A flat circular coil P carrying a current produces a magnetic field. When a second coil Q is placed with its centre a distance x from the centre of coil P, as shown in Fig. 1.1, an e.m.f. V may be induced in coil Q. [Figure 1.1] It is suggested that V is related to x by the relationship V = Voe-kx where Vo and k are constants. Design a laboratory experiment to test the relationship between V and x. Explain how your results could be used to determine a value for k. 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 (Oct/Nov 2017). The mark or mark type is shown in brackets.

1. [1] x is the independent variable and V is the dependent variable or vary x and measure V
2. [1] keep current (in the coil P) constant
3. [1] labelled diagram showing both coils supported
4. [1] two correct circuit diagrams for coil P and coil Q: power supply connected to one coil and voltmeter/c.r.o. connected to other coil
5. [1] method to determine x, e.g. use a ruler or drawn labelled horizontal ruler adjacent to coils with x indicated
6. [1] method to measure x from centre of coil P to centre of coil Q, e.g. measure width of (each) coil and divide by 2 and add to separation of coils
7. [1] plots a graph of In V against x [or log V against x etc.]
8. [1] relationship valid if a straight line produced
9. [1] k = -gradient
10. [1] D1 do not touch hot coil/use gloves to position hot coil/heat-proof gloves to position coil
11. [1] D2 use large current/number of turns/iron core (to produce large magnetic field/induced e.m.f.)
12. [1] D3 use high frequency (to produce larger induced e.m.f.)
13. [1] D4 use an a.c. power supply or signal generator (connected to coil P)
14. [1] D5 keep the number of turns (on each coil) constant/frequency constant
15. [1] D6 method described to check that current is constant, e.g. use an ammeter and variable resistor/variable power supply
16. [1] D7 repeat measurements of x for different parts of the coil and average
17. [1] D8 method to position ruler horizontally to measure x described e.g. use a spirit level or same height from bench at both ends
18. [1] D9 method to keep coils parallel/co-axial e.g. adjust coil Q until maximum reading or use set square to ensure that coils are at right angles to the axis
19. [1] D10 InV = -kx + In Vo