Fig. 1.1 shows a bar magnet attached to a spring. -spring N bar magnet S Fig. 1.1 The bar magnet is displaced a distance x from its equilibrium position and released. It then oscillates vertically. A student investigates how the maximum induced electromotive force (e.m.f.) E in a coil placed below the magnet depends on x. It is suggested that the relationship between E and x is E = αBNx√(k/m) where B is the magnetic flux density at one of the poles of the bar magnet, N is the number of turns on the coil, k is the spring constant, m is the mass of the magnet and α is a constant. Design a laboratory experiment to test the relationship between E and x. Explain how your results could be used to determine a value for α. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to: • 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.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

1. [1] x is the independent variable and E is the dependent variable, or vary x and measure E.
2. [1] Keep B or m constant and keep k or N constant.
3. [1] Labelled diagram of workable experiment including: labelled spring supported by stand and clamp; labelled magnet; labelled coil positioned so that magnet is vertically above the coil by eye in the correct orientation.
4. [1] Circuit diagram showing voltmeter / multimeter set to p.d. range / oscilloscope connected to the ends of the coil. Do not accept other electrical components.
5. [1] Method to measure x, e.g. labelled ruler drawn parallel to spring/magnet and equilibrium position and displaced position indicated and x indicated or difference determined or description of use of ruler to measure equilibrium position and displaced position and difference determined.
6. [1] Method to measure mass of magnet e.g. use balance or use newton-meter to measure weight and divide by g.
7. [1] Plots a graph of E against x or equivalent. Allow lg E against lg x.
8. [1] Relationship valid if a straight line passing through the origin is produced. (for lg E against lg x: relationship valid if a straight line with gradient = 1).
9. [1] α = (gradient / BN) * √(m/k) (for E against x) OR α = 10^(y-intercept) / (BN * √(m/k)) (for lg E against lg x).
10. [6] Max 6 for Additional detail including safety considerations:
11. Use safety goggles / safety screen to prevent injury (to eyes) from (detached) spring/magnet; do not accept from oscillating magnet or use cushion / sand box in case magnet falls or use g clamp / weights on stand to prevent toppling.
12. Keep distance between equilibrium position and coil constant.
13. Check that the unstretched length of the spring has not changed or is not permanently deformed (after removing load/magnet).
14. Expression to determine k from relevant experiment, e.g. k = mg / extension or gradient of F – extension graph. Weight/force must be defined.
15. Measure B using a (calibrated) Hall probe.
16. 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.
17. Method to maximise E, e.g. position magnet so that equilibrium position is at the centre of the coil or use a large number of turns.
18. Explanation to determine max E e.g. use of video and slow-motion playback.
19. Repeat experiment for each x and average E.
20. Method to ensure clamped rule to measure x is vertical, e.g. correctly positioned set square indicated at right angles between the rule and the horizontal surface or plumb line supported on a surface shown in appropriate position.