Where can I learn Electromagnetic induction for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 20.5 (Electromagnetic induction) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/20-5-electromagnetic-induction.

Is Electromagnetic induction (20.5) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Electromagnetic induction.

How do I revise Electromagnetic induction for 9702 exams?

Start with the visual steps on this page, note the key exam points, then attempt a 9702 past-paper question on Electromagnetic induction using MarkScheme's /mark tool. Mark strictly against the official scheme and re-read any marks you lost.

MarkScheme 9702

Opening…

20.5Physics25 min readPREMIUM

Electromagnetic induction

Ever wondered how electricity is generated in power plants? It's largely thanks to electromagnetic induction! This fundamental principle describes how a changing magnetic field can create an electric current. We'll explore the concepts of magnetic flux, Faraday's Law, Lenz's Law, and the fascinating Hall Effect, all crucial for understanding how generators and sensors work. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 20.5.

BY THE END, YOU CAN…

exam checklist — tick these off

1Define and apply concepts of magnetic flux and flux linkage.
2Explain and use Faraday's and Lenz's Laws to determine induced EMF and current direction.
3Describe the Hall Effect and its application in measuring magnetic fields.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Electromagnetic induction

Cambridge 9702 Paper 4 — Electromagnetic induction (20.5). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
$\Phi$ is the magnetic flux (in Webers, Wb).
2
B is the magnetic flux density (in Tesla, T).
3
A is the area through which the field lines pass (in m²).
4
$\theta$ is the angle between the magnetic field B and the normal to the area A.

What this topic covers

The official Cambridge syllabus points this lesson works through.

20.5.1
Define magnetic flux as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density
20.5.2
Recall and use $Φ = BA$
20.5.3
Understand and use the concept of magnetic flux linkage
20.5.4
Understand and explain experiments that demonstrate: that a changing magnetic flux can induce an e.m.f. in a circuit; that the induced e.m.f. is in such a direction as to oppose the change producing it; the factors affecting the magnitude of the induced e.m.f.
20.5.5
Recall and use Faraday's and Lenz's laws of electromagnetic induction

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Faraday’s Law

Move the magnet — flux through the coil changes.

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

Magnetic flux Φ = BA cos θ through a coil.

24 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

24 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

3JCN PhysicsStart here · 19702 20.5 · IB D.4
Faraday's Law of Induction
Move a magnet through a coil; read induced emf versus rate of flux change
Why this one: Move the magnet faster and watch the induced emf grow with the rate of change of flux.
Try this
1. Move the magnet slowly through the coil and read the emf.
2. Move it quickly and compare.
3. Hold it still inside the coil and read the emf.
Look for The induced emf is proportional to the rate of change of flux and is zero when the flux is steady.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 29702 20.5 · IB D.4
Demonstration of Lenz's Law
Drop a magnet through a conducting tube; see the opposing induced current
Why this one: Drop a magnet down a conducting tube and see the induced current oppose its fall — Lenz's law.
Try this
1. Drop the magnet through the conducting tube and watch its fall.
2. Watch the direction of the induced current as the magnet approaches and leaves.
Look for The induced current opposes the change in flux, so it slows the falling magnet.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 39702 20.5 · IB D.4
Magnetic Flux
Tilt a loop in a field and read the magnetic flux
Why this one: Tilt the loop and read how flux falls with cos θ; only the component of B through the area counts.
Try this
1. Set the loop perpendicular to the field and read the flux.
2. Tilt the loop and read it again.
3. Lay the loop along the field and read the flux.
Look for Flux equals BA cos θ, zero when the loop lies along the field.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 49702 20.5 · 9702 21.1 · IB D.4
AC Generator
Spin a coil in a magnetic field and watch the sinusoidal emf
Why this one: Spin a coil in a field and watch the emf trace a sine wave, peaking where the flux changes fastest.
Try this
1. Spin the coil and watch the emf trace.
2. Spin it faster and compare the peak emf and the frequency.
3. Note the coil position when the emf is zero.
Look for The emf is sinusoidal, zero when the coil faces the field and largest when its flux is changing fastest.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
SimuPhysicsStart here · 59702 20.5 · IB D.4
Flux and EMF Graphs
A flux–time graph and the e.m.f. it produces are drawn side by side in real time
Why this one: Watch emf drawn as the gradient of the flux–time graph — the exam's graph-reading skill.
Try this
1. Watch the e.m.f. where the flux graph is steepest.
2. Watch it where the flux graph is flat.
3. Watch it where the flux graph changes direction.
Look for The e.m.f. equals the negative gradient of the flux–time graph.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations19 more on this topic — core ones first

oPhysicsCore9702 20.5 · IB D.4
Electromagnetic Induction
Move a bar magnet through a coil; see the induced current direction and size
Try this
1. Push the magnet in slowly, then quickly.
2. Pull it back out.
3. Hold the magnet still inside the coil.
Look for Current flows only while the flux changes, grows with speed and reverses when the magnet reverses.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsCore9702 20.5 · 9702 21.1 · IB D.4
3D AC Dynamo
A coil turns between magnet poles and the induced e.m.f. is drawn against angle; slip rings keep each brush on the same end of the coil
Try this
1. Turn the coil and watch the e.m.f. trace.
2. Find the angle where the e.m.f. is largest.
3. Find where it reverses.
Look for The e.m.f. reverses every half turn, giving a sinusoidal output.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 20.5 · IB D.4
Faraday's Law Lab — Magnet, Coil and Galvanometer
Push a bar magnet into a coil and the galvanometer needle kicks; hold it still and the needle falls back to zero
Try this
1. Push the magnet in and watch the needle.
2. Hold it still inside the coil.
3. Pull it out and compare the kick.
Look for An e.m.f. is induced only while the flux through the coil is changing.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 20.5 · IB D.4
Magnet Dropped in a Ring or a Coil
A magnet falls through a coil under gravity and the induced e.m.f. is graphed in real time
Try this
1. Drop the magnet and watch the e.m.f. graph.
2. Compare the two pulses.
3. Drop from higher and compare.
Look for The second pulse is shorter and taller because the magnet is moving faster on the way out.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 20.5 · IB D.4
Coils Entering and Exiting a Magnetic Field
Triangles, circles, squares and rectangles cross the same field boundary and their e.m.f. traces are plotted for comparison
Try this
1. Run the square coil and read the trace.
2. Run the triangle and compare.
3. Run the circle.
Look for The e.m.f. follows the rate at which the area inside the field changes.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsCore9702 20.5 · 9702 21.1 · 9702 21.2
DC Generator
Add a commutator to a generator and see the rectified DC output
Try this
1. Spin the coil and watch the commutator output.
2. Compare the output with the AC generator's trace.
Look for The commutator reverses the connections every half turn, so the output is a rectified, one-direction emf.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$\Phi = BA \cos \theta$

Tap a symbol — great for exam definitions

KEY RELATION

$\lambda = N\Phi = NBA \cos \theta$

Tap a symbol — great for exam definitions

KEY RELATION

$\mathcal{E} = |\frac{\Delta \lambda}{\Delta t}| \quad \text{ or } \quad \mathcal{E} = |N\frac{\Delta \Phi}{\Delta t}|$

Tap a symbol — great for exam definitions

KEY RELATION

$\mathcal{E} = -\frac{\Delta (N\Phi)}{\Delta t}$

Tap a symbol — great for exam definitions

KEY RELATION

$V_H = \frac{BI}{nqt}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Magnetic Flux ($\Phi$)

Magnetic flux quantifies the total amount of magnetic field lines passing through a specific area. Think of it as how much 'magnetic field' is piercing through a surface. The angle between the field and the surface is crucial.

$\Phi = BA \cos \theta$

$\Phi$ is the magnetic flux (in Webers, Wb).
B is the magnetic flux density (in Tesla, T).
A is the area through which the field lines pass (in m²).
$\theta$ is the angle between the magnetic field B and the normal to the area A.
Maximum flux occurs when the field is perpendicular to the area ( $\theta = 0^\circ$ , $\cos 0^\circ = 1$ ), so $\Phi = BA$ .
Zero flux occurs when the field is parallel to the area ( $\theta = 90^\circ$ , $\cos 90^\circ = 0$ ).

Not clear?

Magnetic Flux Linkage ($\lambda$)

When a coil has multiple turns, the magnetic flux interacts with each turn. Magnetic flux linkage is the total magnetic flux interacting with the entire coil. It's simply the magnetic flux through one turn multiplied by the number of turns.

$\lambda = N\Phi = NBA \cos \theta$

N is the number of turns in the coil.
$\Phi$ is the magnetic flux through a single turn.
The unit for magnetic flux linkage is also Weber (Wb), or more specifically, Weber-turns.

Not clear?

Faraday's Law of Electromagnetic Induction

Faraday's Law provides the quantitative relationship for induced EMF. It states that the magnitude of an induced electromotive force (EMF) is directly proportional to the rate at which the magnetic flux linkage changes through a conductor or coil.

$\mathcal{E} = |\frac{\Delta \lambda}{\Delta t}| \quad \text{ or } \quad \mathcal{E} = |N\frac{\Delta \Phi}{\Delta t}|$

$\mathcal{E}$ is the induced EMF (in Volts, V).
$\Delta \lambda$ is the change in magnetic flux linkage (in Wb).
$\Delta t$ is the time taken for the change (in seconds, s).
A faster change in flux linkage results in a larger induced EMF.

Not clear?

Lenz's Law

While Faraday's Law tells us how much EMF is induced, Lenz's Law tells us its direction. It states that the induced current will flow in a direction that creates a magnetic field which opposes the original change in magnetic flux that caused it. This is a consequence of the conservation of energy.

$\mathcal{E} = -\frac{\Delta (N\Phi)}{\Delta t}$

The negative sign mathematically incorporates Lenz's Law.
It signifies that the induced EMF opposes the change in flux.
If flux is increasing, the induced field tries to decrease it. If flux is decreasing, the induced field tries to increase it.

Not clear?

The Hall Effect

The Hall Effect describes the induction of a potential difference (called Hall Voltage, $V_H$ ) across a conductor when it carries a current and is placed in a perpendicular magnetic field. This occurs because the magnetic force separates the charge carriers to opposite sides of the conductor.

$V_H = \frac{BI}{nqt}$

B is the magnetic flux density.
I is the current flowing through the conductor.
n is the charge carrier number density.
q is the charge of a single carrier (e.g., electron charge e).
t is the thickness of the conductor slice perpendicular to B and I.

Not clear?

The Hall Probe

A Hall probe is a practical application of the Hall Effect. It's a small, flat device that can be used to accurately measure magnetic field strength (magnetic flux density). By measuring the Hall Voltage for a known current and material, the magnetic field can be determined, as $V_H$ is directly proportional to B.

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A coil with 500 turns has a magnetic flux of 2.0 mWb passing through it. If this flux is uniformly reduced to 0.5 mWb in 0.25 seconds, calculate the magnitude of the induced EMF.

1
Calculate the initial magnetic flux linkage:

EXAMPLE 2

A straight conductor of length 25 cm moves at a constant speed of 8.0 m/s at right angles to a uniform magnetic field of flux density 40 mT. Calculate the EMF induced across the ends of the conductor.

1
Identify the formula for motional EMF: $\mathcal{E} = BLv$ , where B, L, and v are mutually perpendicular.

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAElectromagnetic induction

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

Electromagnetic induction: The process of generating an electromotive force (EMF) in a conductor due to a changing magnetic field or relative motion.
magnetic flux ( $\Phi$ ): Magnetic flux is the measure of the total magnetic field lines passing perpendicularly through a given area. Its SI unit is the Weber (Wb).
Magnetic flux linkage ( $\lambda$ ): The total magnetic flux interacting with all turns of a coil. For N turns, $\lambda = N\Phi$ .
main idea behind Lenz's: The induced current's magnetic field always opposes the change in magnetic flux that caused it.
Briefly explain the Hall: A potential difference (Hall Voltage) is induced across a current-carrying conductor when placed in a perpendicular magnetic field, due to charge carrier separation.
purpose of a laminated: The soft iron core concentrates the magnetic flux. It is laminated (split into thin, insulated sheets) to reduce energy losses due to eddy currents.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 15 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

$\Phi$ is the magnetic flux (in Webers, Wb).
B is the magnetic flux density (in Tesla, T).
A is the area through which the field lines pass (in m²).
$\theta$ is the angle between the magnetic field B and the normal to the area A.
Maximum flux occurs when the field is perpendicular to the area ( $\theta = 0^\circ$ , $\cos 0^\circ = 1$ ), so $\Phi = BA$ .
Zero flux occurs when the field is parallel to the area ( $\theta = 90^\circ$ , $\cos 90^\circ = 0$ ).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q7(b)(i)

PhysicsMay/June 2024

(b) (i)

The coil consists of 340 turns, each of cross-sectional area 3.2 x 10⁻⁴ m². (i) Calculate the maximum magnetic flux through one turn of the coil.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q7(a)

PhysicsMay/June 2024

(a)

State Faraday's law of electromagnetic induction.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

Why is electromagnetic induction so important in daily life?

How do Faraday's Law and Lenz's Law work together?

What is the difference between magnetic flux and magnetic flux linkage?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q7(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS20.4 Magnetic fields due to currents NEXT →21.1 Characteristics of alternating currents

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Revise Electromagnetic induction for Cambridge 9702 (20.5)

Looking for free Physics 9702 notes on Electromagnetic induction? This A-Level lesson covers official syllabus point 20.5 on Paper 4: A Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Electromagnetic induction 9702 revision", "9702 20.5 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

20.5Physics25 min readPREMIUM

Electromagnetic induction

BY THE END, YOU CAN…

exam checklist — tick these off

1Define and apply concepts of magnetic flux and flux linkage.
2Explain and use Faraday's and Lenz's Laws to determine induced EMF and current direction.
3Describe the Hall Effect and its application in measuring magnetic fields.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Electromagnetic induction

Cambridge 9702 Paper 4 — Electromagnetic induction (20.5). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
$\Phi$ is the magnetic flux (in Webers, Wb).
2
B is the magnetic flux density (in Tesla, T).
3
A is the area through which the field lines pass (in m²).
4
$\theta$ is the angle between the magnetic field B and the normal to the area A.

What this topic covers

The official Cambridge syllabus points this lesson works through.

20.5.1
Define magnetic flux as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density
20.5.2
Recall and use $Φ = BA$
20.5.3
Understand and use the concept of magnetic flux linkage
20.5.4
Understand and explain experiments that demonstrate: that a changing magnetic flux can induce an e.m.f. in a circuit; that the induced e.m.f. is in such a direction as to oppose the change producing it; the factors affecting the magnitude of the induced e.m.f.
20.5.5
Recall and use Faraday's and Lenz's laws of electromagnetic induction

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Faraday’s Law

Move the magnet — flux through the coil changes.

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

Magnetic flux Φ = BA cos θ through a coil.

24 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

24 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

3JCN PhysicsStart here · 19702 20.5 · IB D.4
Faraday's Law of Induction
Move a magnet through a coil; read induced emf versus rate of flux change
Why this one: Move the magnet faster and watch the induced emf grow with the rate of change of flux.
Try this
1. Move the magnet slowly through the coil and read the emf.
2. Move it quickly and compare.
3. Hold it still inside the coil and read the emf.
Look for The induced emf is proportional to the rate of change of flux and is zero when the flux is steady.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 29702 20.5 · IB D.4
Demonstration of Lenz's Law
Drop a magnet through a conducting tube; see the opposing induced current
Why this one: Drop a magnet down a conducting tube and see the induced current oppose its fall — Lenz's law.
Try this
1. Drop the magnet through the conducting tube and watch its fall.
2. Watch the direction of the induced current as the magnet approaches and leaves.
Look for The induced current opposes the change in flux, so it slows the falling magnet.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 39702 20.5 · IB D.4
Magnetic Flux
Tilt a loop in a field and read the magnetic flux
Why this one: Tilt the loop and read how flux falls with cos θ; only the component of B through the area counts.
Try this
1. Set the loop perpendicular to the field and read the flux.
2. Tilt the loop and read it again.
3. Lay the loop along the field and read the flux.
Look for Flux equals BA cos θ, zero when the loop lies along the field.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 49702 20.5 · 9702 21.1 · IB D.4
AC Generator
Spin a coil in a magnetic field and watch the sinusoidal emf
Why this one: Spin a coil in a field and watch the emf trace a sine wave, peaking where the flux changes fastest.
Try this
1. Spin the coil and watch the emf trace.
2. Spin it faster and compare the peak emf and the frequency.
3. Note the coil position when the emf is zero.
Look for The emf is sinusoidal, zero when the coil faces the field and largest when its flux is changing fastest.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
SimuPhysicsStart here · 59702 20.5 · IB D.4
Flux and EMF Graphs
A flux–time graph and the e.m.f. it produces are drawn side by side in real time
Why this one: Watch emf drawn as the gradient of the flux–time graph — the exam's graph-reading skill.
Try this
1. Watch the e.m.f. where the flux graph is steepest.
2. Watch it where the flux graph is flat.
3. Watch it where the flux graph changes direction.
Look for The e.m.f. equals the negative gradient of the flux–time graph.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations19 more on this topic — core ones first

oPhysicsCore9702 20.5 · IB D.4
Electromagnetic Induction
Move a bar magnet through a coil; see the induced current direction and size
Try this
1. Push the magnet in slowly, then quickly.
2. Pull it back out.
3. Hold the magnet still inside the coil.
Look for Current flows only while the flux changes, grows with speed and reverses when the magnet reverses.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsCore9702 20.5 · 9702 21.1 · IB D.4
3D AC Dynamo
A coil turns between magnet poles and the induced e.m.f. is drawn against angle; slip rings keep each brush on the same end of the coil
Try this
1. Turn the coil and watch the e.m.f. trace.
2. Find the angle where the e.m.f. is largest.
3. Find where it reverses.
Look for The e.m.f. reverses every half turn, giving a sinusoidal output.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 20.5 · IB D.4
Faraday's Law Lab — Magnet, Coil and Galvanometer
Push a bar magnet into a coil and the galvanometer needle kicks; hold it still and the needle falls back to zero
Try this
1. Push the magnet in and watch the needle.
2. Hold it still inside the coil.
3. Pull it out and compare the kick.
Look for An e.m.f. is induced only while the flux through the coil is changing.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 20.5 · IB D.4
Magnet Dropped in a Ring or a Coil
A magnet falls through a coil under gravity and the induced e.m.f. is graphed in real time
Try this
1. Drop the magnet and watch the e.m.f. graph.
2. Compare the two pulses.
3. Drop from higher and compare.
Look for The second pulse is shorter and taller because the magnet is moving faster on the way out.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 20.5 · IB D.4
Coils Entering and Exiting a Magnetic Field
Triangles, circles, squares and rectangles cross the same field boundary and their e.m.f. traces are plotted for comparison
Try this
1. Run the square coil and read the trace.
2. Run the triangle and compare.
3. Run the circle.
Look for The e.m.f. follows the rate at which the area inside the field changes.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsCore9702 20.5 · 9702 21.1 · 9702 21.2
DC Generator
Add a commutator to a generator and see the rectified DC output
Try this
1. Spin the coil and watch the commutator output.
2. Compare the output with the AC generator's trace.
Look for The commutator reverses the connections every half turn, so the output is a rectified, one-direction emf.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$\Phi = BA \cos \theta$

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KEY RELATION

$\lambda = N\Phi = NBA \cos \theta$

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KEY RELATION

$\mathcal{E} = |\frac{\Delta \lambda}{\Delta t}| \quad \text{ or } \quad \mathcal{E} = |N\frac{\Delta \Phi}{\Delta t}|$

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KEY RELATION

$\mathcal{E} = -\frac{\Delta (N\Phi)}{\Delta t}$

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KEY RELATION

$V_H = \frac{BI}{nqt}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Magnetic Flux ($\Phi$)

$\Phi = BA \cos \theta$

$\Phi$ is the magnetic flux (in Webers, Wb).
B is the magnetic flux density (in Tesla, T).
A is the area through which the field lines pass (in m²).
$\theta$ is the angle between the magnetic field B and the normal to the area A.
Maximum flux occurs when the field is perpendicular to the area ( $\theta = 0^\circ$ , $\cos 0^\circ = 1$ ), so $\Phi = BA$ .
Zero flux occurs when the field is parallel to the area ( $\theta = 90^\circ$ , $\cos 90^\circ = 0$ ).

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Magnetic Flux Linkage ($\lambda$)

$\lambda = N\Phi = NBA \cos \theta$

N is the number of turns in the coil.
$\Phi$ is the magnetic flux through a single turn.
The unit for magnetic flux linkage is also Weber (Wb), or more specifically, Weber-turns.

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Faraday's Law of Electromagnetic Induction

$\mathcal{E} = |\frac{\Delta \lambda}{\Delta t}| \quad \text{ or } \quad \mathcal{E} = |N\frac{\Delta \Phi}{\Delta t}|$

$\mathcal{E}$ is the induced EMF (in Volts, V).
$\Delta \lambda$ is the change in magnetic flux linkage (in Wb).
$\Delta t$ is the time taken for the change (in seconds, s).
A faster change in flux linkage results in a larger induced EMF.

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Lenz's Law

$\mathcal{E} = -\frac{\Delta (N\Phi)}{\Delta t}$

The negative sign mathematically incorporates Lenz's Law.
It signifies that the induced EMF opposes the change in flux.
If flux is increasing, the induced field tries to decrease it. If flux is decreasing, the induced field tries to increase it.

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The Hall Effect

$V_H = \frac{BI}{nqt}$

B is the magnetic flux density.
I is the current flowing through the conductor.
n is the charge carrier number density.
q is the charge of a single carrier (e.g., electron charge e).
t is the thickness of the conductor slice perpendicular to B and I.

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The Hall Probe

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Worked examples

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EXAMPLE 1

A coil with 500 turns has a magnetic flux of 2.0 mWb passing through it. If this flux is uniformly reduced to 0.5 mWb in 0.25 seconds, calculate the magnitude of the induced EMF.

1
Calculate the initial magnetic flux linkage:

EXAMPLE 2

1
Identify the formula for motional EMF: $\mathcal{E} = BLv$ , where B, L, and v are mutually perpendicular.

How it all connects

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MAIN IDEAElectromagnetic induction

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Glossary

Key terms for this topic — skim now; the Check step will test them.

Electromagnetic induction: The process of generating an electromotive force (EMF) in a conductor due to a changing magnetic field or relative motion.
magnetic flux ( $\Phi$ ): Magnetic flux is the measure of the total magnetic field lines passing perpendicularly through a given area. Its SI unit is the Weber (Wb).
Magnetic flux linkage ( $\lambda$ ): The total magnetic flux interacting with all turns of a coil. For N turns, $\lambda = N\Phi$ .
main idea behind Lenz's: The induced current's magnetic field always opposes the change in magnetic flux that caused it.
Briefly explain the Hall: A potential difference (Hall Voltage) is induced across a current-carrying conductor when placed in a perpendicular magnetic field, due to charge carrier separation.
purpose of a laminated: The soft iron core concentrates the magnetic flux. It is laminated (split into thin, insulated sheets) to reduce energy losses due to eddy currents.

10Apply

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11Understand

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12Remember

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Key takeaways

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$\Phi$ is the magnetic flux (in Webers, Wb).
B is the magnetic flux density (in Tesla, T).
A is the area through which the field lines pass (in m²).
$\theta$ is the angle between the magnetic field B and the normal to the area A.
Maximum flux occurs when the field is perpendicular to the area ( $\theta = 0^\circ$ , $\cos 0^\circ = 1$ ), so $\Phi = BA$ .
Zero flux occurs when the field is parallel to the area ( $\theta = 90^\circ$ , $\cos 90^\circ = 0$ ).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q7(b)(i)

PhysicsMay/June 2024

(b) (i)

The coil consists of 340 turns, each of cross-sectional area 3.2 x 10⁻⁴ m². (i) Calculate the maximum magnetic flux through one turn of the coil.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q7(a)

PhysicsMay/June 2024

(a)

State Faraday's law of electromagnetic induction.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

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Frequently asked

Why is electromagnetic induction so important in daily life?

How do Faraday's Law and Lenz's Law work together?

What is the difference between magnetic flux and magnetic flux linkage?

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Faraday's Law of Induction

Demonstration of Lenz's Law

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