Electromagnetic induction (A-level only) — AQA A-Level Physics

Electromagnetic induction is a fundamental topic in A-level Physics that explains how a changing magnetic field can generate an electromotive force (emf) and hence a current in a conductor. It is the principle behind many technologies, including electrical generators, transformers, and induction cookers. Understanding this topic is crucial for explaining energy transfer and the relationship between electricity and magnetism.

In the AQA A-level specification, this topic builds on prior knowledge of magnetic fields and forces on current-carrying conductors. It introduces Faraday's law and Lenz's law, which are essential for quantitative analysis and for explaining the direction of induced currents. Mastery of electromagnetic induction is required for further study of alternating currents and power transmission.

• →Magnetic flux (Phi) is the product of the magnetic flux density (B) and the area (A) perpendicular to the field: Phi = B * A * cos(theta), where theta is the angle between the field and the normal to the area. The unit is the weber (Wb).
• →Magnetic flux linkage is the product of the number of turns (N) and the magnetic flux per turn: N * Phi. It is measured in weber-turns (Wb-turns).
• →Faraday's law states that the induced emf is directly proportional to the rate of change of magnetic flux linkage: emf = -N * (delta Phi / delta t). The negative sign represents Lenz's law.
• →Lenz's law states that the direction of the induced emf is such that it opposes the change in magnetic flux that produced it, in accordance with conservation of energy.
• →For a straight conductor moving perpendicular to a uniform magnetic field, the induced emf is given by emf = B * l * v, where l is the length of the conductor and v is its speed.

• Describe at least two simple experimental arrangements that demonstrate electromagnetic induction, such as a magnet moving relative to a coil or one coil connected to a changing current placed near another coil.
• State the observation that an induced e.m.f. or current occurs only while flux linkage is changing, and that steady flux linkage produces no induced effect.
• Relate the observed induced e.m.f. to the rate of change of flux linkage and the number of turns, using Faraday's law qualitatively or quantitatively.
• Explain the direction of the induced current using Lenz's law, noting that the induced effect opposes the change producing it, for example the coil face becomes a like pole as a magnet approaches.
• Identify control variables and measurement methods in these experiments, such as using a sensitive galvanometer, data logger or oscilloscope, and changing one factor at a time.
• Faraday’s law: the magnitude of the induced emf is proportional to the rate of change of magnetic flux linkage, ε = −N ΔΦ/Δt for a coil of N turns.
• Flux linkage is NΦ, where Φ = BA cos θ for a uniform field through a flat coil, so changing B, A or the angle θ changes the linkage.
• Lenz’s law: the induced current flows in a direction that opposes the change in flux linkage that produced it.
• Lenz’s law follows from conservation of energy because the induced current transfers energy and work must be done against the opposing force or torque.
• A qualitative direction question is answered by identifying the change in flux linkage, then choosing the induced current direction whose field opposes that change.
• A quantitative question uses the magnitude relationship and treats the minus sign as a direction indicator rather than a numerical size.
• The magnitude of the induced emf is the rate of change of flux linkage, ε = N ΔΦ/Δt, with ΔΦ measured in webers and Δt in seconds.
• For a straight conductor of length L moving at speed v perpendicular to a uniform field B, the induced emf is ε = BLv.
• The BLv result follows because the conductor sweeps area at rate Lv, so the rate of change of flux linkage is B × Lv for a single conductor.
• The direction of the induced emf or current is determined by Lenz’s law or by the right-hand rule for a moving conductor.
• If the conductor moves parallel to the magnetic field, it cuts no flux lines and the induced emf is zero.
• Applications include a rod sliding on conducting rails, a conductor falling through a magnetic field and a search coil moving through a field.
• States that the flux linkage through the rotating coil is NΦ = BAN cos ωt, identifying the cosine variation with the angle between the field and the coil normal.
• Applies Faraday's law as the rate of change of flux linkage, differentiating BAN cos ωt to obtain ε = BANω sin ωt.
• Identifies the peak emf as ε₀ = BANω and explains that it occurs when the coil plane is parallel to the magnetic field, where flux linkage is zero but changing at its greatest rate.
• Explains that the emf is zero at maximum flux linkage, when the coil plane is perpendicular to the field, because the rate of change of flux linkage is momentarily zero.
• Relates the angular frequency ω to the rotation frequency f using ω = 2πf, and links the sinusoidal emf to the sinusoidal variation of flux linkage.
• Describes how increasing B, A, N or ω increases the peak induced emf, and that changing ω also changes the frequency of the output.

• 💡Describe the experimental set-up, the change made, and the resulting observation in a clear sequence, using terms such as flux linkage, induced e.m.f. and galvanometer deflection.
• 💡When explaining direction, name the law (Lenz's law) and state the opposing change explicitly rather than simply saying the current goes the other way.
• 💡Use a sketch of the field lines or coil face to support your explanation, and keep the distinction between flux, flux linkage and induced e.m.f. clear.
• 💡When asked for the direction of an induced current, first state whether the flux linkage is increasing or decreasing, then apply Lenz’s law to choose the current direction.
• 💡Show the substitution into ε = N ΔΦ/Δt with consistent units, and keep the magnitude separate from the direction discussion.
• 💡Use energy conservation to justify Lenz’s law in explanation questions, referring to the work done against the opposing force or torque.
• 💡Identify the quantity changing with time before choosing between ε = N ΔΦ/Δt and ε = BLv.
• 💡For a straight conductor, check that the velocity component is perpendicular to the field and use that component in ε = BLv.
• 💡State the direction of the induced current separately from the magnitude calculation, using Lenz’s law or the moving-conductor rule.
• 💡Sketch the flux linkage and emf graphs on the same time axis, labelling the quarter-cycle phase difference, to show clearly how the sine and cosine variations are related.
• 💡When substituting values, convert a rotation rate in revolutions per second to angular frequency using ω = 2πf before calculating BANω.
• 💡State explicitly that the derivation uses Faraday's law and the chain rule, so the examiner can see the physics behind each mathematical step.
• 💡Always define your terms clearly: state what is meant by magnetic flux and flux linkage before using formulas. Use correct units (Wb for flux, V for emf) and show all steps in calculations.
• 💡When explaining Lenz's law, explicitly link it to conservation of energy. For example, the induced current creates a force that opposes the motion, so work must be done against this force, converting mechanical energy to electrical energy.
• 💡For questions involving graphs, remember that the gradient of a flux linkage-time graph gives the induced emf. A constant gradient means a constant emf, while a changing gradient means a changing emf.

• Believing that a steady magnetic field through a stationary coil induces a current; correct this by stating that flux linkage must change, so movement, rotation or a changing current is required.
• Confusing the direction of induced current with the direction of the applied field; correct this by applying Lenz's law and identifying the pole induced on the coil face nearest the approaching or receding magnet.
• Assuming the induced e.m.f. depends only on the strength of the magnet; correct this by explaining that the rate of change of flux linkage and the number of turns also determine the magnitude.
• Treating the minus sign in ε = −N ΔΦ/Δt as making the emf negative in magnitude calculations; the correct approach is to calculate the magnitude from the rate of change and use Lenz’s law separately for direction.
• Confusing magnetic flux Φ with flux linkage NΦ; the correction is to multiply the flux through one turn by the number of turns before finding the rate of change.
• Stating that the induced current opposes the magnetic field itself rather than the change in flux linkage; the correction is to say it opposes the change, so the induced field may be in the same direction as the original field when that field is decreasing.
• Using ε = BLv when the conductor moves parallel to the field; the correction is to recognise that no flux is cut and the induced emf is zero.
• Forgetting to include the number of turns N when a coil rather than a single conductor is moving; the correction is to use ε = N ΔΦ/Δt or multiply the single-conductor result by N where appropriate.
• Mixing up the direction rule for a moving conductor with the direction rule for a current-carrying conductor in a field; the correction is to use the moving-conductor rule or Lenz’s law consistently.
• Treating the induced emf as proportional to the flux linkage rather than to its rate of change; the correction is to differentiate the flux linkage expression, giving a sine term from the cosine term.
• Using degrees in the differentiation or in ωt; the correction is to work in radians, since ω is in rad s⁻¹ and the derivative of cos ωt is −ω sin ωt.
• Assuming the emf is maximum when flux linkage is maximum; the correction is that maximum emf occurs when flux linkage is zero and changing fastest, and zero emf occurs at maximum flux linkage.
• Students often think that an emf is induced only when a conductor cuts magnetic field lines, but it is actually the change in magnetic flux linkage that matters. A stationary conductor in a changing magnetic field also experiences induction.
• Many students believe that the induced current always flows in a direction that opposes the magnetic field itself, rather than opposing the change in flux. Lenz's law specifies opposition to the change, not the field.
• Some students confuse the direction rules: Fleming's right-hand rule is for generators (induced current), while Fleming's left-hand rule is for motors (force on a current-carrying conductor).

1. 1Step 1: Review the definitions of magnetic flux and flux linkage. Practice calculating flux for different angles between the field and the area. Use the formula Phi = B * A * cos(theta).
2. 2Step 2: Learn Faraday's law and Lenz's law. Work through examples of calculating induced emf for a changing flux, including cases with multiple turns and varying angles.
3. 3Step 3: Apply Lenz's law to determine the direction of induced current in various scenarios, such as a magnet falling through a coil or a coil rotating in a magnetic field. Use the right-hand grip rule.
4. 4Step 4: Practice calculations involving the motional emf formula (emf = B * l * v) and problems combining electromagnetic induction with circuits (e.g., finding induced current using Ohm's law).
5. 5Step 5: Attempt past paper questions on this topic, focusing on 6-mark explanations and calculations. Review mark schemes to understand the level of detail required.

• 📋Calculation questions: These often involve using Faraday's law to find the average induced emf given a change in flux linkage over a time interval, or using the motional emf formula for a moving conductor. Advice: Show all working, including the calculation of flux or flux linkage, and give the final answer with the correct unit and direction if asked.
• 📋Explanation questions: These require you to explain phenomena using Faraday's and Lenz's laws, such as why a magnet falling through a copper tube is slowed down. Advice: Structure your answer logically: state the change in flux, apply Faraday's law to explain the induced emf, then apply Lenz's law to explain the direction and the opposing effect.
• 📋Graph analysis: You may be given a graph of magnetic flux linkage against time and asked to determine the induced emf at a point or sketch the emf-time graph. Advice: Remember that emf is the negative gradient of the flux linkage-time graph. Calculate gradients carefully, and for sketches, ensure the emf is zero when the gradient is zero and changes sign appropriately.
• 📋Practical-based questions: These might involve describing an experiment to demonstrate electromagnetic induction, such as moving a magnet through a coil connected to a galvanometer. Advice: Describe the setup clearly, state what is observed (deflection of galvanometer), and explain the observations using the laws of induction.