HSC Exam Practice

Sample response. Lenz’s Law states that the direction of an induced current is always such that the magnetic field it produces opposes the change in magnetic flux that caused it. It predicts that when flux through a loop increases, the induced current produces a field opposing that increase; when flux decreases, the induced current produces a field reinforcing the decreasing flux.

Marking notes. 1 mark for correctly stating Lenz’s Law (opposition principle, flux change). 1 mark for correctly describing the prediction: induced current direction creates a field that opposes the flux change (not the field itself). Accept equivalent wording.

Sample response. (1) Identify the direction of the external magnetic field through the loop. (2) Determine whether the magnetic flux through the loop is increasing or decreasing. (3) The induced magnetic field must oppose the change: if flux is increasing, the induced B points opposite to the external B; if flux is decreasing, the induced B points in the same direction as the external B. (4) Apply the right-hand grip rule: point the thumb of the right hand in the direction of the required induced B field; the fingers curl in the direction of the induced current.

Marking notes. 1 mark per correct step. Accept equivalent wording for each step. All four must be present for full marks.

Sample response. The negative sign encodes Lenz’s Law mathematically. The induced emf (ϵ) has the opposite sign to the rate of change of flux (ΔΦ/Δt), meaning the induced emf drives a current that opposes the change. If the flux is increasing (positive ΔΦ/Δt), the emf is negative (drives current in the opposing direction). This sign convention ensures energy is not created from nothing — it is the mathematical expression of opposition.

Marking notes. 1 mark for identifying that the negative sign means the induced emf opposes the flux change. 1 mark for linking this to Lenz’s Law (opposition principle) or to conservation of energy (the emf drives a current that opposes, so work must be done by an external agent).

Sample response. The claim is incorrect. Lenz’s Law is not merely a mnemonic — it is a direct consequence of the conservation of energy. If the induced current aided the flux change (rather than opposing it), the resulting force on a moving magnet would be attractive rather than repulsive. The magnet would accelerate indefinitely, generating increasing electrical energy from no external source. This is a perpetual motion machine — prohibited by conservation of energy. Therefore Lenz’s Law must hold: the induced current opposes the motion, requiring external work to be done against the opposing force. This work is the source of the electrical energy. Lenz’s Law is a direct expression of energy conservation, not an empirical shortcut.

Marking notes. 1 mark for identifying that the student’s claim is incorrect and stating why (Lenz’s Law is a consequence of conservation of energy). 1 mark for describing the perpetual motion scenario that would result if the current aided the change. 1 mark for explicitly linking Lenz’s Law to conservation of energy — the work done against the opposing force is the source of electrical energy.

Sample response. Given: N = 50; ΔΦ = 20 − 80 = −60 mWb = −60 × 10⁻³ Wb; Δt = 0.30 s. ϵ = −N ΔΦ/Δt = −50 × (−60 × 10⁻³)/0.30 = −50 × (−0.200) = +10 V. Magnitude of induced emf = 10 V.

Marking notes. 1 mark for correctly substituting values (including conversion to Wb). 1 mark for correct application of formula. 1 mark for correct answer with correct unit (10 V). Award marks if the student uses |ΔΦ/Δt| and obtains 10 V. Deduct 1 mark for unit error only if the final answer is otherwise correct.

Sample response (a). The two intervals with induced emf are: (1) approximately 0.20–0.26 s (positive peak), during which the north pole of the magnet is entering the coil — the flux through the coil is increasing; (2) approximately 0.36–0.42 s (negative peak), during which the north pole of the magnet is exiting the coil downward — the flux is decreasing. Between 0.26 and 0.36 s the magnet is centred in the coil; flux is momentarily constant so emf is zero. [1 — correct identification of both intervals; 1 — correct event (entering/exiting) for each]

Sample response (b). By Faraday’s Law, emf = −N ΔΦ/Δt, so the magnitude of the induced emf is proportional to the rate of flux change, which depends on the speed of the magnet. When the magnet enters the coil (positive peak), the magnet is moving relatively slowly (it has just begun to fall from rest). When the magnet exits the coil (negative peak), it has been accelerating under gravity for longer and is therefore moving faster. A faster magnet sweeps through the coil more quickly, producing a larger rate of flux change and hence a larger induced emf (−26 mV > 18 mV in magnitude). By Lenz’s Law the direction reverses because the flux change reverses: entering = increasing flux = positive peak; exiting = decreasing flux = negative peak. [1 — faster at exit; 1 — links speed to rate of flux change and emf; 1 — direction reversal explained by Lenz’s Law]

Sample response (c). During the positive peak, ϵ = +18 mV = 18 × 10⁻³ V; R = 5.0 Ω. I = ϵ/R = (18 × 10⁻³)/5.0 = 3.6 × 10⁻³ A (3.6 mA). [1 — correct formula; 1 — correct answer with unit]

Sample response.

Named scenario and four-step reasoning: Consider a generator: a rectangular coil rotates in a uniform magnetic field. As the coil rotates from perpendicular to the field toward parallel, the magnetic flux through the coil decreases. Step 1: external B field points from north to south pole of the generator magnet (e.g. to the right). Step 2: flux is decreasing as the coil rotates. Step 3: by Lenz’s Law, the induced B field must reinforce the decreasing flux — it points to the right. Step 4: right-hand grip rule with thumb pointing right — fingers curl so current flows in a specific direction in the coil sides (determined by the coil geometry). The induced current always opposes the rotation that causes the flux change, meaning the coil requires a mechanical torque to keep rotating — this mechanical work is the source of the electrical energy.

Conservation of energy argument: Lenz’s Law is a necessary consequence of conservation of energy. Suppose the induced current aided the flux change. A magnet approaching a loop would experience an attractive force, accelerating toward the loop. The faster it moved, the larger the emf, the larger the induced current, the stronger the attracting force — the magnet would accelerate indefinitely, generating ever-increasing electrical energy from no energy input. This is a perpetual motion machine, which is prohibited by the First Law of Thermodynamics (energy cannot be created from nothing). Therefore the induced current must oppose the change — Lenz’s Law must hold.

Source of electrical energy: Because the induced current opposes the motion, an external agent must do work against the opposing force to maintain the flux change. This mechanical work (by the person pushing the magnet, or by the engine driving the generator) is the source of the electrical energy produced. Energy is converted from mechanical form to electrical form; no energy is created. The amount of electrical energy produced equals the work done by the external agent against the Lenz’s Law force (in an ideal system without resistive losses).

Practical application — electromagnetic braking: In electromagnetic (EM) braking systems used in trains and roller-coasters, powerful magnets on the vehicle induce eddy currents in stationary conducting fins or rails. By Lenz’s Law, these eddy currents produce a magnetic field that opposes the relative motion of the vehicle — a retarding force that decelerates the vehicle. The kinetic energy of the vehicle is converted to electrical energy in the eddy currents and then to thermal energy (heat) in the conductor. EM brakes have no physical contact, so there is no wear; the braking force is greatest at high speed (large ΔΦ/Δt) and decreases as the vehicle slows (self-regulating). A key limitation is that the braking force falls to zero when the vehicle is stationary (zero ΔΦ/Δt), so EM brakes cannot hold a vehicle at rest and must be supplemented by friction locks.

Marking criteria (9 marks): 1 = names a scenario other than a simple bar magnet and loop (accept: generator, transformer secondary, induction cooktop, metal detector, EM brake) and correctly identifies the direction of flux change. 1 = correctly applies all four steps to determine induced current direction in that scenario. 1 = explains why the induced current must oppose the flux change (links to perpetual motion argument). 1 = clearly describes the perpetual motion scenario and explains why it violates conservation of energy. 1 = identifies that the source of electrical energy is mechanical work done against the opposing force. 1 = names a specific practical application and correctly describes the role of Lenz’s Law in its operation. 1 = correctly identifies the retarding/opposing force as a consequence of Lenz’s Law in that application. 1 = describes one advantage of the application (e.g. contactless, self-regulating with speed). 1 = describes one limitation of the application (e.g. zero force when stationary, heat dissipation in conductor). Deduct 1 mark if the response lacks explicit linking language (i.e. does not use the phrase “conservation of energy” or equivalent).