Experimental design and analysis (LAB)
Measuring the vacuum permeability with a long wire
- Unit 12
- 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 an experimental value of the vacuum permeability μ₀ by measuring the magnetic field near a long, straight, current-carrying wire.
Part A: Available equipment
A long, straight, vertical wire connected to a DC power supply whose current can be adjusted and is shown on a built-in ammeter (the return wires can be run far from the long wire); a magnetic field sensor that measures the field component along the direction it points and can be zeroed; a stand to hold the sensor; a ruler; and a meterstick.
Source: Hypothetical lab setup
Part B: Table 1. Another group's data (current held at 5.0 A)
| Distance from center of wire to sensor r (cm) | Magnetic field B (μT) |
|---|---|
| 1.0 | 100 |
| 2.0 | 49 |
| 3.0 | 34 |
| 4.0 | 25 |
| 5.0 | 20 |
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 μ₀. 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 μ₀. Include what you would graph and how the graph would give you μ₀.
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 μ₀. Calculate the values you would plot.
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 μ₀.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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