Electromagnetism — OCR A-Level Physics
Test yourself on Electromagnetism with OCR A-Level practice questions.
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Electromagnetism explained
Magnetic flux Φ measures the amount of magnetic field passing through a surface.
Read the full explanation
For a uniform field B through area A, Φ = BA cos θ, where θ is the angle between the field direction and the normal to the surface. The unit of flux is the weber, Wb, and 1 Wb = 1 T m². When the field is perpendicular to the surface, θ = 0° and Φ = BA; when the field is parallel to the surface, θ = 90° and Φ = 0. Example: a coil of area 2.0 × 10⁻³ m² in a field of 0.50 T with its normal at 60° to the field has Φ = 0.50 × 2.0 × 10⁻³ × cos 60° = 5.0 × 10⁻⁴ Wb.
(b) magnetic flux linkage
Magnetic flux linkage extends magnetic flux Φ to a coil of N turns: each turn links the same flux, so linkage NΦ is measured in webers (Wb) or weber-turns. Flux itself is Φ = BA cos θ, where B is flux density in tesla, A is area in m² and θ is the angle between B and the normal to the area. If B = 0.20 T, A = 3.0 × 10⁻³ m² and the field is perpendicular to the coil, Φ = 6.0 × 10⁻⁴ Wb; a 250-turn coil then has linkage NΦ = 0.15 Wb. Linkage changes when B, A or orientation changes, and this changing linkage drives induced e.m.f. in the next specification point.
(c) Faraday’s law of electromagnetic induction and Lenz’s law
Faraday's law states that the magnitude of an induced e.m.f. equals the rate of change of magnetic flux linkage, so a faster change or a larger change in NΦ gives a larger e.m.f. Lenz's law states that the induced e.m.f. drives a current whose magnetic effect opposes the change producing it, which is why the minus sign appears in E = −N ΔΦ/Δt. For example, pushing a magnet towards a coil induces a current whose field repels the approaching magnet; pulling it away reverses the induced current so it attracts the receding magnet. Together the laws explain the direction and size of induced e.m.f. and current in generators, transformers and moving conductors.
(d)
This row is a specification sub-heading with no assessed content of its own, so it is a reading and orientation point rather than an examinable statement. Read it as the opening of the sub-section that follows, which develops the induction equations and their applications. Your task is to locate the sub-section in the specification, note how it connects to the preceding points on flux linkage and the induction laws, and identify the later statements it introduces. Do not invent definitions, equations or mark allocations for a bare heading. Use it to build a map of the topic: flux linkage, Faraday's and Lenz's laws, then the quantitative treatment of induced e.m.f.
(i) e.m.f. = − rate of change of magnetic flux linkage; ( ) E t N T T z =-
This statement gives the quantitative form of Faraday's law: the induced e.m.f. E equals the negative rate of change of magnetic flux linkage, E = −N ΔΦ/Δt, where N is the number of turns, ΔΦ is the change in flux through one turn in webers and Δt is the time interval in seconds. The negative sign expresses Lenz's law. For a 200-turn coil in which flux through each turn falls from 4.0 × 10⁻³ Wb to zero in 0.050 s, ΔΦ/Δt = −8.0 × 10⁻² Wb s⁻¹, so E = −200 × (−8.0 × 10⁻²) = 16 V. The unit check is Wb s⁻¹ = V.
(ii) techniques and procedures used to investigate magnetic flux using search coils
A search coil is a small flat coil of N turns and known area A connected to a sensitive meter or data logger. Place it in a magnetic field so that its plane is perpendicular to the field; the flux linkage through it is NΦ = NBA. To investigate magnetic flux, rotate or withdraw the coil, or switch the field on and off, so that the flux linkage changes; the induced e.m.f. is proportional to the rate of change of flux linkage. A calibrated search coil in a known field lets you measure flux density B = Φ/A. Record the meter reading against time, note the peak, and compare coils of different N or A.
(e) simple a.c. generator
A simple a.c. generator is a coil rotating at constant angular speed in a uniform magnetic field. As the coil turns, the angle between the coil plane and the field changes, so the flux linkage NΦ = NBA cos θ varies sinusoidally. By Faraday's law the induced e.m.f. equals the negative rate of change of flux linkage, giving a sinusoidal output that reverses each half turn. Slip rings and brushes connect the rotating coil to the external circuit without reversing the connections, so the current alternates. Increasing N, B, A or the rotation frequency increases the peak e.m.f.; the output frequency equals the rotation frequency.
(f)
This row is a guided-reading item for section 6.3.3 Electromagnetism. The statement is only the label (f), so the learner should use the official OCR A Level Physics A specification to identify the full learning outcome that follows (f) in this section. Read the specification text carefully, note any equations, definitions and practical techniques it names, and check how it links to earlier statements on magnetic flux, flux linkage and electromagnetic induction. Use the specification's own wording to decide what must be learned, then work through the relevant textbook or class notes, making a summary that covers each clause. Do not treat this label as a stand-alone fact.
(i) simple laminated iron-cored transformer; Ns/Np = Vs/Vp = Ip/Is for an ideal transformer
A simple transformer has two coils wound on a laminated iron core. Alternating current in the primary coil produces a changing magnetic flux in the core, which links the secondary coil and induces an alternating e.m.f. there. Laminations reduce eddy currents and energy loss. For an ideal transformer, power in equals power out, so Ns/Np = Vs/Vp = Ip/Is, where N is the number of turns, V the voltage and I the current in the secondary (s) and primary (p). A step-up transformer has more secondary turns and raises voltage while lowering current; a step-down transformer does the reverse.
(ii) techniques and procedures used to investigate transformers.
A transformer has two coils on a shared laminated iron core. An alternating current in the primary produces a changing magnetic flux in the core, which links the secondary and induces an alternating emf. To investigate this, connect an a.c. supply to the primary and measure primary and secondary voltages with a.c. voltmeters, or use a signal generator and oscilloscope. Vary the number of turns on each coil and record the ratio of secondary to primary voltage, comparing it with the turns ratio. Keep frequency constant when testing turns, and keep turns constant when testing frequency. Laminated cores reduce eddy currents; the core links flux between coils.
Your focus
- Define magnetic flux and state its unit, the weber.
- Apply Φ = BA cos θ to calculate flux through a surface at a given angle to a uniform magnetic field.
- Explain how the orientation of a surface affects the magnetic flux through it.
Show all 30 objectives
- State that magnetic flux linkage is the product of the number of turns and the flux through each turn.
- Apply NΦ = NBA cos θ to calculate flux linkage in a uniform magnetic field.
- Explain how changing B, A or the orientation of a coil changes the flux linkage.
- State Faraday's law of electromagnetic induction and apply it to calculate an induced e.m.f.
- State Lenz's law and use it to determine the direction of an induced current.
- Explain the meaning of the minus sign in E = −N ΔΦ/Δt in terms of energy conservation.
- Identify the sub-section of the specification introduced by this heading.
- Relate the heading to the preceding statements on flux linkage and the induction laws.
- Use the heading to organise revision of the following numbered statements.
- Apply E = −N ΔΦ/Δt to calculate an induced e.m.f. from a change in flux linkage.
- Interpret the negative sign in the equation as an expression of Lenz's law.
- Check that units of flux, time and e.m.f. are consistent in a calculation.
- Describe how a search coil is used to investigate magnetic flux.
- Apply NΦ = NBA to a search coil in a perpendicular field.
- Explain how changing flux linkage produces an induced e.m.f. that can be measured.
- Describe the construction and operation of a simple a.c. generator.
- Explain how the rotating coil produces a sinusoidal alternating e.m.f.
- Relate peak e.m.f. and frequency to the generator's parameters.
- Locate and read the full specification statement that follows label (f) in section 6.3.3.
- Identify the equations, definitions and techniques named in that statement.
- Produce a summary that covers every clause of the statement and links it to earlier work on electromagnetism.
- Describe the construction and operation of a simple laminated iron-cored transformer.
- Apply Ns/Np = Vs/Vp = Ip/Is to ideal transformer problems.
- Explain how laminations reduce energy losses and why alternating current is required.
- Describe how to set up a transformer investigation using an alternating supply and a laminated iron core.
- Explain how changing the number of turns on the primary or secondary coil affects the induced secondary voltage.
- Select appropriate measuring instruments and identify variables that must be controlled in the investigation.
Electromagnetism exam tips
Marking Points
- Defines magnetic flux as the product of flux density and the area perpendicular to the field.
- Uses Φ = BA cos θ with θ measured between the field direction and the normal to the surface.
- States that the unit of magnetic flux is the weber, where 1 Wb = 1 T m².
- Applies the equation to calculate flux for a given field, area and orientation.
- Magnetic flux linkage is defined as NΦ, the product of the number of turns N and the magnetic flux Φ through one turn.
- Magnetic flux Φ = BA cos θ, with B in tesla, A in m² and θ measured between B and the normal to the area.
- The unit of flux and of flux linkage is the weber (Wb); flux linkage may also be quoted in weber-turns.
- Flux linkage changes if B changes, if the area A changes, or if the angle θ between field and normal changes.
- A numerical check: B = 0.20 T, A = 3.0 × 10⁻³ m², N = 250 gives Φ = 6.0 × 10⁻⁴ Wb and NΦ = 0.15 Wb.
- Faraday's law: the magnitude of the induced e.m.f. is equal to the rate of change of magnetic flux linkage, |E| = N |ΔΦ/Δt|.
- Lenz's law: the induced e.m.f. and resulting current act in a direction that opposes the change in flux linkage producing them.
- The minus sign in E = −N ΔΦ/Δt expresses Lenz's law and indicates the opposing direction of the induced e.m.f.
- A larger rate of change of flux linkage, for example by faster motion or more turns, produces a larger induced e.m.f.
- Reversing the direction of the change in flux linkage reverses the direction of the induced e.m.f. and current.
- The induced e.m.f. is given by E = −N ΔΦ/Δt, the negative rate of change of magnetic flux linkage.
- N is the number of turns, ΔΦ is the change in flux through one turn in webers and Δt is the time interval in seconds.
- The unit of ΔΦ/Δt is Wb s⁻¹, which is equivalent to the volt.
- The negative sign represents Lenz's law: the induced e.m.f. opposes the change in flux linkage.
- Worked check: N = 200, ΔΦ = −4.0 × 10⁻³ Wb, Δt = 0.050 s gives E = −200 × (−4.0 × 10⁻³ ÷ 0.050) = 16 V.
- A search coil is a flat coil of N turns and known area A used to sample the magnetic flux in a region.
- With the coil plane perpendicular to the field, the flux linkage is NΦ = NBA.
- Changing the flux linkage, by rotating, withdrawing or switching the field, induces an e.m.f. proportional to the rate of change of flux linkage.
- A calibrated search coil in a known field allows flux density to be found from B = Φ/A.
- The induced e.m.f. can be displayed on a galvanometer, oscilloscope or data logger and its peak compared for different N or A.
- A simple a.c. generator consists of a coil rotating in a uniform magnetic field.
- The flux linkage varies as NΦ = NBA cos θ, where θ is the angle between the field and the normal to the coil.
- The induced e.m.f. is the negative rate of change of flux linkage, so the output is sinusoidal and reverses direction.
- Slip rings and brushes transfer the alternating current to the external circuit.
- Peak e.m.f. increases with N, B, A and angular speed; output frequency equals rotation frequency.
- A transformer consists of primary and secondary coils on a laminated iron core.
- Alternating current in the primary produces a changing flux that induces an alternating e.m.f. in the secondary.
- Laminations reduce eddy currents, improving efficiency.
- For an ideal transformer, Ns/Np = Vs/Vp = Ip/Is.
- A step-up transformer has Ns greater than Np and increases voltage while decreasing current; a step-down transformer does the opposite.
- A transformer requires a changing magnetic flux, so the primary must carry alternating current; a steady direct current induces no continuous secondary emf.
- The laminated iron core links magnetic flux from the primary coil to the secondary coil, increasing the induced emf.
- Secondary voltage depends on the ratio of secondary turns to primary turns, so changing turns changes the output voltage.
- Measurements use a.c. meters or an oscilloscope; a signal generator can supply a variable-frequency alternating input.
- Keeping other variables constant, such as frequency when varying turns, makes the investigation a fair test.
Examiner Tips
- 💡Identify the normal to the surface first, then measure θ from the field direction to that normal.
- 💡Check the orientation: θ = 0° gives maximum flux BA, and θ = 90° gives zero flux.
- 💡Convert area to m² and flux density to T before calculating flux in Wb.
- 💡Write the defining equation NΦ = NBA cos θ before substituting values so the role of each symbol is clear.
- 💡Check that area is in m² and that the angle used is measured from the normal to the coil.
- 💡When a question asks for a change in flux linkage, calculate the initial and final values separately and subtract, rather than assuming the change equals the final value.
- 💡Quote Faraday's law in words and as an equation before applying it to a numerical change in flux linkage.
- 💡Use Lenz's law to justify the direction of an induced current by identifying what change is being opposed.
- 💡When calculating, find the change in flux linkage and divide by the time interval, keeping the sign to show direction.
- 💡Use the sub-heading to build a topic map linking flux linkage, Faraday's law, Lenz's law and induced e.m.f. calculations.
- 💡Check the numbered statements that follow the heading and revise each one against the specification wording.
- 💡When revising, write the heading at the top of a summary page and list the equations and definitions beneath it.
- 💡Write E = −N ΔΦ/Δt and identify N, ΔΦ and Δt before substituting numerical values.
- 💡Check units: flux in webers, time in seconds, e.m.f. in volts.
- 💡Use the sign of ΔΦ to decide the direction of the induced e.m.f. and state that it opposes the change.
- 💡State the orientation of the coil relative to the field before quoting NΦ = NBA.
- 💡Link any observed meter deflection to a change in flux linkage, not to the field being present.
- 💡When comparing results, keep either N or A constant so the effect of the other is clear.
- 💡Sketch the sinusoidal e.m.f. against time and mark where the coil plane is parallel and perpendicular to the field.
- 💡Use NΦ = NBA cos θ and differentiate to show the sinusoidal form when needed.
- 💡State clearly that slip rings allow the current to alternate rather than being rectified.
- 💡Open the official specification and read the complete statement that follows (f) before revising.
- 💡Highlight the command words and any equations in the full statement so you know what to practise.
- 💡Make a short summary that covers every clause of the full statement, then test yourself without notes.
- 💡Write the ratio as Ns/Np = Vs/Vp = Ip/Is and substitute values carefully, checking which coil is primary.
- 💡Use power conservation to check your answer: VpIp should equal VsIs for an ideal transformer.
- 💡State that the input must be alternating so that the flux changes and induces an e.m.f.
- 💡State clearly that the input must be alternating, because electromagnetic induction needs changing flux.
- 💡Describe the measurement method: a.c. voltmeters across each coil, or an oscilloscope to compare input and output waveforms.
- 💡When comparing results, identify the controlled variable, such as keeping frequency constant while changing the number of turns.
Common Mistakes
- Measuring θ between the field and the surface rather than between the field and the normal; the correction is that θ is the angle between B and the normal to the area.
- Forgetting the cos θ factor when the surface is tilted; the correction is that only the component of B perpendicular to the area contributes to the flux.
- Using the wrong unit for flux; the correction is that flux is measured in weber, Wb, equivalent to T m².
- Treating flux linkage as simply BA and forgetting to multiply by the number of turns N; the correction is to use NΦ = NBA cos θ.
- Measuring θ from the plane of the coil instead of from the normal to the area; the correction is that θ is the angle between B and the normal, so a field parallel to the plane gives zero flux.
- Using area in cm² without converting to m²; the correction is to convert, for example 30 cm² = 3.0 × 10⁻³ m², before multiplying.
- Stating that the induced e.m.f. equals the flux linkage rather than its rate of change; the correction is that e.m.f. depends on how quickly flux linkage changes.
- Ignoring the minus sign or treating it as an arithmetic detail; the correction is that the sign represents Lenz's law and the opposing direction of the induced effect.
- Claiming that Lenz's law opposes the flux itself rather than the change in flux; the correction is that the induced current opposes the change producing it.
- Treating a bare sub-heading as a full specification statement and inventing content for it; the correction is to read it as a signpost to the statements that follow.
- Assuming the heading carries its own mark scheme or assessment objective; the correction is that assessment comes from the numbered statements it introduces.
- Skipping the heading and losing the structure of the section; the correction is to use it to organise revision around flux linkage and induction.
- Using the total flux linkage change without dividing by the time interval; the correction is that e.m.f. is a rate of change, so divide Δ(NΦ) by Δt.
- Forgetting to multiply the flux change per turn by the number of turns N; the correction is to use the change in flux linkage NΔΦ.
- Dropping the negative sign when the direction of the induced e.m.f. is required; the correction is to keep the sign to represent Lenz's law.
- Thinking the search coil measures flux directly: it responds to the rate of change of flux linkage, so a steady field gives no reading.
- Confusing flux Φ with flux linkage NΦ; the e.m.f. depends on the change in NΦ, not Φ alone.
- Assuming the coil area or number of turns does not matter; both scale the flux linkage and hence the induced e.m.f.
- Forgetting to keep the coil plane perpendicular to the field when measuring flux density, which reduces the effective flux.
- Believing the e.m.f. is largest when the coil is perpendicular to the field; in fact the rate of change of flux linkage is then zero, so the e.m.f. is zero.
- Confusing slip rings with a split-ring commutator; a split-ring commutator would give a d.c. output, not a.c.
- Thinking the output frequency is twice the rotation frequency; it equals the rotation frequency.
- Ignoring the negative sign in Faraday's law, which indicates the direction of the induced e.m.f. opposes the change.
- Treating the label (f) as the whole learning outcome; the learner must look up the full statement in the specification.
- Assuming the content is optional because the statement is short; every specification point in this section is examinable.
- Skipping the practical or mathematical detail that the full statement may require, such as an equation or technique.
- Studying the section in isolation instead of linking it to earlier statements on flux linkage and induction.
- Using the turns ratio the wrong way round, for example writing Np/Ns = Vs/Vp; the correct relation is Ns/Np = Vs/Vp.
- Assuming current also increases in a step-up transformer; for an ideal transformer, voltage rises while current falls so power is conserved.
- Thinking a transformer works with direct current; a steady d.c. produces no changing flux and so no induced e.m.f.
- Ignoring the role of laminations and treating the core as solid, which would allow large eddy currents and energy loss.
- Thinking a transformer works with direct current: a steady d.c. gives constant flux and no induced secondary emf, so an alternating supply is needed.
- Assuming the core carries current between the coils: the core links magnetic flux, while current flows in the coils themselves.
- Ignoring the turns ratio and expecting output voltage to depend only on input voltage: the ratio of secondary to primary turns controls the voltage change.