The method and the results are on the faraday's law lab. Do the analysis yourself first, then check the answers below.
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. These answers go with the AP Physics C lab on faraday's law: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Model answers use the sample results from the table. Your own gradient will depend on your coil and magnet, but the proportional trend should be the same.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 13
v = √(2 × 9.81 × h): 0.99, 1.40, 1.98, 2.43, 2.80 m/s for 5, 10, 20, 30, 40 cm.
Question 2 Graph
The points lie close to a straight line through (or very near) the origin, so ε is directly proportional to v.
Question 3 Gradient
The best-fit line has gradient about 39 mV per m/s (units mV·s/m, equivalent to 3.9 × 10⁻² V·s/m).
Question 4 Link to Faraday’s law
The flux linkage through the coil changes as the magnet moves. A faster magnet changes the flux over a shorter time, so dΦ/dt, and therefore ε, increases in proportion. ε ∝ v.
Question 5 Sources of error
Air resistance and friction with the tube reduce the speed, and eddy-current braking in the coil also slows the magnet. The true v is lower than √(2gh).
Question 6 Uncertainty
At 5 cm: 3/37 × 100 = 8 %. At 40 cm: 3/108 × 100 = 2.8 %. The uncertainty is about 8 % and 2.8 %: the same absolute spread matters more for small signals.
Question 7 Improvement
Use a pair of light gates to measure the speed directly, and integrate the logged emf over time to find the flux change ΔΦ = (1/N)∫ε dt. Then compare the integral with the flux change expected from the magnet’s field.
