Physics • Year 12 • Module 6: Electromagnetism • Lesson 21
Module 6 Consolidation
Lock in all key formulas, vocabulary, and concept linkages across all four inquiry questions before tackling exam-style problems.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: magnetic flux, Faraday’s Law, Lenz’s Law, torque on a coil, back emf, commutator, transformer, eddy current, velocity selector, slip (induction motor). 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The product of magnetic field strength and the area through which it passes, weighted by the cosine of the angle between the field and the area normal; measured in webers (Wb). | |
| 1.2 | The magnitude of the induced emf in a coil equals the rate of change of total magnetic flux linkage through the coil. | |
| 1.3 | The direction of an induced current is always such that its own magnetic effect opposes the change in flux that produced it. | |
| 1.4 | The rotational force experienced by a current-carrying coil in a magnetic field; maximised when the plane of the coil is parallel to the field. | |
| 1.5 | An emf generated in a running motor by the rotating coil; it acts in opposition to the supply voltage and limits current draw. | |
| 1.6 | A device that reverses the current direction in a motor coil every half-turn, ensuring the force (and torque) always acts in the same rotational direction. | |
| 1.7 | A device that uses electromagnetic induction between two coupled coils on a shared iron core to step AC voltage up or down. | |
| 1.8 | A circulating loop of induced current within a solid conductor placed in a changing or non-uniform magnetic field; may be useful (braking) or wasteful (core heating). | |
| 1.9 | A device using crossed electric and magnetic fields so that only particles with a specific speed v = E/B travel in a straight line. | |
| 1.10 | The difference between the synchronous speed of the rotating stator field and the actual rotor speed in an AC induction motor; required for rotor current and torque to exist. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 The torque on a current-carrying coil in a magnetic field is maximum when the plane of the coil is perpendicular to the field. T / F
2.2 When a motor stalls (rotor stops), the back emf is zero and the current through the armature reaches its maximum value V/R. T / F
2.3 Power loss in a transmission line is calculated using Ploss = V2/R, where V is the transmission voltage. T / F
2.4 A large, constant magnetic flux through a coil produces a large induced emf. T / F
2.5 In a velocity selector, a charged particle travels undeflected when the electric force and magnetic force on it are equal in magnitude and opposite in direction. T / F
2.6 An AC induction motor requires a commutator to function because it runs on alternating current. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)
Word bank:
opposes · rate of change · laminated · step-up · I²R · circular · qvB · mv/(qB)
A charged particle moving perpendicular to a uniform magnetic field experiences a force F = ___________ directed perpendicular to its velocity, causing it to follow a ___________ path. The radius of this path is r = ___________, so a heavier particle curves less for the same charge and speed. According to Faraday’s Law, the induced emf depends on the ___________ of magnetic flux, not the flux itself. Lenz’s Law adds that the induced current always ___________ the flux change that caused it, which is a consequence of energy conservation. Transformer cores are made ___________ to reduce eddy current losses. To transmit power over long distances with low loss, a ___________ transformer is used at the power station, reducing current and therefore ___________ losses in the transmission lines.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What is the function of the radial magnetic field in a DC motor?
4.2 Why does the current through a motor armature decrease as the motor speed increases?
4.3 What is the function of the turns ratio Np/Ns in a transformer?
4.4 Why can an AC induction motor never reach the synchronous speed of the stator field?
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “induces”, “opposes”, “is limited by”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: changing flux · induced emf · Lenz’s Law · back emf · motor speed · armature current.
6. Formula recall
Complete the table. Write the formula, state every variable, and give the SI units for the quantity calculated. 6 marks (1 per row: 0.5 formula + 0.5 units)
| Physical quantity | Formula | SI unit for the quantity |
|---|---|---|
| Force on a current-carrying conductor | ||
| Maximum torque on a coil (angle = 0°) | ||
| Magnetic flux | ||
| Induced emf (Faraday’s Law) | ||
| Transformer voltage ratio | ||
| Power loss in transmission line |
Q1 — Term–definition match
1.1 magnetic flux • 1.2 Faraday’s Law • 1.3 Lenz’s Law • 1.4 torque on a coil • 1.5 back emf • 1.6 commutator • 1.7 transformer • 1.8 eddy current • 1.9 velocity selector • 1.10 slip (induction motor).
Q2 — True / false with correction
2.1 False. Torque is maximum when the plane of the coil is parallel to the field (θ = 0° in τ = nBAI cos θ, where θ is the angle between the coil plane and B). When the plane is perpendicular to the field, torque is zero.
2.2 True. At stall, rotor speed = 0, so back emf = 0. Current = V/R, which is the maximum possible (only limited by armature resistance).
2.3 False. Power loss in transmission lines is Ploss = I2R, where I is the line current. The formula P = V2/R would use the voltage drop across the line resistance, not the full transmission voltage.
2.4 False. A large, constant flux produces zero induced emf. Induced emf depends on the rate of change of flux (ε = −NΔΦ/Δt), not the flux magnitude itself.
2.5 True. In a velocity selector, electric force qE acts upward and magnetic force qvB acts downward (or vice versa) on a particle. When qE = qvB, the net force is zero and the particle travels in a straight line. Solving gives v = E/B.
2.6 False. AC induction motors do not require a commutator. The commutator is a feature of DC motors. AC induction motors work by the rotating stator field inducing currents in the rotor — no brushes or commutator are needed.
Q3 — Cloze paragraph
In order: qvB / circular / mv/(qB) / rate of change / opposes / laminated / step-up / I2R.
Q4.1 — Radial magnetic field function
The radial (curved-pole) magnetic field ensures that the field is always parallel to the plane of the coil at every position in the rotation. This means cos θ = 1 throughout and the torque τ = nBAI is constant rather than varying sinusoidally, producing smooth continuous rotation.
Q4.2 — Motor current decreases with speed
As the motor speeds up, the rotating armature coil cuts the magnetic flux faster, generating a greater back emf. The armature current is given by I = (V − εback)/R. As εback increases, the numerator decreases, so the current decreases.
Q4.3 — Turns ratio function
The turns ratio Np/Ns determines the voltage ratio: Vp/Vs = Np/Ns. A turns ratio greater than 1 (Np > Ns) steps voltage down; a turns ratio less than 1 steps voltage up. For an ideal transformer, power is conserved (Pp = Ps) so current changes inversely with voltage.
Q4.4 — Induction motor cannot reach synchronous speed
If the rotor reached synchronous speed, it would rotate at exactly the same rate as the stator’s rotating magnetic field. There would be no relative motion, no change in flux through the rotor bars, no induced current, and therefore no rotor force (torque). The motor would slow down again, always remaining slightly behind the stator field frequency. This difference in speeds is called slip and is essential for operation.
Q5 — Sample concept map
Correct maps should include arrows such as:
- changing flux — produces (Faraday’s Law) → induced emf
- Lenz’s Law — determines direction of → induced emf
- induced emf — in a running motor becomes → back emf
- back emf — increases with → motor speed
- back emf — reduces → armature current
- armature current — generates → changing flux (closing the loop)
Award 1 mark per valid labelled arrow with a linking phrase (minimum 6).
Q6 — Formula recall
Force on a current-carrying conductor: F = BIl (B = magnetic field strength, I = current, l = length of conductor in field); unit: newton (N).
Maximum torque on a coil: τ = nBAI (n = number of turns, B = field strength, A = coil area, I = current); unit: newton metre (N m).
Magnetic flux: Φ = BA cos θ (B = field strength, A = area, θ = angle between B and area normal); unit: weber (Wb).
Induced emf: ε = −NΔΦ/Δt (N = number of turns, ΔΦ/Δt = rate of change of flux); unit: volt (V).
Transformer voltage ratio: Vp/Vs = Np/Ns; this is a dimensionless ratio.
Power loss: Ploss = I2R (I = line current, R = line resistance); unit: watt (W).