Quick answer: Faraday's law states that a changing magnetic flux through a coil induces an emf equal to −N dΦ/dt, with its direction set by Lenz's law. This AP Physics C lab on faraday's law gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
A falling magnet induces a short pulse of emf in a coil. In this lab you test whether the peak emf grows in proportion to the speed of the magnet, a direct consequence of Faraday’s law.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 13
Aim
To test how the peak emf induced in a coil depends on the speed of a magnet passing through it.
Equipment
- Coil of 400 turns
- Small cylindrical magnet
- Plastic guide tube, clamp stand and ruler
- Voltage sensor or data logger
- Foam pad
Safety
Keep the magnet away from phones and cards, and hold the magnet by its sides to avoid trapped fingers. Clamp the stand firmly so it cannot topple.
Method
- Clamp the tube vertically with its lower end about 2 cm above the coil.
- Release the magnet from rest at height h above the middle of the coil.
- Record the peak emf from the logger trace.
- Repeat three times for each height and take the mean.
- Use five heights from 5 cm to 40 cm.
Results
| Height h (cm) | Mean peak emf (mV) |
|---|---|
| 5 | 37 |
| 10 | 54 |
| 20 | 74 |
| 30 | 93 |
| 40 | 108 |
Analysis questions
Question 1 Speed at the coil
Use v = √(2gh) with g = 9.81 m/s² to find the speed for each height. Tabulate your answers to 2 decimal places.Question 2 Graph
Plot peak emf (y) against v (x) and describe the shape.Question 3 Gradient
Find the gradient of the best-fit line and state its unit.Question 4 Link to Faraday’s law
Explain why the peak emf should be roughly proportional to the speed of the magnet.Question 5 Sources of error
Suggest two reasons the real speed at the coil differs from √(2gh).Question 6 Uncertainty
The emf readings vary by ± 3 mV between repeats. Calculate the percentage uncertainty in the reading at 5 cm and at 40 cm and comment.Question 7 Improvement
Suggest a change of method that would let you check ε = −N dΦ/dt more directly.
