Physics 9702/51 October/November 2022: question paper and mark scheme

Mark scheme

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

Mark scheme

2(a) πYZd 2 1 gradient = 4ρ 2(b) 1 1 / 10–3 Ω–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 Δy / Δx. 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 Δy / Δx. 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) ρ determined using gradient and ρ given to two or three significant figures. 1 πYZd 2 π × 22 × 22 × (d)2 ρ= = 4 × gradient 4 × (c)(iii) ρ determined using gradient and given with correct SI unit (Ω m) and correct power of ten 1 2(e)(ii) percentage uncertainty in ρ: 1 2 × Δd Δgradient percentage uncertainty = + + 0.05 + 0.05 × 100 d gradient or correct substitution for max/min methods π × (1.05 × 22) × (1.05 × 22) × ( d + Δd ) 2 max ρ = 4 × min gradient π × ( 0.95 × 22 ) × ( 0.95 × 22 ) × ( d − Δd ) 2 min ρ = 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 πYZd 2 π × 22 × 22 × (d)2 R= = 4ρL 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: Δgradient ΔR = ×R gradient or for R determined using (d) and (e)(i): 2 × Δd Δρ ΔR = + + 0.05 + 0.05 × R d ρ or correct substitution for max/min methods: π × (1.05 × 22) × (1.05 × 22 ) × ( d + Δd ) 2 max R = 4 × min ρ × 0.950 π × ( 0.95 × 22 ) × ( 0.95 × 22 ) × ( d − Δd ) 2 min R = 4 × max ρ × 0.950