This unit is ≈16% of the A-Level Physics, across 6 lessons. Full syllabus
Lesson 5 of 6 · Fields and their consequences
Electromagnetic induction, AC and transformers
8 min read · about 1 h 50 min with practice3 quick checks≈3% of the testStretch: Stretch: harder material that separates the top grades
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Electromagnetic induction is one of the most heavily examined topics in the fields papers. It supplies definition marks, multi-step calculations (moving rods, rotating coils, transformers, cable losses), graph interpretation and some of the most common 6-mark extended responses. All boards test the same core physics. They differ in notation, and in whether transformers and the rotating-coil equation are examinable.
By the end you’ll be able to
Define flux (Φ = BA cos θ) and flux linkage (NΦ) and apply Faraday’s law ε = NΔΦ/Δt
Use Lenz’s law to predict the direction of induced current and explain it as energy conservation
Derive ε = BNAω sin ωt for a rotating coil and describe the search-coil required practical
Relate peak and rms values, and measure period and peak voltage with an oscilloscope
Use Ns/Np = Vs/Vp, efficiency and eddy-current losses, and explain high-voltage power transmission
What the exam asks
Definitions: magnetic flux, the weber, flux linkage, Faraday’s law and Lenz’s law, each in one precise sentence.
Calculations:ε=NΔtΔΦ, ε=, , rms values, transformer ratios and efficiency, and cable losses .
vii.Check your understanding
3 questions on electromagnetic induction, AC and transformers. Every option is explained once you answer.
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The first 3 of 11 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.
PromptCard 1 of 3
Define magnetic flux and give its unit.
BLv
ε=BANωsinωt
I2R
Graphs: turning a flux-linkage–time graph into an emf–time graph, and explaining the two pulses produced when a magnet falls through a coil.
Practical: the search-coil investigation of flux linkage against angle (AQA required practical 11; OCR A search-coil techniques), and reading an oscilloscope trace.
Extended response: how a transformer works and loses energy, and why the grid transmits at high voltage.
Core ideas
Magnetic flux and flux linkage
Φ=BAcosθ
Here θ is the angle between the field and the normal to the area. The unit is the weber: 1Wb=1T m2. Flux linkage is NΦ=BANcosθ (AQA writes the unit as “Wb turns”).
Orientation of the coil
θ
Flux linkage
Plane perpendicular to B
0∘
Maximum, BAN
Plane parallel to B
90∘
Zero
Plane at 30∘ to B
60∘
0.5
Faraday’s law and Lenz’s law
Faraday’s law: the magnitude of the induced emf equals the rate of change of flux linkage.
ε=NΔtΔΦorε=−dtd(NΦ)
Lenz’s law: the induced emf, and any induced current, acts in the direction that opposes the change producing it; the minus sign expresses this. It is a consequence of conservation of energy. If the induced current helped the change, a magnet pushed towards a coil would speed up with no energy input. Because the current opposes the change, work must be done, and that work becomes electrical energy.
Two graph facts carry many marks:
emf =−(gradient of the NΦ–t graph). A flat section of the graph means zero emf.
The area under an ε–t graph equals the change in flux linkage.
A conductor moving through a field
A rod of length L moving at speed v perpendicular to B sweeps an area LvΔt in time Δt, cutting flux BLvΔt, so
ε=BLv
Use Fleming’s right-hand rule (thumb = motion, first finger = field, second finger = current) or Lenz’s law for the direction. In a complete circuit, the current feels a force F=BIL that opposes the motion. At constant speed, the applied force equals BIL and the mechanical power Fv equals the electrical power εI.
The rotating coil: an a.c. generator
A coil rotating at angular speed ω in a uniform field has NΦ=BANcosωt, so
ε=BANωsinωt,ε0=BANω
The emf is greatest when the plane of the coil is parallel to the field. At that instant the flux linkage is zero but changing fastest. The emf is zero when the flux linkage is at its maximum. Doubling the rotation rate doubles both the peak emf and the frequency.
Alternating current, rms values and the oscilloscope
The rms value is the steady direct current (or pd) that would dissipate the same mean power in a resistor:
Irms=2I0,Vrms=2V0,mean power21I0V0
UK mains is 230 V rms, so the peak is 325 V and the peak-to-peak value is 650 V. On an oscilloscope, the peak is (divisions from the centre line to the peak) × Y-gain, and the period is (divisions per cycle) × time-base. For better precision, measure peak-to-peak and halve it, and time several cycles.
Transformers
An alternating current in the primary produces an alternating flux in the soft-iron core. The core links this flux to the secondary, and the changing flux linkage induces an alternating emf there. A steady d.c. supply induces nothing, because the flux does not change.
NpNs=VpVs,efficiency=IpVpIsV
Energy loss
Cause
Remedy
Eddy currents
Currents induced in the core heat it
Laminated core of thin insulated sheets
Heating in the coils
I2R in the windings
Thick, low-resistance copper wire
Magnetising and demagnetising the core
The magnetisation reverses every cycle
Soft iron alloy core
Flux leakage
Some primary flux misses the secondary
Coils wound on top of each other on a closed core
High-voltage transmission
For a fixed power P=VI, raising the voltage by a factor n cuts the current by n, so the cable loss I2R falls by n2. Step-up transformers raise the voltage at the power station, and step-down transformers lower it for safe use.
Worked examples
Exam technique
Faraday calculations: find Δ(NΦ)=NΔ(BAcosθ) first, then divide by the time. Convert cm² to m² (÷ 10⁴), and check whether you were given a radius or a diameter.
Direction questions: state the change in flux, then say the induced current’s field opposes it, and name the resulting pole or force. A bare “by Lenz’s law” earns nothing.
Sketching emf from flux: plot the gradient. Flat sections give zero emf, steep sections give large emfs, and a sine becomes a cosine.
Efficiency: find Ps=IsVs, divide by the efficiency to get Pp, then Ip=VpP.
Six-markers on transformers: link three strands: the mechanism (a.c. → changing flux → flux linkage → induced emf), the losses with their remedies, and the transmission argument.
Common mistakes
Quick recap
Φ=BAcosθ in Wb (T m²), with θ measured from the normal; flux linkage =NΦ.
Faraday: emf = rate of change of flux linkage. Lenz: the emf opposes the change, as conservation of energy requires.
Moving rod: ε=BLv, and the induced current feels a force BIL opposing the motion.
Rotating coil: ε=BANωsinωt, with its maximum when the coil plane is parallel to B.
Vrms=2; mean power in a resistor is half the peak power.
Transformers: NpNs=; laminations, thick copper and a soft-iron core reduce the losses.
Transmitting at n times the voltage cuts the cable loss by a factor of n2.