Physics • Year 12 • Module 6 • Lesson 14
Lenz's Law and Direction
Build HSC Band 5–6 extended-response technique by evaluating electromagnetic braking, designing a Lenz's Law investigation, and constructing a conservation-of-energy argument.
1. Data + scenario: electromagnetic braking in a roller-coaster (Band 5–6)
8 marks Band 5–6
Scenario. Modern roller-coasters use electromagnetic brakes (EM brakes) instead of friction brakes in some sections. A series of powerful permanent magnets is mounted on the train carriage. As the carriage passes through the brake zone, these magnets sweep past aluminium fins fixed to the track. The table below shows data for a test run.
| Measurement | Value |
|---|---|
| Mass of carriage + passengers | 2 400 kg |
| Speed of carriage entering brake zone | 28 m s−1 |
| Speed of carriage leaving brake zone | 8 m s−1 |
| Length of brake zone | 12 m |
| Number of aluminium fin pairs in zone | 6 |
| Material of fins | Aluminium (non-magnetic) |
Illustrative data. Assume horizontal track throughout the brake zone.
Q1. Analyse and evaluate the electromagnetic braking scenario above. In your response you must:
- Explain, using Lenz’s Law, why the aluminium fins exert a braking (retarding) force on the carriage even though aluminium is not ferromagnetic.
- Calculate the kinetic energy lost by the carriage in the brake zone and state where this energy is transferred (conservation of energy).
- Explain why the braking force is greatest when the carriage moves fastest, and decreases as the carriage slows down.
- Identify one advantage of EM brakes over friction brakes in this application, and one limitation of EM brakes.
- Predict what would happen to the braking force if the magnets were replaced with ones twice as strong, justifying with reference to the induced emf equation.
2. Experimental design — verifying Lenz’s Law with a coil and oscilloscope (Band 5–6)
7 marks Band 5–6
Research question. A student claims: “The direction of the induced current in a coil is always such that it opposes the flux change that caused it, and the magnitude of the induced emf is proportional to the rate of flux change.” Design a scientific investigation to test both claims simultaneously using a bar magnet and a coil connected to an oscilloscope.
Available equipment: A 200-turn coil (resistance 10 Ω), a bar magnet with labelled north/south poles, a digital oscilloscope set to voltage vs time mode, a ruler, a stopwatch, and standard laboratory supports.
Q2. Design the investigation in the structured format below.
- State two separate hypotheses (one for direction, one for magnitude).
- Identify the independent variable, dependent variable, and at least two controlled variables.
- Describe the procedure in at least five numbered steps, including how you will determine the direction of the induced current from the oscilloscope trace, and how you will vary the rate of flux change.
- Explain what specific oscilloscope result would support each hypothesis.
- State two sources of error and one way to improve reliability.
Q1 — Sample Band 6 response (8 marks), annotated
Lenz's Law in aluminium fins: Although aluminium is non-magnetic (not ferromagnetic), it is a good electrical conductor. As the carriage magnets sweep past each aluminium fin, the magnetic flux through the fin changes rapidly. By Faraday’s Law, this changing flux induces an emf in the fin, driving eddy currents within the bulk aluminium. By Lenz’s Law, these eddy currents flow in a direction such that the magnetic field they produce opposes the change in flux — which means they oppose the relative motion of the magnet and fin. This opposition appears as a retarding force on the carriage, slowing it down without any physical contact. [2 — 1 for Faraday/eddy current mechanism, 1 for Lenz opposition = retarding force]
Kinetic energy calculation: KE lost = ½mvi2 − ½mvf2 = ½ × 2400 × 282 − ½ × 2400 × 82 = 940 800 − 76 800 = 864 000 J (864 kJ). By conservation of energy, this energy is transferred to the aluminium fins as electrical energy in the eddy currents, then dissipated as thermal energy (heat) in the fins. [1 — correct KE calculation; 1 — explicit conservation statement: electrical → heat in fins]
Force greater at higher speed: The rate of flux change (ΔΦ/Δt) is proportional to the speed of the carriage. By Faraday’s Law, a higher rate of flux change induces a larger emf in each fin, which drives larger eddy currents. Larger currents in the external magnetic field experience a larger opposing force (F = BIL). As the carriage slows, ΔΦ/Δt decreases, the induced emf and eddy currents decrease, and the braking force decreases. The system is self-regulating: it brakes more strongly at high speed and less at low speed. [1 — links speed to ΔΦ/Δt to emf to force]
Advantage and limitation: Advantage: no physical contact means no wear or friction heat on the braking surfaces — maintenance-free and reliable over millions of cycles. Limitation: EM braking force falls to zero when the carriage is stationary (zero ΔΦ/Δt = zero induced emf), so EM brakes cannot hold a stationary carriage — a separate friction or mechanical lock is needed. [1 — valid advantage; accept: contactless, no sparks, smooth braking. 0.5 + 0.5 or 1 mark total for this criterion]
Stronger magnets prediction: The induced emf is given by ϵ = −N ΔΦ/Δt. If the magnetic field strength doubles, the flux Φ = BA doubles, so ΔΦ/Δt doubles at the same carriage speed. This doubles the induced emf and hence the eddy currents. The force F ∝ I ∝ emf ∝ B, and since the force on a current in a field is F = BIL, the braking force scales as B2: doubling B quadruples the braking force. [1 — prediction with F ∝ B2 reasoning from emf & force equations]
Marking criteria (8 marks): 1 = explains eddy currents in aluminium via Faraday’s Law and Lenz’s Law correctly. 1 = states the induced force opposes relative motion (retarding, not accelerating). 1 = correct KE calculation (864 kJ). 1 = conservation of energy stated: KE → electrical → heat in fins. 1 = explains force–speed relationship using ΔΦ/Δt. 1 = valid advantage of EM over friction brakes. 1 = valid limitation (cannot hold stationary carriage OR any other valid limitation). 1 = predicts braking force increases (ideally states quadruples for double B) with equation-based justification.
Q2 — Sample Band 6 response (7 marks), annotated
Hypotheses: (1) Direction: if Lenz’s Law holds, pushing a north pole into the coil will produce an upward deflection on the oscilloscope trace (positive emf), and pulling it out will produce a downward deflection (negative emf) of the same magnitude, indicating current reversal that opposes the change. (2) Magnitude: if emf ∝ rate of flux change, pushing the magnet faster into the coil will produce a larger peak voltage on the oscilloscope than pushing it slowly. [1 — two hypotheses: one for direction, one for magnitude]
Variables: Independent variable: (a) direction of magnet motion (in/out) for hypothesis 1; (b) speed of magnet entry for hypothesis 2. Dependent variable: the voltage–time trace displayed on the oscilloscope (peak voltage and sign). Controlled variables: number of coil turns (200), distance through which magnet is pushed (10 cm), magnet used (same magnet throughout), orientation of coil relative to magnet. [1 — IV, DV and two controlled variables named]
Procedure: (1) Connect the 200-turn coil to the oscilloscope input, set to voltage vs time, with the coil axis horizontal and the oscilloscope set to DC-coupled mode. (2) Hold the magnet 15 cm from the coil with the north pole facing the coil. Note the baseline (zero voltage). (3) Push the north pole steadily into the coil at approximately 10 cm s−1 over 1 s; observe and record the sign and magnitude of the peak voltage on the oscilloscope. (4) Allow the trace to return to zero (hold magnet stationary). Then pull the magnet out at the same speed; observe and record the sign and magnitude of the peak voltage. (5) Repeat step 3 three times — once slowly (~5 cm s−1), once at the standard speed (~10 cm s−1), and once quickly (~20 cm s−1) — recording peak voltage each time. (6) Use the right-hand grip rule to predict the expected current direction for each case, and compare with the oscilloscope sign. [1 — five or more steps; 1 — includes direction test with in/out and sign comparison; 1 — includes speed variation to test magnitude]
Expected results supporting hypotheses: Hypothesis 1 supported if: pushing north pole in gives positive peak; pulling out gives negative peak of equal magnitude. This confirms the induced current reverses direction when flux change reverses, consistent with Lenz’s Law. Hypothesis 2 supported if: peak voltage increases proportionally with pushing speed (e.g. 4 mV at 10 cm s−1; 8 mV at 20 cm s−1), confirming emf ∝ ΔΦ/Δt. [1 — correct prediction for each hypothesis]
Sources of error and improvement: Error 1: Difficulty maintaining a constant pushing speed by hand introduces variability in ΔΦ/Δt, making magnitude comparisons unreliable. Error 2: The coil axis may not be perfectly aligned with the magnet’s field, reducing flux linkage and causing a smaller emf than predicted. Improvement: use a motion sensor or a rail guide to ensure the magnet is moved at a precisely controlled, repeatable speed; repeat each measurement five times and average the peak voltages to improve reliability. [1 — two errors; 1 — improvement]
Marking criteria (7 marks): 1 = two clearly distinct hypotheses (one directional, one quantitative/proportional). 1 = IV, DV, and at least two controlled variables identified. 1 = five or more procedural steps in logical order. 1 = direction test clearly described (in vs out → sign reversal). 1 = speed variation to test magnitude hypothesis. 1 = two valid sources of error. 1 = one specific improvement to reliability with justification.