity T / s and T 2 / s2 and the unit, i.e. “in”; “/”; (unit) e.g. T (s). T2 Must be values in the table. 3.57 or 3.572 3.20 or 3.204 2.79 or 2.789 2.40 or 2.403 1.99 or 1.988 1.59 or 1.588 U1 From ± 0.04 to ± 0.02 or ± Allow more than one significant figure, e.g. ± 0.038. 0.03 (c) (i) G1 Six points plotted correctly Must be within half a small square. Ecf allowed from table. U2 Error bars in T 2 plotted Check first and last point. Must be accurate within correctly. half a small square. All plots must have error bars. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (37, 1.5) and (38, 1.5) and upper end of line should pass between (92, 3.7) and (94, 3.7). Allow ecf from points plotted incorrectly – examiner judgement. G3 Worst acceptable straight Line should be clearly labelled or dashed. Should line. pass from top of top error bar to bottom of bottom Steepest or shallowest error bar or bottom of top error bar to top of bottom possible line that passes error bar. Mark scored only if error bars are plotted. through all the error bars. (iii) C1 Gradient of best fit line 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. U3 Error in gradient Method of determining absolute error. Difference in worst gradient and gradient. (d) C2 g = 4π2/gradient = Gradient must be used correctly. 39.5/gradient Allow ecf from (c)(iii). U4 Determines uncertainty in g Uses worst calculated g value or fractional method. Do not check calculation. C3 Consistent unit: cm s–2 or Penalise POT. Allow equivalent cm/s2 and m/s2 m s–2 Unit must be consistent with working. GCE AS/A LEVEL – May/June 2010 9702 52 (e) (i) C4 24.6 to 25.9 given to 3 sf Allow m, etc. or 25 or 26 given to 2 sf. (ii) U5 Determines percentage Check method; allow with or without consideration uncertainty in l of ∆T. [Total: 15] Uncertainties in Question 2 (c) (iii) Gradient [E3] 1. Uncertainty = gradient of line of best fit – gradient of worst acceptable line 2. Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (d) [E4] 1. Uncertainty = g from gradient – g from worst acceptable line ∆g ∆gradient 2. = g gradient (e) [E5] 1. Works out worst l then finds difference then uses 2 ∆g ∆gradient ∆l 2. × 100 = × 100 = × 100 g gradient l ∆g  2 ∆T  ∆gradient  2 ∆T  ∆l 3.  +  × 100 =  +  × 100 = × 100 g  T  gradient  T  l

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