Physics • Year 12 • Module 6 • Lesson 13
Faraday's Law of Induction
Build HSC Band 5–6 extended-response technique by analysing multi-step scenarios, evaluating experimental data, and connecting Faraday's Law to real technology.
1. Multi-step analysis: the falling-magnet braking experiment (Band 5–6)
9 marks Band 5–6
Scenario. A student drops a neodymium magnet through a vertical copper tube (length 0.50 m, wall thickness 1.0 mm). She measures that the magnet takes 2.8 s to exit the tube, compared with 0.32 s in free-fall through air over the same distance. She repeats with a weaker ferrite magnet and observes the copper tube barely slows it at all. She also tries the neodymium magnet in a copper tube that has been cut along its length into a C-shape: the magnet now falls at essentially free-fall speed.
| Trial | Tube type | Magnet | Fall time (s) | Approximate average speed (m/s) |
|---|---|---|---|---|
| 1 | Complete copper tube | Neodymium (strong) | 2.8 | |
| 2 | Complete copper tube | Ferrite (weak) | 0.38 | |
| 3 | C-shaped copper tube | Neodymium (strong) | 0.33 |
Illustrative data. Tube length = 0.50 m. Free-fall time through air = 0.32 s.
Q1. Analyse and evaluate the experimental data above to explain the braking effect and assess the role of Faraday's Law and Lenz's Law. In your response you must:
- Calculate the average speed of the magnet in Trials 1, 2 and 3, and compare with free-fall. Enter your speeds in the table above.
- Explain, using Faraday's Law, why the neodymium magnet is braked much more strongly than the ferrite magnet.
- Explain, using the concept of closed eddy-current loops, why cutting the tube into a C-shape eliminates the braking effect.
- State what would happen to the braking force as the magnet's speed increases (reference the rate of flux change).
- Identify one source of experimental uncertainty and suggest how it could be reduced.
2. Experimental design — testing Faraday's Law quantitatively (Band 5–6)
8 marks Band 5–6
Research question. A student wants to verify that the magnitude of the induced emf is directly proportional to the rate of change of magnetic flux, as stated by Faraday's Law. Design a controlled investigation that would allow this relationship to be tested quantitatively.
Constraints: You have access to a multi-turn coil (N = 100 turns, area = 2.0 × 10−3 m2), a calibrated bar magnet, a sensitive voltmeter or datalogger, a stopwatch, and a ruler. You may not use any power supply.
Q2. Design the investigation and present it in the format below.
- State your hypothesis as a testable prediction, identifying the independent variable, dependent variable, and at least two controlled variables.
- Describe a procedure in at least four numbered steps that varies the rate of flux change in a controlled way and measures the induced emf.
- Explain what pattern of results would support your hypothesis (describe the expected graph).
- Identify two limitations of your design and one improvement to increase reliability.
Q1 — Sample Band 6 response (9 marks), annotated
Average speeds: Trial 1: v = 0.50/2.8 = 0.18 m/s. Trial 2: v = 0.50/0.38 = 1.3 m/s. Trial 3: v = 0.50/0.33 = 1.5 m/s. Free-fall (air): v = 0.50/0.32 = 1.6 m/s. (1 mark for correctly calculating all three speeds and entering in the table.)
Why neodymium is braked more than ferrite: The neodymium magnet has a much stronger magnetic field, so as it moves through the copper tube, the rate of change of flux through each cross-section of the tube (ΔΦ/Δt) is much larger than for the ferrite magnet. By Faraday's Law (ε = −ΔΦ/Δt for each elemental loop), a larger ΔΦ/Δt induces a larger emf in the tube, driving larger eddy currents. By Lenz's Law, these eddy currents produce a magnetic field opposing the magnet's motion, creating a greater braking force. The ferrite magnet induces much weaker eddy currents, hence negligible braking. (2 marks: 1 for Faraday's Law explanation with ΔΦ/Δt, 1 for Lenz's Law direction of braking.)
Why the C-shaped tube eliminates braking: Eddy currents are circulating loops of current induced in the conducting material. In a complete tube, these loops can flow in closed circular paths around the tube's circumference, allowing large currents. Cutting the tube into a C-shape breaks the conducting path: the gap prevents the induced currents from completing their circuit. With no closed current loops, no significant eddy currents flow, so no opposing magnetic force is produced and the magnet falls at free-fall speed. (2 marks: 1 for explaining closed loops are needed, 1 for explaining that the gap breaks the circuit.)
Braking force as speed increases: As the magnet's speed increases, it sweeps more quickly through the changing field region, increasing ΔΦ/Δt. By Faraday's Law, this increases the induced emf, which increases the eddy current magnitude. By Lenz's Law, the opposing braking force also increases. This self-regulating mechanism means that the faster the magnet falls, the greater the braking force, until the braking force equals gravity and the magnet reaches terminal velocity — it cannot continue to accelerate. (2 marks: 1 for linking speed to ΔΦ/Δt, 1 for explaining terminal velocity via force balance.)
Uncertainty and improvement: One source: human timing with a stopwatch introduces reaction-time error of ∼0.1–0.2 s, which is significant when total fall times are less than 0.4 s (Trials 2 and 3). Improvement: use a light gate or datalogger at the bottom of the tube to record transit time electronically, reducing timing uncertainty to <1 ms. (1 mark for identifying a valid uncertainty; 1 mark for a specific, actionable improvement.)
Marking criteria summary (9 marks): 1 = correct speeds in table; 2 = Faraday/Lenz explanation of neodymium vs ferrite; 2 = closed-loop explanation for C-shape; 2 = speed–braking force–terminal velocity reasoning; 1 = valid uncertainty named; 1 = specific improvement.
Q2 — Sample Band 6 response (8 marks), annotated
Hypothesis: If the magnitude of the induced emf is directly proportional to the rate of change of magnetic flux (ΔΦ/Δt), then increasing the speed at which the bar magnet passes through the coil will produce a proportionally larger peak emf, as predicted by ε = NΔΦ/Δt. Independent variable: speed of the magnet entering the coil (varied by pushing the magnet at different consistent speeds). Dependent variable: peak induced emf (measured in mV by voltmeter or datalogger). Controlled variables: same bar magnet, same coil (N = 100, A = 2.0 × 10−3 m2), same direction of entry (N-pole first), same temperature. (1 mark for hypothesis with IV and DV named.)
Procedure: (1) Connect the 100-turn coil to a peak-reading voltmeter or datalogger set to record the maximum emf reading. (2) Hold the magnet at a fixed distance (e.g. 30 cm) above the coil entry. Drop the magnet from this height in a controlled manner so it enters the coil at a consistent speed; use a ruler and stopwatch to estimate entry speed (v ≈ 2d/t where d = drop distance). Record the peak emf. Repeat 3 times and average. (3) Repeat step 2 from different drop heights (e.g. 10 cm, 20 cm, 40 cm, 50 cm) to vary the entry speed. (4) Plot peak emf (y-axis) against estimated entry speed (x-axis). (1 mark for four clear, logical steps that control the flux change rate.)
Expected results supporting the hypothesis: The graph of emf vs estimated entry speed should show a linear (straight-line) relationship passing through the origin, consistent with ε ∝ ΔΦ/Δt ∝ v. Any non-linearity would indicate additional factors (e.g. changing coil alignment). (1 mark for describing a linear graph with correct axes.)
Limitations: (1) Estimating speed from drop height (v = √2gd) assumes the magnet is in free-fall, but air resistance and hand-release inconsistency introduce error. (2) The magnet's flux distribution is non-uniform; as it enters the coil at different heights, the effective ΔΦ is not simply proportional to speed, making the relationship approximate. (1 mark each for two valid limitations.)
Improvement: Use a photogate positioned at the coil entry to precisely measure the magnet's speed as it enters, removing dependence on estimated speeds and reducing the dominant source of uncertainty. Alternatively, mount the coil vertically and use a datalogger to plot emf vs time continuously for multiple speeds. (1 mark for a specific, actionable improvement.)
Marking criteria summary (8 marks): 1 = testable hypothesis with IV, DV; 1 = controlled variables (at least two); 1 = four steps varying ΔΦ/Δt and measuring emf; 1 = expected linear graph described; 1 = first limitation; 1 = second limitation; 1 = one specific improvement; 1 = uses precise terminology (ΔΦ/Δt, Faraday's Law, eddy currents, datalogger).