What is magnetic flux and how is it calculated?

Magnetic flux $\Phi = B A \cos\theta$ where B is magnetic field strength, A is the area enclosed by the loop, and theta is the angle between B and the area normal. Units are weber (Wb) or T m squared. Flux is a measure of the field lines threading the loop.

What is Faraday's law of electromagnetic induction?

An EMF is induced in a loop whenever the magnetic flux through it changes. $\varepsilon = -N \frac{d\Phi}{dt}$ where N is the number of turns. The minus sign expresses Lenz's law: the induced EMF opposes the change in flux.

Lenz's law states that the direction of any induced current is such that the magnetic field it produces opposes the change in flux that caused it. This is a statement of energy conservation: the induced current cannot reinforce the change, or perpetual motion would result.

How does a DC motor differ from an AC generator?

A DC motor turns electrical energy into rotational kinetic energy: current in a coil in a magnetic field experiences a torque ($\tau = nBIA \cos\theta$). A commutator reverses the current every half turn so torque stays in one direction. An AC generator does the reverse: a rotating coil in a magnetic field induces an alternating EMF; slip rings (not a commutator) deliver this to the external circuit.

How does an ideal transformer work?

An ideal transformer has zero losses and uses two coils on a shared iron core. The varying flux from the primary induces a varying EMF in the secondary. The voltage ratio equals the turns ratio: $V_p / V_s = N_p / N_s$. Conservation of power for the ideal case gives $V_p I_p = V_s I_s$, so $I_p / I_s = N_s / N_p$.

NSWPhysics

HSC Physics Module 6 Electromagnetism: deep-dive 2026 guide

Deep-dive on HSC Physics Module 6 Electromagnetism. Magnetic flux, Faraday and Lenz, the motor and generator effects, transformers, and the calculation patterns that recur in NESA papers.

Generated by Claude Opus 4.816 min readNESA-PHY-MOD-6Updated 2026-06-20

Reviewed by: AI editorial process; not yet individually human-reviewed

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How Module 6 fits into HSC Physics
Magnetic flux and the flux density model
The motor effect: force on a current-carrying conductor
Torque on a current loop
Faraday's law
Lenz's law: direction of induced current
Eddy currents
AC generators
Transformers
AC power transmission
Worked example: induced EMF in a coil
Common HSC Module 6 examiner traps
Check your knowledge

How Module 6 fits into HSC Physics

Module 6 is the central module of Year 12 NESA Physics: it provides the conceptual machinery (magnetic flux, induction, Lenz, Faraday) that Modules 7 and 8 reuse for relativity and quantum effects, and it is heavily examined.

NESA's Module 6 outcomes require students to model and analyse motor effect, induction, transformers, and AC power transmission with quantitative reasoning, not just qualitative description.

Magnetic flux and the flux density model

\Phi = B A \cos\theta

Where $\Phi$ is magnetic flux (Wb), B is flux density (T), A is loop area (m squared) and $\theta$ is the angle between B and the area normal.

Two ways flux changes:

The field B changes (e.g. magnet moving toward a fixed coil).
The geometry changes (loop area or orientation, theta).

In a rotating generator, $\theta$ changes; in a transformer, B changes; in a moving conductor, A changes.

The motor effect: force on a current-carrying conductor

A straight wire carrying current I, length L, in a uniform field B perpendicular to the wire:

F = BIL

In general $F = BIL \sin\theta$ . Use the right-hand rule (palm pushes in the direction of force, fingers point in the direction of current, thumb in direction of B for conventional current) or the slap rule.

For two parallel current-carrying conductors:

\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi r}

Currents in the same direction attract; opposite direction repel. This definition historically grounded the ampere.

Two synchronised views of the field of a long straight wire. The top view applies the grip rule directly; the side view shows the same field as perspective ellipses with dashed back halves.

Torque on a current loop

For a rectangular coil of n turns, area A, in a uniform field B, with the loop normal at angle $\theta$ to B:

\tau = nBIA \cos\theta

(Some texts write $\sin$ if $\theta$ is from the loop plane; check the convention.) Torque is maximum when the loop plane is parallel to B (normal perpendicular).

The commutator in a DC motor reverses I every half turn so the torque keeps the same rotational sense.

Faraday's law

\varepsilon = -N \frac{d\Phi}{dt}

For a moving conductor of length L moving at velocity v perpendicular to B:

\varepsilon = BLv

For a rotating coil of n turns, area A in a uniform field B rotating at angular frequency $\omega$ :

\varepsilon(t) = nBA\omega \sin(\omega t)

Peak EMF $\varepsilon_0 = nBA\omega$ .

Lenz's law: direction of induced current

The induced current flows in the direction whose magnetic field opposes the change in flux. Worked example: a bar magnet, north pole approaching a coil. The flux into the coil from the approaching north pole increases; the induced current flows so that its own magnetic field points back toward the approaching pole (creating a north on the coil's face), which repels the magnet.

Energy conservation: external work must be done to push the magnet against the repulsive force; this work appears as electrical energy in the coil.

An approaching N pole drives an induced current whose own field pushes back at it. The minus sign in Faraday's law is Lenz's law; direction follows from energy conservation, not algebra.

Eddy currents

A solid conductor moving through a non-uniform magnetic field experiences induced currents in closed loops within the bulk material. These currents dissipate energy as heat, damping the motion (used in roller-coaster brakes) and waste energy in transformer cores (mitigated by laminations).

AC generators

A coil rotated at $\omega$ in field B produces:

\varepsilon(t) = \varepsilon_0 \sin(\omega t)

with peak EMF $\varepsilon_0 = nBA\omega$ .

Slip rings (continuous) keep the output sinusoidal; a commutator (split rings) inverts every half cycle to give a DC pulsed output.

RMS values are used for AC: $V_{rms} = V_0 / \sqrt{2}$ , $I_{rms} = I_0 / \sqrt{2}$ .

Transformers

Ideal transformer:

\frac{V_p}{V_s} = \frac{N_p}{N_s}, \qquad V_p I_p = V_s I_s

A step-up transformer ( $N_s > N_p$ ) increases voltage and reduces current; step-down does the opposite.

A 1:2 step-up transformer. The shared iron core couples the alternating flux from primary to secondary; the turns ratio sets the voltage ratio, and ideal-transformer power conservation sets the current ratio.

Real transformers are not ideal: copper losses ( $I^2 R$ in windings), iron losses (hysteresis and eddy currents in the core), flux leakage. Efficiencies above 95 percent are typical.

AC power transmission

Power $P = VI$ is delivered through a transmission line of resistance R. Line losses are $I^2 R$ . For a fixed transmitted power, raising V lowers I, so $I^2 R$ losses fall as $1/V^2$ .

This is the central motivation for high-voltage transmission (around 500 kV between cities), stepped down to 11 kV for suburbs and 240 V at homes.

Worked example: induced EMF in a coil

A 100-turn circular coil of radius 0.050 m sits in a uniform field. B changes from 0.20 T to 0.50 T in 0.30 s, with the field perpendicular to the coil plane.

Area $A = \pi r^2 = 7.85 \times 10^{-3}$ m squared.

\varepsilon = N \frac{\Delta \Phi}{\Delta t} = 100 \times \frac{(0.50 - 0.20) \times 7.85 \times 10^{-3}}{0.30} = 0.785 \text{ V}

The induced current direction is set by Lenz: opposes the increase in flux, so its magnetic field points against the increasing applied field.

Common HSC Module 6 examiner traps

Confusing flux with flux density.
Dropping the cos $\theta$ in flux calculations when the coil is tilted.
Forgetting the minus sign / direction reasoning in Lenz.
Treating real transformer voltages as ideal (the question often gives efficiency).
Using peak instead of RMS in AC power calculations.

Check your knowledge

A mix of definitional, calculation/explanation, and exam-style multi-part questions covering this topic. Aim to answer all under exam conditions, then check against the solutions block.

Constants: $\mu_0 = 4\pi \times 10^{-7}$ T m A $^{-1}$ ; $e = 1.60 \times 10^{-19}$ C; $m_e = 9.11 \times 10^{-31}$ kg.

Define magnetic flux and explain, with a sketch, how the flux through a fixed loop changes when (a) the magnetic field strength increases, (b) the loop is tilted, (c) the loop area is reduced. (4 marks)
A 0.250 m long copper rod slides on parallel conducting rails at $v = 4.0$ m s $^{-1}$ in a uniform 0.30 T magnetic field directed into the page. (a) Calculate the EMF induced in the rod. (b) If the circuit has a total resistance of 1.5 ohm, calculate the current. (c) Calculate the magnitude of the force required to keep the rod moving at constant velocity. (5 marks)
The diagram shows a circular coil viewed from above with a north-pole magnet held above it. The magnet is pushed downward toward the coil. (a) State the direction of the induced current as viewed from above (clockwise or counter-clockwise) and justify with Lenz's law. (b) State whether the induced current would reverse if the magnet were instead a south pole approaching at the same speed. (c) Describe one industrial application of the principle. (5 marks)
(a, 2) Calculate the radius of the circular path of a 5.0 MeV proton moving perpendicular to a 0.80 T magnetic field. ( $m_p = 1.67 \times 10^{-27}$ kg, $e = 1.60 \times 10^{-19}$ C). (b, 2) State whether the radius would increase or decrease if the proton's kinetic energy were doubled. (c, 3) Describe the structure and operation of a cyclotron, identifying the role of (i) the magnetic field, (ii) the alternating voltage across the dees, (iii) the spiral path. (7 marks)
A square coil of side 0.10 m, with 50 turns, is rotated at 50 Hz in a uniform 0.20 T magnetic field. (a, 2) Calculate the peak EMF generated. (b, 2) Calculate the RMS EMF. (c, 3) The coil is connected to a 100 ohm resistor; calculate the average power dissipated. (d, 2) State and justify whether eddy currents in the coil's iron core would be greater or smaller if the core were a solid block rather than laminated. (9 marks)
(a) Calculate the magnetic force per unit length between two parallel wires 5.0 mm apart carrying currents of 12 A in opposite directions. (b) State whether the wires attract or repel and explain the direction with a labelled diagram referenced to the right-hand rule. (4 marks)
Compare and contrast the structural and operational differences between an ideal transformer and a real transformer. Address (a) at least three loss mechanisms in real transformers, (b) the design strategies used to minimise each loss, and (c) a brief comment on typical efficiencies for NSW grid-scale transformers. (6 marks)
The Snowy 2.0 pumped-hydro scheme in southern NSW uses motor-generators of 333 MW each. During pumping, electricity drives the generators in motor mode to pump water uphill; during generation, falling water drives the same machines as generators. Suppose a single unit operates as an AC generator producing 16 kV at 60 percent of rated power. (a, 3) Calculate the peak voltage, the RMS current, and the resistance of a transmission line that would dissipate 1 percent of the transmitted power. (b, 3) The generator output is stepped up to 330 kV for transmission to Sydney 400 km away. Calculate the percentage reduction in $I^2R$ losses compared with transmitting at 16 kV. (c, 2) Discuss two practical reasons why the transmission voltage is not raised even higher than 330 kV. (8 marks)

Solutions

Q1: Magnetic flux $\Phi = BA\cos\theta$ measures the amount of magnetic field "threading" a surface, in webers (Wb). (a) Increasing field strength $B$ proportionally increases flux. (b) Tilting the loop increases $\theta$ (angle between $B$ and normal); flux decreases as $\cos\theta$ (zero at $\theta = 90°$ ). (c) Reducing area $A$ proportionally reduces flux. A sketch shows field lines passing through the loop; the number of lines is proportional to $\Phi$ .
Q2: (a) $\varepsilon = BLv = 0.30 \times 0.250 \times 4.0 = 0.30$ V. (b) $I = \varepsilon/R = 0.30/1.5 = 0.20$ A. (c) Force on the rod from the magnetic field acting on the current: $F = BIL = 0.30 \times 0.20 \times 0.250 = 0.015$ N. To maintain constant velocity an equal and opposite external force must be applied: $F_\text{applied} = 0.015$ N. (Equivalently $P_\text{input} = Fv = 0.015 \times 4.0 = 0.060$ W $= \varepsilon I = 0.30 \times 0.20 = 0.060$ W, confirming energy conservation.)
Q3: (a) The north pole approaching downward increases the downward flux through the coil. By Lenz's law, the induced current creates a magnetic field opposing the change, that is pointing upward through the coil. Using the right-hand rule (thumb in direction of induced field, fingers curl in direction of current), the induced current flows counter-clockwise as viewed from above. (b) Yes: a south pole approaching produces an increasing upward-directed flux through the coil (the field lines point into the south pole from outside), and Lenz's law requires opposing this, so the induced current creates a downward field, that is the current flows clockwise as viewed from above. (c) Electromagnetic braking on roller coasters and trams: a conducting plate moves through a magnetic field; induced currents (eddy currents) create a magnetic field that opposes the motion, slowing the vehicle without mechanical friction.
Q4: (a) $KE = 5.0$ MeV $= 5.0 \times 10^6 \times 1.60 \times 10^{-19} = 8.0 \times 10^{-13}$ J. $v = \sqrt{2 KE / m_p} = \sqrt{2 \times 8.0 \times 10^{-13} / 1.67 \times 10^{-27}} = \sqrt{9.58 \times 10^{14}} = 3.10 \times 10^7$ m s $^{-1}$ . $r = m_p v / (eB) = (1.67 \times 10^{-27} \times 3.10 \times 10^7) / (1.60 \times 10^{-19} \times 0.80) = 0.404$ m. (b) Doubling KE multiplies $v$ by $\sqrt{2}$ and $r$ by $\sqrt{2} \approx 1.41$ . (c) A cyclotron has two D-shaped electrodes ("dees") in a uniform magnetic field perpendicular to their plane. (i) The magnetic field provides centripetal force for circular motion. (ii) An alternating voltage applied between the dees accelerates the proton each time it crosses the gap, increasing its kinetic energy. (iii) Because $r \propto v$ , the proton spirals outward to larger radii as it gains energy. The frequency of the alternating voltage matches the cyclotron frequency $f = qB/(2\pi m)$ , ensuring synchronisation.
Q5: (a) $\omega = 2\pi f = 100\pi$ rad s $^{-1}$ . Area $A = 0.10 \times 0.10 = 0.010$ m $^2$ . $\varepsilon_0 = NBA\omega = 50 \times 0.20 \times 0.010 \times 100\pi = 31.4$ V. (b) $\varepsilon_\text{rms} = 31.4/\sqrt{2} = 22.2$ V. (c) $P_\text{avg} = V_\text{rms}^2 / R = (22.2)^2 / 100 = 4.94$ W. (d) A solid iron core would experience much larger eddy currents than a laminated core. The induced electric field within the core drives circulating currents through the bulk conductor; lamination introduces high-resistance insulation between thin sheets, restricting the area of any single eddy-current loop. Power dissipation is proportional to the square of the loop area, so lamination can reduce eddy-current losses by an order of magnitude.
Q6: (a) $F/L = \mu_0 I_1 I_2 / (2\pi r) = (4\pi \times 10^{-7})(12)(12)/(2\pi \times 5.0 \times 10^{-3}) = (4 \times 10^{-7})(144)/(0.010) = 5.76 \times 10^{-3}$ N m $^{-1}$ . (b) Currents in opposite directions repel. Diagram: two parallel wires shown with one current upward and one downward; by the right-hand rule, the magnetic field of wire 1 at the location of wire 2 (which has anti-parallel current) gives a force on wire 2 directed away from wire 1.
Q7: (a) Three loss mechanisms in real transformers: (i) copper losses ( $I^2 R$ heating in the primary and secondary windings); (ii) iron losses (hysteresis loss from cyclic magnetisation of the core, and eddy currents induced in the core); (iii) flux leakage (some of the primary flux does not link the secondary, reducing voltage transfer). (b) Design strategies: thicker wire (lower R) reduces copper losses; high-permeability silicon-steel laminations reduce iron losses; close primary-secondary coupling and shell-type core geometry reduce leakage. (c) NSW grid-scale transformers (TransGrid step-up at power stations and step-down at distribution substations) typically operate at 98 to 99.5 percent efficiency, with the largest losses occurring during light loading when fixed iron losses dominate.
Q8: (a) Operating power $P = 0.60 \times 333 = 200$ MW $= 2.0 \times 10^8$ W. Peak voltage $V_0 = V_\text{rms}\sqrt{2} = 16000 \times 1.414 = 22.6$ kV. RMS current at the generator output: $I_\text{rms} = P/V_\text{rms} = 2.0 \times 10^8 / 1.6 \times 10^4 = 12500$ A. Transmission line resistance for 1 percent loss: $P_\text{loss} = I^2 R = 0.01 P$ , so $R = 0.01 P / I^2 = 0.01 \times 2 \times 10^8 / (12500)^2 = 0.0128$ ohm. (b) After step-up to 330 kV, new current $I' = 2.0 \times 10^8 / 3.3 \times 10^5 = 606$ A. Ratio of $I'^2 / I^2 = (606/12500)^2 = 2.35 \times 10^{-3}$ . Loss reduction = $1 - 2.35 \times 10^{-3} = 99.77$ percent. The new losses are about 0.23 percent of the original. (c) Practical limits on transmission voltage include (i) insulation requirements: higher voltage requires longer insulator strings on towers, larger air clearances, and bulkier cables, increasing capital cost; (ii) corona discharge: at high field strengths around conductors, air ionises and produces audible/radio-frequency noise plus a measurable power loss. NSW transmission is standardised around 132, 220, 330 and 500 kV.