Cambridge A Level Physics 9702 — 2011 Oct/Nov Paper 5 · Variant 2

1 A current-carrying coil produces a magnetic field. For Examiner’s It is suggested that the strength B of the magnetic field at the centre of a flat circular coil is Use inversely proportional to the radius r of the coil. Design a laboratory experiment that uses a Hall probe to test the relationship between B and r. 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. [15] Diagram For Examiner’s Use ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... For ......................................................................................................................................................... Examiner’s Use ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... ......................................................................................................................................................... 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) 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) M1 Diagram showing coil and labelled Hall probe positioned in the centre of a coil. Solenoids will not be credited. [1] M2 Circuit diagram for coil connected to a (d.c.) power supply. [1] M3 Connect Hall probe to voltmeter/c.r.o. Allow galvanometer but do not allow ammeter. [1] M4 Measure diameter or radius with a ruler/vernier callipers. [1] M5 Method to locate centre of coil. e.g. determine max VH; cross rules; projection [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] A Relationship is valid if the graph is a straight line passing through the origin [if lg-lg then straight line with gradient = –1 (ignore reference to y-intercept)] [1] 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] 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 of rheostat to keep current constant in coil. 3 Monitor constant current with ammeter to check current is constant. 4 Hall probe at right angles to direction of magnetic field/plane of coil. 5 Reasoned method to keep Hall probe in constant orientation (e.g. use of set square, fix to rule, optical bench or equivalent). 6 B is proportional to voltage across Hall probe/calibrate Hall probe in a known magnetic field. 7 Repeat experiment with Hall probe reversed and average. 8 Repeat measurement for r or d and average. Do not allow vague computer methods. [Total: 15] GCE AS/A LEVEL – October/November 2011 9702 52

More questions on Concept of a magnetic field

2 A scientist is observing some of the moons orbiting the planet Jupiter. For Examiner’s Use Fig. 2.1 For six different moons, the scientist records the distance r from the centre of Jupiter and the period T of the orbit. Question 2 continues on the next page. It is suggested that T and r are related by the equation For Examiner’s T 2 = kr 3 Use where k is a constant. (a) A graph is plotted of lg T on the y-axis against lg r on the x-axis. Determine the value of the gradient and express the y-intercept in terms of k. gradient = ..................................................... y-intercept = ..................................................... [1] (b) Values of r and T are given in Fig. 2.2. r / 106 m T / 103 s lg (r / m) lg (T / s) 129 24 ± 4 181 42 ± 4 422 154 ± 8 671 304 ± 8 1070 590 ± 15 1880 1420 ± 15 Fig. 2.2 Calculate and record values of lg (r / m) and lg (T / s) in Fig. 2.2. Include the absolute uncertainties in lg (T / s). [3] (c) (i) Plot a graph of lg (T / s) against lg (r / m). Include error bars for lg (T / 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 uncertainty in your answer. gradient = ................................................ [2] For 6.4 Examiner’s Use 6.2 lg (T / s) 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6 4.4 4.2 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 lg (r / m)

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 1.5 or 3/2 Ignore y-intercept (incorrect y-intercept will be penalised in (d)(i)). (b) T1 Allow a mixture of decimal places. 8.111 or 8.1106 4.38 T2 T1 must be table values. 8.258 or 8 2577 4.62 T2 must be a minimum of 2 d.p. 8.625 or 8.6253 5.188 (5.19) Ignore rounding errors. 8.827 or 8.8267 5.483 (5.48) 9.029 or 9.0294 5.771 (5.77) 9.274 or 9.2742 6.152 (6.15) U1 From ± 0.07 or ± 0.08, to ± 0.005 Allow more than one significant figure. (c) (i) G1 Six points plotted correctly Must be within half a small square. Do not allow ‘blobs’ (more than half a small square). Ecf allowed from table. U2 Error bars in lg T plotted correctly All error bars to be plotted. Must be accurate to less than half a small square. (c) (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (8.0, 4.20) and (8.0, 4.28) and upper end of line should pass between (9.4, 6.32) and (9.4, 6.38). Allow ecf from points plotted incorrectly – examiner judgement. G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Steepest or shallowest possible line Examiner judgement on worst acceptable that passes through all the error bars. line. Lines must cross. Mark scored only if error bars are plotted. (c) (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 Uncertainty in gradient Method of determining absolute uncertainty Difference in worst gradient and gradient. (c) (iv) C2 Negative y-intercept Must be negative. FOX does not score. Check substitution into y = mx + c. Allow ecf from (c)(iii). U4 Uncertainty in y-intercept Uses worst gradient and point on WAL. Do not check calculation. FOX does not score. (d) (i) C3 Method to determine k k= 102 × y-intercept [k is about 10–16, if FOX 108] U5 Uncertainty in k Best k – worst k using y-intercept. Allow ecf for method from (c)(iv). (d) (ii) C4 M between 2.36 × 1026 and 2.36 × 1028 Must be in range. Allow between 2.4 × 1026 given to 2 or 3 s.f. and 2.4 × 1028 for 2 s.f. [Total: 15] GCE AS/A LEVEL – October/November 2011 9702 52 Uncertainties in Question 2 (c) (iii) Gradient [E3] Uncertainty = gradient of line of best fit – gradient of worst acceptable line Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (iv) [E4] Uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (d) (i) [E5] Uncertainty = best k –worst k

More questions on Gravitational field