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Theme D — Fields

D.4 Induction — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 34 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
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pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
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Lesson summary

D.4 Induction — IB PHYSICS HL notes: Define magnetic flux and flux linkage, apply Faraday's and Lenz's laws, and explain induced e.m.f. in moving conductors, transformers and a.c. generators.Electromagnetic induction — an e.m.f.

  • Closed circuit
  • Moving rod
  • Increase ε
  • Ways to change it
  • Faster change
  • Combined equation

Part 1 of 7Induced e.m.f.

1Electromagnetic induction
  • Electromagnetic induction an e.m.f. is induced in a conductor by relative movement between the conductor and a magnetic field
2Cause
  • Cause free electrons feel a magnetic force and are separated, so mechanical work becomes electric potential energy
3Induced e.m.f.
  • Induced e.m.f. the work done per unit charge separating charges to the ends of a conductor
4Closed circuit
  • Closed circuit an induced current flows
5Moving rod
  • ε = BLv for a rod of length L moving at speed v perpendicular to the field
  • For N turns ε = BLvN
6Increase ε
  • Increase ε a longer conductor, a stronger field, faster cutting or more turns

Part 2 of 7Magnetic flux and flux linkage

Flux
  • Φ = BA cos θ in webers, where θ is the angle between the field and the normal to the area
Maximum
  • Φ = BA when the field is perpendicular to the plane of the area
Zero
  • Φ = 0 when the field is parallel to the plane
Flux linkage
  • NΦ = BAN cos θ in weber turns
Ways to change it
  • Ways to change it a changing B, a changing area A or a changing angle θ

Part 3 of 7Faraday's law

Statement
  • Statement the magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage
Equation
  • ε = N(ΔΦ)/Δt
Graph
  • Graph the e.m.f. is the gradient of a flux linkage–time graph
No change
  • No change no e.m.f. is induced when a magnet is held still in or out of a coil
Faster change
  • Faster change moving the magnet faster, more turns or a stronger magnet gives a larger e.m.f.
Reversal
  • Reversal withdrawing the magnet induces an e.m.f. in the opposite direction

Part 4 of 7Lenz's law

Statement
  • Statement the induced e.m.f. is such that it opposes the change causing it
Combined equation
  • ε = −N(ΔΦ)/Δt, where the minus sign represents Lenz's law
Test
  • Test a north pole pushed into a coil induces a north pole at that end, which repels it
  • Pulling it out induces a south pole that attracts it
Direction of current
  • Direction of current find the induced pole, then use the right-hand grip rule
Energy
  • Energy work must be done against the opposing force, so energy is conserved

Part 5 of 7Self-induction, mutual induction and transformers

1
Self-induction
  • Self-induction a change in current in a circuit induces a back e.m.f. in the same circuit that opposes the change
2
Mutual induction
  • Mutual induction a change in current in one circuit induces an e.m.f. in a neighbouring circuit
3
Transformer
  • Transformer a primary coil and secondary coil wound on a soft iron core
  • A changing flux linkage in the core induces an alternating e.m.f. of the same frequency in the secondary
4
Step-up
  • Step-up more turns on the secondary, so a higher secondary voltage
5
Step-down
  • Step-down more turns on the primary, so a lower secondary voltage
6
Soft iron
  • Soft iron it is easily magnetised and demagnetised and strengthens the field linking the coils
7
Eddy currents
  • Eddy currents a changing flux in bulk metal drives currents that dissipate energy, used in induction braking

Part 6 of 7Alternating current generator

1Principle
  • Principle a coil rotated in a magnetic field has a changing flux linkage, so an alternating e.m.f. is induced
2Parts
  • Parts a rectangular coil, slip rings and brushes that give a continuous connection to the circuit
3Flux linkage
  • NΦ = BAN cos ωt
4E.m.f.
  • ε = BANω sin ωt = ε0 sin ωt
5Phase
  • Phase the e.m.f. is sinusoidal and 90° out of phase with the flux linkage
6Doubling the rotation rate
  • Doubling the rotation rate doubles both the peak e.m.f. and the frequency

Part 7 of 7More from the specification

1Induced emf
  • Induced emf a changing magnetic flux through a circuit induces an emf equal to the rate of change of flux linkage.
2Magnetic flux density
  • Magnetic flux density the strength of field, shown by the density of field lines, in tesla.
3Motional emf
  • Motional emf a conductor moving across a uniform magnetic field has emf equal to B times L times v.
4Faraday's law
  • Faraday's law the size of the induced emf is proportional to the rate at which field lines are cut.
5Lenz's law
  • Lenz's law the induced current opposes the change causing it, so a voltmeter reading changes sign when direction reverses.
6Density
  • Mass per unit volume.
7Voltmeter
  • Instrument that measures p.d., connected in parallel.
8Field lines
  • Lines showing the direction and strength of a magnetic field.
9Potential difference
  • Work done by a unit charge passing through a component.
10Constant speed
  • Speed that does not change.

Key terms

TermMeaning
Magnetic fluxThe product of the magnetic flux density and the area perpendicular to the field.
Flux linkageThe product of the flux through a coil and its number of turns.
Faraday's lawThe induced e.m.f. is proportional to the rate of change of flux linkage.
Lenz's lawThe induced e.m.f. opposes the change that causes it.
Self-inductionInduction of an e.m.f. in a circuit by a change of current in the same circuit.
Mutual inductionInduction of an e.m.f. in one circuit by a change of current in a neighbouring circuit.
AlternatorA rotating coil in a magnetic field connected through slip rings that produces alternating current.

Avoid these mistakes

1
Saying an e.m.f. is induced when a magnet is simply near a coil — the flux linkage must change.
2
Forgetting that the e.m.f. is zero when the flux linkage is maximum in a rotating coil.
3
Dropping the minus sign and ignoring Lenz's law.
4
Using the area of the coil in cm2 without converting to m2.
5
Using a calculator in degrees for sin ωt.

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