Experimental design and analysis (LAB)
Counting a solenoid's turns with induction
- Units 12 and 13
- 10 points
- About 27 minutes
You can use a calculator on this question, just like on exam day.
A two-part lab question. First you design an experiment to answer a question: what you change, what you measure, the equipment and how you would analyze the data. Then you get a data table from a similar experiment, choose what to graph (often so the points fall on a straight line), plot it and use the slope, the intercept or the graph’s shape to answer a question. On the exam: Question 3 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator and equation sheet allowed. The CED suggests 25–30 minutes.
The question and its sources
Students want to determine the number of turns per unit length n of a long solenoid whose windings are hidden under tape. They will use the emf induced in a small coil placed inside the solenoid.
Part A: Available equipment
The long solenoid; a power supply that can make the solenoid's current increase at a steady rate the students choose; a current sensor connected to a computer that graphs current against time; a small search coil with N = 500 turns and cross-sectional area A = 4.0 cm², which fits inside the solenoid; a sensitive voltmeter that reads in millivolts; and a ruler.
Source: Hypothetical lab setup
Part B: Table 1. Another group's data (search coil at the center of the solenoid, coaxial with it)
| Rate of increase of solenoid current dI/dt (A/s) | Emf induced in search coil (mV) |
|---|---|
| 2.0 | 0.77 |
| 4.0 | 1.49 |
| 6.0 | 2.28 |
| 8.0 | 3.00 |
| 10.0 | 3.79 |
Source: Hypothetical data
Suggested time: 27 minutes
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Part (A(i))
3 pointsDescribe an experimental procedure you could use, with only the equipment listed, to collect data that would allow you to determine n. Include what you would measure, what you would change, and any steps you would take to reduce experimental uncertainty.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (A(ii))
2 pointsDescribe how you would use your data to determine n. Include what you would graph and how the graph would give you n.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(i))
1 pointUsing the data in Table 1, indicate which quantities you would graph to produce a straight line that could be used to determine n, and explain why that graph should be a straight line.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(ii))
2 pointsPlot the quantities you chose and draw a best-fit line. You can't draw here, so describe the graph you would draw: what goes on each axis (with units), the scale, the points you would plot (list their values), and the best-fit line.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (B(iii))
2 pointsUse your best-fit line to calculate an experimental value for n.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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