HSC Exam Practice

Sample response. Eddy currents are loops of electric current induced within a bulk conductor (not along a defined wire path) when the magnetic flux through the conductor changes. The required condition is a changing magnetic flux through the conductor; a static field produces no emf and therefore no eddy currents.

Marking notes. 1 mark for defining eddy currents as induced current loops within a conductor (not along a wire). 1 mark for correctly stating the condition: changing magnetic flux (accept: moving conductor in a field, changing field through a stationary conductor, or any situation causing dΦ/dt ≠ 0). 1 mark for explicitly contrasting with a static field (no induction).

Sample response. As the magnet falls through the copper pipe, the magnetic flux through each cross-section of the copper wall changes continuously. By Faraday’s Law, this changing flux induces an emf in the copper, driving eddy currents in large closed loops within the pipe wall. Copper is a good conductor, so these currents are large. By Lenz’s Law, the eddy currents create a magnetic field that opposes the change in flux — i.e., they produce an upward force on the falling magnet, decelerating it. No current flows in plastic (non-conductor), so there is no opposing force and the magnet falls almost freely.

Marking notes. 1 mark for identifying changing flux as the cause (Faraday’s Law). 1 mark for stating eddy currents are induced in the copper and are large due to high conductivity. 1 mark for applying Lenz’s Law to identify an opposing (upward) force on the magnet. 1 mark for correctly contrasting with plastic (no conductor, no eddy currents, near free-fall).

Sample response. Lamination divides the iron core into thin, mutually insulated sheets. The insulation between layers confines eddy currents to each lamination, breaking large loops into many small ones. Each small loop has a much shorter path and greater resistance (path length shorter, cross-section smaller). By Ohm’s Law, smaller currents flow, so the I²R power loss is greatly reduced, improving transformer efficiency.

Marking notes. 1 mark for stating that lamination breaks large eddy current loops into small ones confined to each layer. 1 mark for explaining that this increases the effective resistance of the eddy current path. 1 mark for linking higher resistance to smaller current and reduced I²R power loss.

Sample response. A useful application is magnetic braking in trains or roller coasters: eddy currents induced in conducting fins or rails create a drag force that decelerates the vehicle. Energy transformation: kinetic energy of the vehicle → electrical energy in eddy currents → heat in the conductor. An unwanted application is eddy currents in transformer iron cores during AC operation: they dissipate energy as heat without contributing to the transformer’s function, reducing efficiency. Energy transformation: magnetic field energy → heat in the core.

Marking notes. 1 mark for a correct useful application (accept: magnetic braking, metal detectors, induction cooktops). 1 mark for the correct energy transformation for that application. 1 mark for a correct unwanted application (accept: transformer/motor core heating, eddy currents in AC generator rotors). 1 mark for the correct energy transformation for the unwanted case.

Sample response. The fall time would decrease dramatically — approaching the free-fall time for a plastic tube. The lengthwise seam breaks the continuous conducting path around the circumference of the tube. Eddy currents require closed loops to flow; without a complete circuit, no significant circumferential current can form. There is therefore no (or minimal) opposing magnetic force on the falling magnet, and it falls almost freely.

Marking notes. 1 mark for correctly predicting a much shorter fall time (close to free fall). 1 mark for explaining that the seam breaks the closed conducting loop. 1 mark for linking the broken loop to the inability to sustain eddy currents, and therefore no opposing force.

Sample response. Conservation of energy requires that the kinetic energy lost by the decelerating carriage is converted into other forms. In magnetic braking: kinetic energy of the carriage → electrical energy in the eddy currents → heat dissipated in the conducting rail. No energy is destroyed; it is transformed. The braking force is greatest at high speed because Faraday’s Law links induced emf to the rate of flux change (ε = −dΦ/dt). At high speed, flux changes faster, inducing a larger emf and larger eddy currents; larger currents produce a stronger opposing force (Lenz’s Law), providing self-regulating deceleration.

Marking notes. 1 mark for correctly identifying the energy transformation chain (kinetic → electrical → heat) and stating energy is conserved. 1 mark for explaining that induced emf (and therefore current and force) is proportional to the rate of flux change. 1 mark for linking higher speed to greater rate of flux change, larger emf, larger currents, and therefore a larger braking force.

Sample response (a). The solid plate decelerates rapidly from 1.2 m s⁻¹ to near zero within approximately 40 mm of entering the field [describe pattern]. As the plate moves through the field, the magnetic flux through the solid aluminium changes, inducing an emf (Faraday’s Law) and driving large eddy currents throughout the plate [1]. By Lenz’s Law, these currents produce a magnetic field opposing the plate’s motion, creating a retarding force that rapidly converts kinetic energy to heat [1]. The force is large because the solid plate provides an uninterrupted, low-resistance path for large eddy currents [1].

Sample response (b). The 6-slot plate barely decelerates, retaining a speed above ~1.1 m s⁻¹ across the full 80 mm field region, whereas the solid plate is nearly stopped by 40 mm [comparison]. The slots divide the plate into narrow vertical strips, confining eddy current loops to small regions between adjacent slots [1]. These small loops have high resistance and carry much smaller currents, producing a much weaker opposing force [1]. With minimal braking force, the 6-slot plate retains most of its initial kinetic energy across the field [1].

Sample response (c). A solid copper plate would produce a stronger braking effect than the aluminium plate. Copper has lower electrical resistivity (ρ ≈ 1.7 × 10⁻&sup8; Ω m) than aluminium (ρ ≈ 2.7 × 10⁻&sup8; Ω m). The same changing flux induces the same emf, but the lower resistance of copper means larger eddy currents flow, generating a stronger opposing force (Lenz’s Law) and faster deceleration [1]. The plate would therefore reach a lower exit speed over the same 80 mm distance [1].

Marking notes. Part (a): 1 mark for describing the steep speed decrease of the solid plate; 1 mark for Faraday’s Law (emf from changing flux, eddy currents); 1 mark for Lenz’s Law (opposing force, energy dissipated as heat). Part (b): 1 mark for comparing the two curves (6-slot retains speed, solid does not); 1 mark for explaining slot effect (small loops, high resistance); 1 mark for linking to smaller currents and weaker opposing force. Part (c): 1 mark for correctly predicting stronger braking for copper; 1 mark for justifying with resistivity comparison (same emf, lower resistance → larger current → stronger force).

Sample response. Eddy currents are induced in any conductor that experiences a changing magnetic flux (Faraday’s Law), and by Lenz’s Law they always create a field opposing the flux change. This single principle underlies both the contexts in which eddy currents are useful and those in which they are harmful. When eddy currents must be minimised — as in transformer or motor cores — the goal is to maximise electrical efficiency by preventing the conversion of magnetic energy into waste heat. Transformer cores operating on the Australian 50 Hz grid are laminated: thin silicon-iron sheets (each ~0.3 mm thick) are insulated from one another, breaking large current loops into many small, high-resistance paths. By Ohm’s Law, smaller currents flow, so I²R losses drop dramatically. Without lamination, large solid cores would overheat within minutes at grid voltages, violating safety standards and wasting enormous amounts of electricity in the national grid. High-resistance iron alloys (silicon-iron, amorphous metal) further reduce losses in modern transformer design. Conversely, eddy currents are deliberately harnessed when a contactless, smooth, and self-regulating force is required. Magnetic braking systems in Australian trains (e.g. linear eddy-current brakes used in modern rail systems) and in roller-coaster installations use large permanent magnets that pass over aluminium or copper conducting plates. The eddy currents induced create a force proportional to speed (because the induced emf ∝ rate of flux change ∝ speed), providing smooth, progressive deceleration without friction, wear, or noise. This speed-proportional character (predicted directly by Faraday’s Law: ε = Blv) makes magnetic braking inherently safer than friction pads, which can overheat. Lenz’s Law unifies both suppression and exploitation: in both cases, eddy currents oppose the relative motion between conductor and field. In transformers, this opposition is an unwanted side effect of AC operation that engineers minimise. In magnetic braking, the same opposition is the desired output. Understanding Lenz’s Law allows engineers to predict the direction and magnitude of the eddy current force and to design geometries — slotted plates, laminated cores, or solid fins — that tailor the effect for the intended application. In summary, eddy currents are neither inherently beneficial nor harmful; their role is entirely context-dependent. The same physics (Faraday + Lenz) demands lamination in transformers and full solid conductors in braking systems.

Marking criteria (7 marks). 1 = correctly explains the physics of eddy current suppression in at least one named application (transformer lamination, motor core design) with reference to resistance and current magnitude. 1 = correctly explains the physics of eddy current exploitation in at least one named application (magnetic braking, metal detection) with reference to Lenz’s Law and the opposing force. 1 = names a specific Australian or global engineering application for suppression (power grid transformers, electric motors). 1 = names a specific Australian or global engineering application for exploitation (rail braking, theme park ride, industrial metal detector). 1 = explains why Lenz’s Law underpins both suppression and exploitation contexts (the opposing force is the same physics; only the engineering intent differs). 1 = makes a quantitative or semi-quantitative link (e.g. I²R loss, ε = Blv, or resistivity comparison) showing depth of understanding beyond purely qualitative description. 1 = reaches an explicit evaluative judgement integrating both contexts — explaining that eddy currents are not inherently good or bad but are engineered to be either suppressed or amplified depending on application requirements.