HSC Exam Practice

Sample response. Faraday's Law states that the magnitude of the induced electromotive force (emf) in a coil is equal to the number of turns multiplied by the rate of change of magnetic flux through the coil: ε = −NΔΦ/Δt. Where: ε = induced emf (volts, V); N = number of turns in the coil (dimensionless); ΔΦ = change in magnetic flux (webers, Wb); Δt = time interval over which the flux changes (seconds, s). The negative sign indicates that the induced emf acts in a direction that opposes the change in flux (Lenz's Law).

Marking notes. 1 mark for a correct word statement of Faraday's Law (emf proportional to rate of change of flux, must mention N); 1 mark for the correct formula ε = −NΔΦ/Δt; 1 mark for defining at least three symbols with correct SI units; 1 mark for explaining the negative sign as related to Lenz's Law / opposing the change.

Sample response. No induced current is produced because the magnetic flux through the coil is not changing. Faraday's Law states ε = −NΔΦ/Δt; when the magnet is stationary, ΔΦ = 0, so ε = 0 V. A voltage (and therefore a current) requires a changing flux, not merely the presence of flux. The large constant flux contributes nothing to the rate of change, so no emf is induced regardless of the flux magnitude.

Marking notes. 1 mark for stating ΔΦ = 0 (flux not changing) when the magnet is stationary; 1 mark for correctly applying Faraday's Law to give ε = 0; 1 mark for the key conceptual point that only changing flux, not static flux, produces emf.

Sample response (a). ΔΦ = 0.080 − 0.040 = 0.040 Wb; ε = 80 × 0.040 / 0.20 = 16 V.

Sample response (b). Same ΔΦ = 0.040 Wb; Δt = 0.050 s; ε = 80 × 0.040 / 0.050 = 64 V. The emf is four times larger because Δt is four times smaller. By Faraday's Law, ε is inversely proportional to Δt: a faster flux change produces a larger emf because the rate of change (ΔΦ/Δt) is greater.

Marking notes. Part (a): 1 mark for correct ΔΦ; 1 mark for correct emf = 16 V with unit. Part (b): 1 mark for correct emf = 64 V; 1 mark for explaining the 4× increase by linking to the 4× decrease in Δt and the inverse relationship in Faraday's Law.

Sample response. An induction cooktop contains a coil beneath the ceramic surface through which an alternating current (at high frequency, typically 20–100 kHz) flows. This alternating current produces a rapidly changing magnetic field above the coil. When a metal (ferromagnetic or conductive) cooking vessel is placed on the surface, this changing magnetic flux passes through the base of the vessel. By Faraday's Law, the rapidly changing flux induces an emf in the vessel base, driving large eddy currents within the metal. These eddy currents heat the vessel directly via Joule heating (P = I²R). The cooktop surface itself remains relatively cool because ceramic is non-conductive and no eddy currents are induced in it.

Marking notes. 1 mark for identifying the alternating current in the coil as the source of the changing magnetic flux; 1 mark for applying Faraday's Law to explain that the changing flux through the pot base induces an emf and therefore eddy currents; 1 mark for explaining that eddy currents produce resistive (Joule) heating in the pot.

Sample response. The negative sign in ε = −NΔΦ/Δt is a mathematical statement of Lenz's Law. It indicates that the induced emf (and the current it drives) acts in a direction that opposes the change in magnetic flux that produced it. If the flux is increasing, the induced current creates a magnetic field in the opposite direction to the increasing flux (opposing the increase). If the flux is decreasing, the induced current creates a field in the same direction as the original flux (opposing the decrease). In both cases, the induced effect acts to resist the change, consistent with energy conservation.

Marking notes. 1 mark for identifying the negative sign as representing Lenz's Law (must name it); 1 mark for stating the induced emf/current opposes the change in flux that produced it; 1 mark for correctly applying this to either increasing or decreasing flux (can describe both for full credit).

Sample response (a) — average speeds and trend. v = d/t = 0.60/t. Trial 1: 0.60/0.35 = 1.71 m/s. Trial 2: 0.60/0.42 = 1.43 m/s. Trial 3: 0.60/2.6 = 0.23 m/s. Trial 4: 0.60/4.1 = 0.15 m/s. Trend: the steel slug (Trial 1) falls fastest at near-free-fall speed because it is not magnetic and induces negligible flux change in the tube. The ferrite magnet (Trial 2) is only slightly braked because its weak field produces a small ΔΦ/Δt and therefore a small induced emf and small eddy current. The neodymium magnets (Trials 3 and 4) are strongly braked: their much stronger fields create a large ΔΦ/Δt as they move through the tube, inducing a large emf by Faraday's Law (ε = −NΔΦ/Δt), which drives large eddy currents. By Lenz's Law, these eddy currents oppose the motion, greatly reducing the average speed. The N52 magnet is slower than the N35 because its stronger field induces even larger eddy currents.

Marking notes (a). 1 mark for correctly calculating all four speeds (accept ±0.05 m/s); 1 mark for correctly explaining Trial 1 (no magnetic field, no flux change); 1 mark for explaining Trials 3–4 with explicit reference to Faraday's Law (ΔΦ/Δt); 1 mark for comparing N35 and N52 in terms of field strength and eddy current magnitude.

Sample response (b) — braking force evaluation. The claim is incorrect. As the magnet enters the tube it accelerates due to gravity, increasing its speed. A higher speed means ΔΦ/Δt is larger, inducing a larger emf and therefore larger eddy currents. By Lenz's Law, the opposing braking force increases with speed. The magnet continues to accelerate until the braking force equals the gravitational force (mg), at which point the net force is zero and the magnet reaches terminal velocity. At terminal velocity the braking force equals gravity — it is only constant at this point, not throughout the fall. In the early part of the fall the magnet accelerates and the braking force increases until terminal velocity is reached.

Marking notes (b). 1 mark for correctly identifying the claim as incorrect with a reason (braking force is not constant throughout); 1 mark for linking increasing speed to increasing ΔΦ/Δt and therefore increasing induced emf and eddy current (Faraday's Law); 1 mark for explaining terminal velocity as the point where braking force = gravity (force balance).

Sample response (c) — PVC tube prediction. In a PVC (plastic) tube, both the neodymium magnets (Trials 3 and 4) would fall at essentially free-fall speed, with fall times close to Trial 1 (≈0.35 s). PVC is non-conductive: no eddy currents can be induced in it by the changing magnetic flux. Without eddy currents, there is no Lenz's Law braking force, and the magnets fall under gravity alone, unimpeded.

Marking notes (c). 1 mark for predicting fall times close to the free-fall value (0.35 s) for both magnets in PVC; 1 mark for explaining that PVC is non-conductive, so no eddy currents can form and no braking force acts.

Sample response. Faraday's Law of induction, ε = −NΔΦ/Δt, is the fundamental principle underlying both generators and transformers. In a generator, a coil of N turns is mechanically rotated within a permanent magnetic field. As the coil rotates, the angle between the coil area vector and the magnetic field continuously changes, so the magnetic flux Φ = BAcosθ oscillates. The rate of change ΔΦ/Δt is at its maximum when the coil is parallel to the field lines (maximum rate of change) and zero when the coil is perpendicular (flux is at maximum but instantaneously not changing). By Faraday's Law, this continuously changing flux induces an alternating emf in the coil. Real-world example: the Snowy Mountains Hydroelectric Scheme uses generators in which turbines driven by falling water rotate coils in strong magnetic fields, producing the alternating current (AC) distributed to the NSW electricity grid. Increasing N for a given mechanical rotation directly scales the output emf, so practical generators use many turns. However, this also increases the coil mass and resistance, creating engineering trade-offs.

In a transformer, there is no mechanical motion. Instead, an alternating current in the primary coil (N_P turns) creates a continuously changing magnetic flux in a shared iron core. This changing flux passes through the secondary coil (N_S turns). By Faraday's Law, the emf induced in each coil is proportional to its number of turns and the same ΔΦ/Δt: ε_P = −N_PΔΦ/Δt and ε_S = −N_SΔΦ/Δt. Dividing these gives the transformer ratio ε_S/ε_P = N_S/N_P. A step-up transformer (N_S > N_P) raises the voltage for long-distance transmission, reducing I²R losses. Real-world example: the high-voltage transmission lines across NSW use step-up transformers (e.g. 11 kV → 330 kV) at power stations to minimise resistive losses, then step-down transformers near homes to reduce voltage back to 230 V.

A limitation of applying Faraday's Law alone is that it gives only the magnitude and scaling of the induced emf — it does not specify the direction of the induced current. Without Lenz's Law (the negative sign), one cannot determine which way the induced current flows, which is essential for understanding how generators produce the correct current direction or how transformer windings must be oriented. Lenz's Law is necessary to explain why generators resist being turned (back-emf effect) and why transformers oppose sudden changes in flux. Therefore, Faraday's Law and Lenz's Law together are needed to fully describe both devices.

Marking criteria (8 marks). 1 = correctly explains the generator using ε = −NΔΦ/Δt with reference to rotating coil changing flux (must include rate of change). 1 = identifies role of N in the generator (scales emf, more turns = larger emf). 1 = named real-world generator example (Snowy Hydro, wind turbine, car alternator, power station — any valid). 1 = correctly explains the transformer using ΔΦ/Δt in both primary and secondary coils. 1 = states and correctly derives or applies the transformer ratio ε_S/ε_P = N_S/N_P. 1 = named real-world transformer example (transmission lines, charger, audio transformer — any valid) with step-up or step-down context. 1 = correctly identifies the limitation of Faraday's Law alone (direction not specified; needs Lenz's Law). 1 = reaches an explicit evaluative judgement: both laws are complementary and needed together to fully describe generator and transformer operation.