A student is investigating the electric potential near a charged metal sphere. The sphere is suspended from the ceiling as shown in Fig. 2.1. [Figure 2.1] A flame probe is used to measure the potential V at a distance L from the surface of the sphere. The experiment is repeated for different distances from the sphere. It is suggested that V and L are related by the equation V = Q / (4πε₀(L + a)) where Q is the charge on the sphere, a is the radius of the sphere and ε₀ is the permittivity of free space.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [1] gradient = 4πε₀/Q
2. [1] y-intercept = 4πε₀a/Q
3. [1] 0.800 or 0.8000; 0.952 or 0.9524; 1.1 or 1.11; 1.3 or 1.25; 1.4 or 1.43; 1.7 or 1.67
4. [1] absolute uncertainties in 1/V: ±0.03 to ±0.05 or ±0.06
5. [1] Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square.
6. [1] Error bars in 1/V plotted correctly. All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
7. [1] Line of best fit drawn. Points must be balanced. Line should pass to the right of (0.019, 0.800) and line should pass between (0.104, 1.6) and (0.108, 1.6).
8. [1] Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted.
9. [1] Gradient determined with clear substitution of points from line of best fit into Δy/Δx. Distance between points must be at least half the length of the drawn line.
10. [1] uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
11. [1] y-intercept determined by substitution into y = mx + c.
12. [1] y-intercept of worst acceptable line determined by substitution into y = mx + c. uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept). Do not allow if false origin used.
13. [1] Q calculated using gradient. Correct substitution of numbers required. Q = 1.11×10⁻¹⁰ / gradient OR Q = 1.11×10⁻¹⁰ / (c)(iii)
14. [1] a calculated using y-intercept. Correct substitution of numbers required. a = (Q × y-intercept) / 1.11×10⁻¹⁰ OR a = y-intercept / gradient
15. [1] Q and a determined using correct method with: Unit of Q with correct power of ten – C, FV; Correct power of ten for a; Q and a given to 2 or 3 significant figures.
16. [1] Percentage uncertainty in a determined. Correct substitution of numbers required. %uncertainty in Q + %uncertainty in y-intercept or %uncertainty in gradient + %uncertainty in y-intercept. Maximum/minimum methods: max a = (max y-intercept × max Q) / 1.11×10⁻¹⁰ OR max a = max y-intercept / min gradient; min a = (min y-intercept × min Q) / 1.11×10⁻¹⁰ OR min a = min y-intercept / max gradient