Cambridge A Level Physics 9702 — 2022 Oct/Nov Paper 5 · Variant 3

1 A thin copper sheet is suspended from a small hole near the top of the sheet and placed in a magnetic field, as shown in Fig. 1.1. t hole copper sheet area A direction of magnetic field Fig. 1.1 (not to scale) The sheet has area A and thickness t. The sheet is displaced from its equilibrium position through a horizontal distance s0 and then released so that it oscillates perpendicular to the direction of the magnetic field. The horizontal distance s of the sheet from its equilibrium position is measured after five complete oscillations. It is suggested that s is related to A by the relationship s = s0e–ABKt where B is the magnetic flux density of the field and K is a constant. Plan a laboratory experiment to test the relationship between s and A. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine a value for K. In your plan you should include: ● 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: Question Answer Marks 1 Defining the problem A is the independent variable and s is the dependent variable or vary A and measure s 1 keep B and t constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • pin / rod through hole • supported by a stand • sheet able to oscillate freely • at least one label from copper/sheet, hole, clamp, stand, rod, pin. drawn clamped rule(r) parallel to the direction of the oscillations (by eye) (to measure s) 1 use rule(r) to measure lengths to determine A 1 and A = length  breadth use of micrometer to measure t 1 Method of Analysis plot a graph of ln s against A or equivalent 1 relationship valid if a straight line (with y-intercept = ln s0) is produced 1 gradient 1 K = − Bt 1 ( K = − for A against ln s) Bt  gradient 1 Additional detail including safety considerations 6 D1 use of cushion/sand box in case sheet falls or use gloves to protect hands from cuts / sharp edges D2 keep (initial) distance between (copper) sheet and (poles of) magnet constant or keep (initial) distance between (copper) sheet and coil(s) constant D3 keep s0 constant D4 method to ensure s0 is constant, e.g. initially line up (corner of) plate with fiducial marker / vertical pin to keep s0 constant D5 method to determine s using video camera: • rule(r) in a position to measure s in the diagram • video camera shown in diagram or description of use of video camera • playback video recording by frame by frame / slow motion (to measure s) D6 repeat measurements of t in different positions and average t D7 measure B/magnetic flux density using a (calibrated) Hall probe D8 additional detail on use of Hall probe, e.g. adjust probe until maximum value or measure B using Hall probe first in one direction and then in the opposite direction and average D9 drawn method to create a magnetic field perpendicular to the area of the sheet, e.g. pair of magnets/horseshoe magnet/pair of coils connected to a (d.c.) supply D10 repeat experiment for each A and average s

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2 A student investigates a circuit containing resistors and a metal wire as shown in Fig. 2.1. Z P Q crocodile clips V metal wire Y L Fig. 2.1 Resistors Y and Z have resistances Y and Z respectively. The student connects a resistor of resistance R between P and Q. The student then adjusts the length of the wire between the crocodile clips until the voltmeter reads zero. The student measures the length L of wire between the crocodile clips. The student repeats the experiment with different values of R. It is suggested that L and R are related by the equation Z 4ρL = R πYd 2 where d is the diameter of the wire and ρ is the resistivity of the metal. 1 (a) A graph is plotted of L on the y-axis against on the x-axis. R Determine an expression for the gradient. gradient = ......................................................... [1] (b) Values of R and L are given in Table 2.1. Each resistance value R has a percentage uncertainty of ± 5%. Table 2.1 1 R / Ω / 10–3 Ω–1 L / cm R 22 71.0 27 57.5 33 45.0 39 36.5 47 27.5 54 23.0 1 Calculate and record values of / 10–3 Ω–1 in Table 2.1. R 1 Include the absolute uncertainties in R. [2] 1(c) (i) Plot a graph of L / cm against / 10–3 Ω–1. R 1 Include error bars for R. [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) YZd 2 1 gradient = 4 2(b) 1 1 / 10–3 –1 R 45 or 45.5 37 or 37.0 30 or 30.3 26 or 25.6 21 or 21.3 19 or 18.5 1 1 Absolute uncertainties in from ± 2 to ± 0.9 or ± 1. R 2(c)(i) Six points from (b) plotted correctly. 1 Must be within half a small square. Diameter of points must be less than half a small square. 1 1 Error bars in plotted correctly. R All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 2(c)(ii) Straight line of best fit drawn. 1 Points must be balanced. Do not accept line from top point to bottom point. Line must pass between (22.0, 30.0) and (23.0, 30.0) and (40.5, 65.0) and (42.0, 65.0). Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). 1 All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x. 1 Distance between data points must be greater than half the length of the drawn line. Gradient of worst acceptable line determined with clear substitution of data points into y / x. 1 uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(d) 0.261 ± 0.003 (mm) 1 2(e)(i) determined using gradient and given to two or three significant figures. 1 YZd 2  22  22  (d)2 = = 4  gradient 4  (c)(iii) determined using gradient and given with correct SI unit ( m) and correct power of ten 1 2(e)(ii) percentage uncertainty in : 1  2 d gradient  percentage uncertainty =  + + 0.05 + 0.05   100  d gradient  or correct substitution for max/min methods  (1.05  22 )  (1.05  22 )  ( d + d ) 2 max = 4  min gradient  ( 0.95  22 )  ( 0.95  22 )  ( d −d ) 2 min = 4  max gradient 2(f) R determined to at least two significant figures from (c)(iii) or (d) and (e)(i) with correct substitution seen. 1 gradient R = 0.950 or YZd 2  22  22  (d) 2 R = = 4L 4  (e)(i)  0.950 Absolute uncertainty in R determined. 1 Method must be consistent with determination of R and correct substitution must be seen. for R determined using the gradient: gradient R =  R gradient or for R determined using (d) and (e)(i):  2 d   R =  + + 0.05 + 0.05   R  d   or correct substitution for max/min methods:  (1.05  22 )  (1.05  22 )  ( d + d ) 2 max R = 4  min  0.950  ( 0.95  22 )  ( 0.95  22 )  ( d −d ) 2 min R = 4  max  0.950

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