Electromagnetic induction & AC

Learning goals

What students should be able to explain, calculate and investigate after completing Electromagnetic Induction.

Goals marked Higher Level are required only for Higher Level students; the remaining goals are for all students.

• Higher Level: Define magnetic flux and explain what causes an induced EMF.
• Higher Level: State Faraday's law and Lenz's law, and explain the physical basis of each.
• Describe how an AC generator and a DC generator work.
• Use the transformer equation and solve problems involving transformer efficiency.
• Discuss electricity transmission losses and issues around electrical generation and distribution.

Key definitions

Precise terms, symbols and SI units used in Electromagnetic Induction.

Magnetic Flux and Faraday's Law

Magnetic flux through a flat area is Φ = BA when the magnetic field is perpendicular to the plane of the area.

Magnetic flux measures how much magnetic field passes through an area. An EMF is induced only while the flux linkage NΦ is changing. The change can be produced by moving the magnet or coil, rotating the coil, changing field strength, or changing the area or orientation within the field. A faster change or more turns gives a larger induced EMF.

• Magnetic flux Φ is measured in webers (Wb).
• Φ = BA when B is perpendicular to the plane of the loop, so B is parallel to the area normal.
• For the specification relationship Φ = BA, the magnetic field is perpendicular to the plane of the area.
• The specification form Φ = BA applies when the magnetic field is perpendicular to the plane of the area.

Lenz's Law

Lenz's law states that the direction of any induced current always opposes the change in flux that caused it.

Lenz’s law is a consequence of conservation of energy. If the induced effect reinforced the change, a moving magnet and coil could increase one another’s energy without an external energy supply. The opposing effect means work must be done to change the flux.

• The induced current produces a magnetic field that opposes the change causing it.
• “Opposes the change” does not mean that it always opposes the original magnetic field.
• Use the direction of change first, then determine the induced field and current.

AC and DC Generators

A generator produces an EMF by continuously changing the magnetic flux through a coil, typically by mechanically rotating the coil within a magnetic field.

Mechanical rotation changes the magnetic flux through the coil, so an EMF is induced. Slip rings keep each coil end connected to the same external terminal, producing alternating voltage. A split-ring commutator reverses the external connections every half-turn, giving a unidirectional output. In both cases, the electrical output comes from mechanical work done on the generator.

Transformers

A transformer consists of a primary coil and a secondary coil wound around a shared iron core.

Alternating current in the primary creates changing magnetic flux in the laminated iron core. The shared flux links the secondary coil and induces an alternating EMF. More secondary turns give a greater secondary voltage. For an ideal transformer, power is conserved, so increasing voltage decreases current by the corresponding factor.

Electricity Transmission and the National Grid

Electrical power is transmitted at high voltage and low current to reduce resistive heating losses in transmission lines.

For a given power transfer, P = VI. Increasing the transmission voltage allows the same power to be carried with a smaller current. Because the heating loss in a line is P_loss = I²R, reducing current greatly reduces wasted thermal power. Step-up transformers raise the voltage before long-distance transmission; step-down transformers reduce it again for distribution and safe use. Transformers require alternating current because a changing magnetic flux is needed to induce an emf in the secondary coil.

• For a transmission line of resistance R carrying current I, P_loss = I²R is the rate of thermal energy loss in the line—not the useful power delivered.

• The grid must transfer a required power P.
• Since P = VI, a larger V means a smaller current I for the same transmitted power.
• Cable heating depends on I²R, so even a moderate reduction in current gives a much larger reduction in heating loss.
• A step-up transformer is used near the generator; substations then step the voltage down in stages before electricity reaches consumers.
• Real transformers and transmission lines are not perfectly efficient, so some energy is still lost.

Do not say that high voltage itself “uses less energy”. The advantage is that high voltage permits a lower current for the same power, and the lower current reduces I²R heating losses.

Diagrams and formulae

Key diagrams and equations for reviewing Electromagnetic Induction.

• Electromagnetic induction: a changing magnetic flux (e.g. a moving magnet) induces a current whose direction opposes the change (Lenz's law).
• AC generator: a coil rotating in a magnetic field, connected via slip rings, produces an alternating EMF.
• Transformer: an alternating current in the primary coil induces an alternating EMF in the secondary coil via the shared iron core.

Electromagnetic induction: a changing magnetic flux (e.g. a moving magnet) induces a current whose direction opposes the change (Lenz's law).

AC generator: a coil rotating in a magnetic field, connected via slip rings, produces an alternating EMF.

Transformer: an alternating current in the primary coil induces an alternating EMF in the secondary coil via the shared iron core.

Worked Example

A step-by-step calculation applying the central relationships in Electromagnetic Induction.

A transformer has 200 turns on its primary coil and 50 turns on its secondary coil. If the primary voltage is 230 V, calculate the secondary voltage.

• Vp/Vs = Np/Ns
• 230/Vs = 200/50
• Vs = 230 × 50/200 = 57.5 V
• (This is a step-down transformer, since Ns < Np and Vs < Vp.)

Practical / Investigation

Experimental planning, measurement and evaluation for Electromagnetic Induction.

Experiment: Investigating electromagnetic induction

• Apparatus: bar magnet, coil, connecting leads and a sensitive centre-zero galvanometer. A voltage sensor/data logger may be used instead when measuring induced emf.
• Method: connect the coil to the galvanometer to form a closed circuit. Move the magnet into the coil, hold it still, and withdraw it. Record the direction and size of each deflection.
• Independent variable: speed of relative motion (or, in a separate investigation, number of turns). Change only one factor at a time.
• Dependent variable: maximum galvanometer deflection, used as a measure of induced current. If a high-resistance voltage sensor is used, record induced emf and its polarity instead.
• Controls: same magnet, coil geometry, motion path and starting/finishing positions.
• Expected observations: no steady deflection when the magnet is stationary; faster motion gives a larger response; reversing the motion reverses the response.
• Physics: faster change of magnetic flux produces a larger induced emf (Faraday’s law). The induced effect opposes the change producing it (Lenz’s law).
• Reliability: repeat each speed several times or use a motion sensor so the speed is measured rather than judged by hand.

• Change one factor only—such as magnet speed or coil turns—and measure peak induced emf with a voltage sensor, or peak deflection as a proxy for current with a centre-zero galvanometer.
• Keep the magnet, coil geometry, motion path and start/end positions fixed. Reverse the motion to test the direction prediction from Lenz’s law.
• A stationary magnet gives no sustained induced emf. Repeat each motion speed using a measured timing or motion sensor where available.
• Transformer turns ratio: use a low-voltage AC supply, a closed laminated iron core, coils of known turns and two AC voltmeters. Keep Vp and Np fixed, change Ns, and compare Vs/Vp with Ns/Np (or plot Vs against Ns). Switch off before changing coils and never connect either coil directly to mains.
• Lenz’s law demonstration: compare a strong magnet and a similar non-magnetic cylinder falling through a copper tube. The magnet falls more slowly because induced eddy currents oppose the changing flux and hence the motion; copper itself is not ferromagnetic.

Quick-Check Questions

Short retrieval questions covering the essential ideas in Electromagnetic Induction.

1. Define magnetic flux and give its unit.

2. State Faraday's law and Lenz's law.

3. Distinguish an AC generator from a DC generator.

4. Why does a transformer not work with a constant DC supply?

5. Why is electricity transmitted at high voltage over long distances?

Common mistakes and exam tips

Common misconceptions and exam-technique checks for Electromagnetic Induction.

• Avoid: Saying a transformer can operate from a constant DC supply. Correct idea: A transformer needs changing magnetic flux; constant DC produces no continuous induced emf in the secondary.
• Avoid: Confusing slip rings with a split-ring commutator. Correct idea: An AC generator uses slip rings; a simple DC motor uses a split-ring commutator.
• Avoid: Saying high transmission voltage itself reduces energy loss. Correct idea: For a given transmitted power, higher voltage permits lower current, which reduces I²R heating losses.

• Use Faraday’s law for induced-emf magnitude and Lenz’s law for direction.
• Check whether a transformer calculation assumes an ideal transformer or supplies an efficiency.
• Link transmission loss explicitly to current and I²R.

Exam-style questions

Five exam-style questions with worked answers on Electromagnetic Induction.

Higher Level — Required Content

Required Higher Level content for this topic.

• Φ is magnetic flux in webers (Wb).
• B is magnetic flux density in teslas (T).
• A is area in square metres (m²).

Faraday's law relates induced EMF to the rate of change of magnetic flux. Lenz's law gives the direction: the induced current opposes the change producing it.

• Increase induced EMF by increasing the number of turns or the rate of change of flux.
• Use Lenz's law to determine the direction of the induced current.

End-of-unit revision

Formulae, definitions, experiments and mixed revision questions for Electromagnetic Induction.

• Φ = BA (B perpendicular to the plane of the area)
• E = −NΔΦ/Δt (Faraday's Law, coil of N turns)
• Vp/Vs = Np/Ns (transformer turns ratio; equivalent to Np/Ns = Vp/Vs)
• IpVp = IsVs (ideal transformer power)
• Vrms = V0/√2, Irms = I0/√2

• Magnetic flux
• Faraday's Law
• Lenz's Law
• AC vs DC generator
• Transformer

• Induced current direction opposing a changing flux (Lenz's law)
• AC generator with slip rings
• Transformer with primary/secondary coils and shared core

• Investigating electromagnetic induction (magnet and coil)
• Investigating the transformer turns-ratio equation

• Thinking a transformer works with DC
• Confusing AC and DC generators
• Treating Faraday's and Lenz's laws as unrelated
• Assuming real transformers are 100% efficient

1. A coil of area 0.02 m² is in a magnetic field of flux density 0.4 T, perpendicular to the coil. Calculate the magnetic flux through the coil.

2. Explain, using Lenz's law, why it becomes harder to push a magnet into a coil more quickly.

3. A transformer steps 11 000 V down to 230 V. If the primary current is 2 A, calculate the secondary current (assume an ideal transformer).

4. Explain why transmitting electricity at 400 000 V rather than 230 V reduces energy losses in the National Grid.

1. Φ = BA = 0.4 × 0.02 = 0.008 Wb = 8 × 10⁻³ Wb.

2. Pushing the magnet in faster increases the rate of change of flux, inducing a larger current (Faraday's law); by Lenz's law this larger induced current creates a stronger opposing field, resisting the magnet's motion more strongly — so more work must be done to push it in at a faster rate.

3. IpVp = IsVs → Is = IpVp/Vs = 2 × 11000/230 ≈ 95.7 A.

4. Transmitting at a much higher voltage allows the same power to be delivered with a much smaller current (P = IV); since resistive heating loss in the cables is P(loss) = I²R, a smaller current dramatically reduces these losses for the same power delivered.

The table below shows which equations from this unit appear in the official State Examinations Commission Formulae and Tables book, and where.

Generators, transformers and transmission are for all students; magnetic flux and quantitative Faraday/Lenz treatment are identified as Higher Level content.