The method and the results are on the faraday's law lab. Do the analysis yourself first, then check the answers below.
Quick answer: Electromagnetic induction produces an emf whenever the magnetic flux Φ = BA cos θ through a loop changes. These answers go with the AP Physics 2 lab on faraday's law: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The sample data show a nearly proportional link between peak emf and speed, with a slope of about 0.21 V·s/m. The answers below link the pattern to Faraday’s law and mention the main limitations.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 12
Question 1 Entry speed
v = √(2 × 9.81 × 0.30) = 2.43 m/s. This assumes free fall, so air resistance and friction with the tube are neglected.
Question 2 Graph
The graph is close to a straight line through the origin: the emf rises in proportion to the speed.
Question 3 Slope of the graph
Slope = (0.59 − 0.21) / (2.80 − 0.99) = 0.38 / 1.81 = 0.21 V·s/m (volts per metre per second).
Question 4 Meaning of the result
The flux linkage changes by about the same amount as the magnet passes the coil, but a faster magnet does it in less time. ε = NΔΦ/Δt is therefore proportional to the speed.
Question 5 Area under a pulse
The area under the emf-time graph equals NΔΦ, so ΔΦ = 2.1 × 10⁻³ / 500 = 4.2 × 10⁻⁶ Wb. Notice that this does not depend on the speed.
Question 6 Two pulses
As the magnet enters, the flux through the coil increases, and as it leaves the flux decreases. By Lenz’s law the induced currents are in opposite directions, so the emf changes sign.
Question 7 Limitations
Air resistance and friction with the tube wall slow the magnet, and eddy currents in any metal nearby also oppose the fall. Use a wider plastic tube, a smoother inner surface, and measure the speed directly by timing between two light gates. The true speed is below √(2gh).
