Electromagnetic Induction: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 18 · 9478 Topic 18 · Read time: ~10 minutes
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Key Formulas
Magnetic flux and flux linkage
Magnetic flux is the product of the flux density and the area perpendicular to it: Φ = BA. If the area is tilted, use only the component of area perpendicular to B.
For a coil of N turns, each turn links the same flux, so the flux linkage is NΦ = NBA.
Trap: For a coil, use flux linkage NΦ, not Φ, in Faraday's law. Missing the N is one of the most common errors.
Faraday's law and Lenz's law
A changing magnetic flux linkage induces an e.m.f. A strong but unchanging flux induces nothing.
Faraday's law: the magnitude of the induced e.m.f. equals the rate of change of flux linkage.
Lenz's law: the induced e.m.f. (and current) acts in a direction that opposes the change producing it. The minus sign in E = −d(NΦ)/dt shows this. It is a consequence of conservation of energy: you must do work against the opposing force to generate electrical energy.
Factors increasing the e.m.f.: faster change, stronger field, larger area, more turns.
Trick: For a rotating coil, NΦ = NBA cos ωt and E = NBAω sin ωt. The e.m.f. is maximum when the flux linkage is zero (coil plane parallel to B), because that is when it changes fastest.
Applications and transformers
Simple applications include the a.c. generator, induction cooktops, metal detectors and eddy current braking.
In an iron-core transformer, an alternating current in the primary produces a changing flux in the core, which links the secondary and induces an alternating e.m.f.
For an ideal transformer: Nₛ/Nₚ = Vₛ/Vₚ = Iₚ/Iₛ. Stepping the voltage up steps the current down by the same factor, since power in equals power out.
Transformers need a changing flux, so they work only with a.c.
Worked Example
A coil of 200 turns and area 0.015 m² rotates at 50 rad s⁻¹ in a uniform field of 0.080 T.
(a) Calculate the maximum flux linkage. [1]
NΦ(max) = NBA = 200 × 0.080 × 0.015 = 0.24 Wb
(b) Calculate the maximum induced e.m.f. [2]
E(max) = NBAω
= 0.24 × 50 = 12 V
(c) State the coil's orientation when the e.m.f. is maximum, and explain. [2]
When the coil's plane is parallel to the field.
The flux linkage is zero there but changing at its fastest rate.
(d) An ideal transformer with 100 primary and 2,000 secondary turns is supplied at 12 V r.m.s. Calculate the output voltage. [1]
Vₛ = Vₚ × Nₛ/Nₚ = 12 × 20 = 240 V r.m.s.
Why this question is a good test of the topic: part (c) catches students who assume maximum e.m.f. means maximum flux. It is the rate of change that matters.
Frequently Asked Questions
What is the difference between flux and flux linkage?
Flux is BA through one turn. Flux linkage is NBA, the flux multiplied by the number of turns in the coil.
What does Faraday's law state?
The magnitude of the induced e.m.f. equals the rate of change of magnetic flux linkage.
What does Lenz's law state?
The induced e.m.f. acts to oppose the change that produces it. This follows from conservation of energy.
When is the e.m.f. in a rotating coil maximum?
When the plane of the coil is parallel to the field, where flux linkage is zero but changing fastest.
Why do transformers only work on a.c.?
They need a changing flux in the core to induce an e.m.f. in the secondary. Steady d.c. gives a constant flux.
Still mixing up flux and rate of change of flux?
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