Electromagnetic Induction

Magnetic Field and Flux

A magnetic field B (measured in Tesla, T) has field lines running from the North pole to the South pole outside a magnet. A current-carrying wire produces a circular magnetic field around it (right-hand rule: thumb points in direction of current, fingers curl in direction of B).

Magnetic flux Φ measures how much magnetic field passes through an area:

Φ = BAcosθ

Symbol	Quantity	Unit
Φ	Magnetic flux	Weber (Wb)
B	Magnetic field strength	Tesla (T)
A	Area of loop perpendicular to B	m²
θ	Angle between B and the normal to the surface	degrees / rad

Key insight: When θ = 0° (B perpendicular to plane of loop, i.e., parallel to the normal), flux is maximum: Φ = BA. When θ = 90° (B parallel to plane of loop), flux is zero: Φ = 0.

Faraday's Law of Electromagnetic Induction

An EMF is induced in a conductor whenever the magnetic flux through it changes. The magnitude of the induced EMF is proportional to the rate of change of flux and the number of turns:

ε = −N ΔΦ/Δt

The negative sign reflects Lenz's Law (see below). For CAPS purposes, we often use the magnitude: |ε| = NΔΦ/Δt.

Ways to change flux and induce EMF:

Moving a magnet into or out of a coil
Changing the strength of the magnetic field (B)
Rotating a coil in a magnetic field (changing θ)
Changing the area of the coil (A)

To increase the induced EMF: increase N (more turns), increase B (stronger magnet), decrease Δt (move faster), increase A (larger coil).

Lenz's Law

The induced current flows in a direction such that its magnetic effect opposes the change in flux that caused it. This is a consequence of the law of conservation of energy.

Worked example: A bar magnet's North pole is pushed toward a coil from the left. The flux through the coil increases (B points right into the coil, Φ increases). By Lenz's Law, the induced current must create a magnetic field that opposes this increase — so the induced B must point to the left (out of the left face). Using the right-hand rule, the induced current flows counter-clockwise when viewed from the left (the left face acts as a North pole to repel the incoming magnet). This means you must do work to push the magnet in — consistent with energy conservation.

AC Generator

A coil of N turns, area A, rotates at angular velocity ω in a uniform magnetic field B. The induced EMF varies sinusoidally:

ε = NBAω sinωt
Peak EMF: ε_max = NBAω

EMF is maximum when the coil is parallel to B (θ = 90°) — flux is zero but changing fastest
EMF is zero when the coil is perpendicular to B (θ = 0°) — flux is maximum but not changing
Slip rings maintain contact as the coil rotates → AC output
Split-ring commutator reverses connections every half-turn → DC output (motor)

Transformers

A transformer uses electromagnetic induction to change AC voltage. An alternating current in the primary coil creates a changing flux in the iron core, which induces an EMF in the secondary coil.

Vs/Vp = Ns/Np
VpIp = VsIs (ideal transformer — 100% efficient)

Step-up transformer: Ns > Np → Vs > Vp; used in power transmission
Step-down transformer: Ns < Np → Vs < Vp; used in household supplies
Transformers only work with AC — DC produces no changing flux, so no induction
Power transmission uses high voltage to reduce current → less I²R heating in cables

Power loss in cables: P_loss = I²R. Doubling voltage (step-up) halves current → power loss reduces to one quarter.

IEB Extension — Back-EMF, Self-Inductance & Three-Phase AC

Back-EMF in motors: A motor's rotating coil also acts as a generator, producing a back-EMF (ε_back) that opposes the supply voltage. The net voltage driving the current is V_supply − ε_back. At start-up, ε_back = 0 so current is highest; as the motor speeds up, ε_back increases and current decreases. If the motor stalls, ε_back drops to zero and the coil can overheat.

Self-inductance L (unit: Henry, H): A coil opposes changes in its own current by inducing a back-EMF. ε = −L(ΔI/Δt). Energy stored in inductor: U = ½LI².

Three-phase AC: Three coils at 120° intervals produce three sinusoidal EMFs, each 120° out of phase. Combined power is constant (not pulsating) — more efficient for industrial motors and long-distance power transmission.

Show all working. For direction questions, justify your answer using the right-hand rule or Lenz's Law explicitly.

Question 1

A rectangular coil of 40 turns has an area of 0.025 m². It is placed in a uniform magnetic field of 0.8 T with the plane of the coil at 30° to the field lines (i.e. θ = 60° between B and the normal). Calculate the magnetic flux through the coil and the total flux linkage (NΦ).

Question 2

A coil of 200 turns experiences a change in magnetic flux from 0.05 Wb to 0.02 Wb in 0.04 s. (a) Calculate the magnitude of the induced EMF. (b) Is flux increasing or decreasing? (c) State whether this represents energy being absorbed or released by the coil, and explain using Lenz's Law.

Question 3

A bar magnet is moved toward a circular coil so that the North pole enters from the right. (a) State whether the flux through the coil is increasing or decreasing. (b) Using Lenz's Law, determine the direction of the induced current in the coil (clockwise or anticlockwise when viewed from the right). (c) Draw a diagram showing the induced magnetic poles on the faces of the coil and explain why this opposes the motion of the magnet.

Question 4

A step-up transformer has 500 primary turns and 2 000 secondary turns. The primary is connected to a 230 V AC supply. (a) Calculate the secondary voltage. (b) If a 40 Ω load is connected to the secondary, calculate the secondary current and primary current. (c) Verify that power is conserved (P_primary = P_secondary).

Question 5

Explain why high-voltage transmission lines are used to carry electricity over long distances. In your answer: (a) state the relationship between transmission voltage and current, (b) explain the effect on power losses in the cable using the formula P = I²R, and (c) give one disadvantage of very high voltage transmission.

Question 6

A bar magnet is pushed steadily towards a 60-turn coil, then held stationary just inside it. The magnetic flux through ONE turn of the coil was recorded at four instants:

Time (s)	Flux per turn, Φ (Wb)
0.00	0.010
0.05	0.030
0.10	0.055
0.15	0.055

(a) Calculate the rate of change of flux, ΔΦ/Δt, between t = 0.00 s and t = 0.10 s. (2 marks)
(b) Using N = 60, calculate the magnitude of the induced EMF during this interval. (2 marks)
(c) Explain, referring to the data, why the induced EMF is zero between t = 0.10 s and t = 0.15 s, even though the flux itself is still 0.055 Wb (not zero) throughout this period. (2 marks)

Electromagnetic Induction

Magnetic Field and Flux

Faraday's Law of Electromagnetic Induction

Lenz's Law

AC Generator

Transformers

Electromagnetic Induction — Magnet and Coil