AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Flux linkage as NΦ where N is the number of turns cutting the flux.
Full specification wording
Magnetic flux and flux linkage (A-level only): Flux linkage as NΦ where N is the number of turns cutting the flux.
Flux linkage extends the idea of magnetic flux to a coil with multiple turns.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 3
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Flux linkage extends the idea of magnetic flux to a coil with multiple turns. When a coil has N turns and each turn encloses the same magnetic flux Φ, the total flux linkage is NΦ. The unit of flux linkage is the weber-turn (Wb-turn), though it is often quoted in webers (Wb) because N is dimensionless. For example, a coil of 200 turns each of area 1.5 × 10⁻³ m² in a uniform field of 0.40 T perpendicular to the coil has Φ = BA = 0.40 × 1.5 × 10⁻³ = 6.0 × 10⁻⁴ Wb, so the flux linkage is NΦ = 200 × 6.0 × 10⁻⁴ = 0.12 Wb-turn. If the field is at an angle θ to the normal, use Φ = BA cos θ first, then multiply by N. Flux linkage is crucial for understanding electromagnetic induction, where a changing flux linkage induces an electromotive force (emf).
What earns the marks
- States that flux linkage is the product of the number of turns N and the magnetic flux Φ through each turn.
- Calculates magnetic flux Φ using Φ = BA or Φ = BA cos θ before multiplying by N.
- Uses the correct unit for flux linkage, recognising that N is dimensionless so the unit is the weber (Wb) or weber-turn (Wb-turn).
- Applies the concept to a coil where each turn cuts the same flux, ensuring N is the total number of turns.
- Explains that a change in flux linkage can induce an emf, linking to Faraday's law.
Common mistakes and how to put them right
Multiplying the area by N before calculating flux, which incorrectly changes the area rather than the number of turns.
Put it right: Calculate Φ for one turn first, then multiply by N.
Using the number of turns per unit length instead of the total number of turns.
Put it right: Use the total number of turns N in the coil.
Forgetting to include the cos θ factor when the field is not normal to the coil.
Put it right: Use Φ = BA cos θ for each turn before multiplying by N.
Exam tips
- Write down the formula NΦ and identify N and Φ separately before substituting values.
- Check that the area used is the area of one turn, not the total area of all turns.
- When the field is at an angle, resolve the field first to find Φ, then multiply by N.
Try the lesson
The start of the Magnetic flux and flux linkage (A-level only): Flux linkage as NΦ where N is the number of turns cutting the flux. lesson, made from checked teaching notes for this specification point.
Have a go first
A coil of 300 turns has a magnetic flux of 4.0 × 10⁻⁴ Wb through each turn. Calculate the magnetic flux linkage of the coil.
Listen
Flux linkage extends the idea of magnetic flux to a coil with multiple turns. When a coil has N turns and each turn encloses the same magnetic flux Φ, the total flux linkage is NΦ. The unit of flux linkage is the weber-turn (Wb-turn), though it is often quoted in webers (Wb) because N is dimensionless. For example, a coil of 200 turns each of area 1.5 × 10⁻³ m² in a uniform field of 0.40 T perpendicular to the coil has Φ = BA = 0.40 × 1.5 × 10⁻³ = 6.0 × 10⁻⁴ Wb, so the flux linkage is NΦ = 200 × 6.0 × 10⁻⁴ = 0.12 Wb-turn. If the field is at an angle θ to the normal, use Φ = BA cos θ first, then multiply by N. Flux linkage is crucial for understanding electromagnetic induction, where a changing flux linkage induces an electromotive force (emf). A strong answer earns marks for these points. States that flux linkage is the product of the number of turns N and the magnetic flux Φ through each turn. Calculates magnetic flux Φ using Φ = BA or Φ = BA cos θ before multiplying by N. Uses the correct unit for flux linkage, recognising that N is dimensionless so the unit is the weber (Wb) or weber-turn (Wb-turn). Applies the concept to a coil where each turn cuts the same flux, ensuring N is the total number of turns. A common slip: Multiplying the area by N before calculating flux, which incorrectly changes the area rather than the number of turns. Instead, calculate Φ for one turn first, then multiply by N. Exam tip: Write down the formula NΦ and identify N and Φ separately before substituting values.
See it
Key words
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Flux linkage
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Unit of flux linkage
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Electromagnetic induction
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See every definition
- Flux linkage
- The product of the number of turns N and the magnetic flux Φ through each turn, where N is the number of turns cutting the flux.
- Unit of flux linkage
- The weber-turn (Wb-turn), though often quoted in webers (Wb) because N is dimensionless.
- Electromagnetic induction
- A changing flux linkage induces an electromotive force (emf).
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