21.1Electromagnetic Induction and Electromagnetism
Electromagnetic Induction — American System Physics Revision Notes & Topical Questions
10 min read 7 parts Lesson 3 of 5 1 quiz
Lesson summary
Describe experiments that demonstrate electromagnetic induction.Magnetic fluxΦ = BA (Wb = T × m2), for field perpendicular to area.Faraday's lawinduced e.m.f. = rate of change of flux linkage, E = NΔΦ/Δt (V = Wb/s).What the symbols mean: ε = induced e.m.f.
- Lenz's law
- Fleming's right-hand rule
- Induced current
- Galvanometer
- Eddy currents
- Self-induction
Part 1 of 7Key ideas
1Magnetic flux
Φ = BA (Wb = T × m2), for field perpendicular to area.
2Faraday's law
Faraday's law induced e.m.f. = rate of change of flux linkage, E = NΔΦ/Δt (V = Wb/s).
What the symbols mean: ε = induced e.m.f. (V) · N = number of turns · ΔΦ = change of flux (Wb) · Δt = time taken (s); the minus sign is Lenz’s law
3
For a straight wire moving perpendicular to a field: E = BLv (V = T × m × m/s).
4
Induced e.m.f. increases with speed of motion, field strength and number of turns.
5Lenz's law
Lenz's law the induced current opposes the change causing it (a consequence of energy conservation).
6
Fleming's right-hand rule gives the direction of the induced current.
7
No relative motion (or no change in flux) → no induced e.m.f.
8
Work done moving the magnet against the opposing force = electrical energy produced.
Part 2 of 7Learning objectives
1
Describe experiments that demonstrate electromagnetic induction.
2
State the factors affecting the size of an induced e.m.f.
3
State Faraday's and Lenz's laws and use them to predict the direction of induced current.
4
Use Fleming's right-hand rule.
5
Calculate induced e.m.f. with E = BLv and E = NΔΦ/Δt.
Part 3 of 7Essential knowledge
1
2
When a wire is moved across a magnetic field, the free electrons in it move with the wire and experience a magnetic force along the wire. Charge separates, creating an e.m.f. between the ends of the wire.
3
If the wire is part of a complete circuit, the induced e.m.f. drives an induced current. With an open circuit there is still an e.m.f. but no current.
4
An e.m.f. is induced only when there is relative motion (or a change in field) — a stationary magnet in a stationary coil produces nothing.
5
The size of the induced e.m.f. depends on the rate at which field lines are cut: moving faster, using a stronger magnet or a coil with more turns (or larger area) increases it.
6Faraday's law
E = NΔΦ/Δt. For a straight rod of length L moving with speed v at right angles to a field B, the e.m.f. is E = BLv.
7Lenz's law
Lenz's law when the N pole of a magnet approaches a coil, the induced current makes the near end of the coil an N pole, which repels the magnet. When it is withdrawn, the near end becomes an S pole, attracting it back. Either way the change is opposed.
8Lenz's law follows from conservation of energy
Lenz's law follows from conservation of energy if the induced current helped the motion, energy would be created from nothing. Instead work must be done against the opposing force, and this work becomes electrical energy.
9Fleming's right-hand rule
Fleming's right-hand rule thuMb = Motion, First finger = Field, seCond finger = induced Current.
10
An e.m.f. can also be induced without movement: switching a current on or off in one coil changes the flux linking a nearby coil, inducing an e.m.f. in it (the principle of the transformer).
11
Eddy currents are induced in solid metal moving in a field; they oppose the motion and are used in induction braking and induction cooktops, but waste energy in transformer cores (reduced by laminating).
12
Applications include generators, transformers, microphones (moving-coil), electric guitar pickups, metal detectors and wireless charging.
Part 4 of 7Process & sequence
1
Connect a coil of wire to a centre-zero galvanometer.
2
Push the N pole of a bar magnet quickly into the coil and note the deflection.
3
Hold the magnet stationary inside the coil: reading returns to zero.
4
Pull the magnet out: deflection is in the opposite direction.
5
Repeat faster, with a stronger magnet, and with more turns: deflection increases.
6
Turn the magnet round and repeat: deflection directions reverse.
7
Conclude that an e.m.f. is induced only while the flux linking the coil changes.
Lenz's law with a falling magnetwrite these steps in this order; each step is a marking point.
1
A magnet falls towards a coil connected in a closed circuit.
2
The flux through the coil increases, inducing a current.
3
The induced current makes the top of the coil the same pole as the approaching magnet end.
4
The coil repels the magnet, opposing its motion.
5
Kinetic energy is transferred into electrical energy, then thermal energy in the circuit.
Part 5 of 7Worked examples
0.40 V
A metal rod 0.40 m long moves at 5.0 m/s at right angles to a field of 0.20 T. Find the induced e.m.f.
- E = BLv = 0.20 × 0.40 × 5.0 = 0.40 V.
12 V
A 200-turn coil has the flux through each turn change from 3.0 × 10−3 Wb to zero in 0.050 s. Find the average induced e.m.f.
- E = NΔΦ/Δt = 200 × (3.0 × 10−3)/0.050 = 12 V.
S pole
The S pole of a magnet is pushed into a coil. What pole appears at the end of the coil facing the magnet?
- By Lenz's law the coil opposes the approach, so it repels: the near end becomes an S pole.
Part 6 of 7Summary
1
An e.m.f. is induced when a conductor cuts magnetic field lines or the field through it changes.
2
Faster motion, stronger field and more turns give a larger e.m.f.
3
Lenz's law: the induced current opposes the change that produces it.
4
Use Fleming's right-hand rule for generators.
5
Energy is conserved: work must be done to produce the induced current.
Part 7 of 7Compare: Compare
| Change | Effect on induced e.m.f. |
|---|---|
| Move magnet/wire faster | Larger |
| Stronger magnet | Larger |
| More turns on coil | Larger |
| Magnet stationary in coil | Zero |
| Move in opposite direction | Reverses |
| Reverse magnet pole | Reverses |
| Wire moves parallel to field | Zero — no field lines cut |
| Feature | Motor effect | Generator effect |
|---|---|---|
| Input | Current + field | Motion + field |
| Output | Force / motion | Induced e.m.f./current |
| Hand rule | Left-hand | Right-hand |
| Energy transfer | Electrical → kinetic | Kinetic → electrical |
Key terms
Command terms
Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.
Exam technique
Keywords the mark scheme looks for in this lesson
Keywords the mark scheme looks for in this lesson
Electromagnetic induction · Induced e.m.f. · Induced current · Magnetic flux · Flux linkage · Faraday's law · Lenz's law · Fleming's right-hand rule · Galvanometer · Eddy currents · Self-induction
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.
How to get full marks (examiner guidance)
1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.
Words to avoid
1
a current is induced when the magnet is in the coilan e.m.f. is induced only while the magnet moves relative to the coil (the flux is changing).
2
a voltage is induced when the magnet is nearan e.m.f. is induced when field lines are cut or the flux linkage changes.
3
the induced current helps the magnetthe induced current opposes the change that produced it (Lenz's law).
4
more magnets make more currenta stronger magnet, faster motion or more turns increases the induced e.m.f.
5
use the left-hand rule for a generatoruse Fleming's right-hand rule for induced current.
Instant feedbackCheck yourself
Q1. A magnet is held still inside a coil connected to a galvanometer. The reading is
- A. large
- B. zero
- C. steadily increasing
- D. alternating
Show answer
B. No change of flux means no induced e.m.f.
Q2. Which would NOT increase the e.m.f. induced when a magnet is pushed into a coil?
1
A. Pushing faster
2
B. Using more turns
3
C. Using a stronger magnet
4
D. Using thicker wire with the same turns
Show answer
D. e.m.f. depends on rate of change of flux linkage, not wire thickness.
Q3. Lenz's law is a consequence of the conservation of
- A. charge
- B. momentum
- C. energy
- D. mass
Show answer
C. The opposing force means work must be done to produce electrical energy.
Q4. A 0.50 m rod moves at 4.0 m/s perpendicular to a 0.10 T field. The induced e.m.f. is
- A. 0.20 V
- B. 2.0 V
- C. 0.80 V
- D. 20 V
Show answer
A. E = BLv = 0.10 × 0.50 × 4.0 = 0.20 V.
Q5. In Fleming's right-hand rule, the thumb represents
- A. field
- B. induced current
- C. motion of the conductor
- D. force on electrons
Show answer
C. thuMb = Motion.
Q6. When a magnet is pulled out of a coil, compared with pushing in, the induced current
- A. is zero
- B. reverses direction
- C. is always larger
- D. is the same direction
Show answer
B. The flux change reverses, so the induced current reverses.
Marked practiceQuizzes for this lesson
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