Magnetic flux and flux linkage (A-level only) — AQA A-Level Physics

Magnetic flux and flux linkage are fundamental concepts in electromagnetism, quantifying how much magnetic field passes through a given area. Flux (Φ) is defined as the product of magnetic flux density (B), area (A), and the cosine of the angle between the field and the area normal. Flux linkage (NΦ) extends this to coils with multiple turns, and both are essential for understanding electromagnetic induction, transformers, and generators.

These concepts are A-level only and form the basis for Faraday's law and Lenz's law, which describe how changing flux induces an electromotive force (emf). Mastery of flux and flux linkage is crucial for solving problems involving rotating coils, changing magnetic fields, and applications like AC generators and induction cookers. It also links to practical skills such as plotting graphs of flux linkage against time or angle.

• →Magnetic flux Φ is defined as Φ = BA cosθ, where θ is the angle between the magnetic field lines and the normal to the area. Unit: weber (Wb).
• →Flux linkage NΦ is the product of the number of turns N and the flux through one turn. Unit: weber-turns (Wb turns).
• →Flux and flux linkage are maximum when the field is perpendicular to the area (θ = 0°) and zero when parallel (θ = 90°).
• →A change in flux linkage induces an emf according to Faraday's law: ε = -N dΦ/dt.
• →Flux linkage can be changed by altering B, A, N, or the angle θ, which is key to understanding electromagnetic induction.

• States that magnetic flux Φ is the product of magnetic flux density B and the area A when B is perpendicular to A.
• Uses the correct SI units: tesla (T) for B, square metre (m²) for A, and weber (Wb) for Φ.
• Applies Φ = BA cos θ when the field is not normal to the area, identifying θ as the angle between B and the normal to the area.
• Calculates flux correctly for a given uniform field and area, including appropriate significant figures and units.
• Explains that flux is a scalar quantity and that its sign depends on the direction chosen for the area normal.
• 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.
• State that magnetic flux Φ is the product of flux density and the area perpendicular to the field, Φ = BAcosθ, with θ measured between the field direction and the normal to the coil.
• For a coil of N turns, define flux linkage as NΦ and derive NΦ = BANcosθ, identifying B, A, N and θ with correct units: T, m², dimensionless and degrees or radians.
• Explain that in an alternating magnetic field, the flux linkage varies continuously, inducing an e.m.f. proportional to the rate of change of flux linkage.
• Describe Required practical 11: place a search coil in an alternating magnetic field, connect it to an oscilloscope, vary the angle between the coil normal and the field, and record the peak induced voltage.
• Interpret the oscilloscope trace: the amplitude of the induced AC voltage is directly proportional to the maximum flux linkage at that angle.
• Use a data table or graph of induced voltage against angle or against cosθ to identify the relationship between orientation and flux linkage, recognising sources of uncertainty such as imperfect alignment.

• 💡Always check that the field is perpendicular to the area before using Φ = BA; if not, resolve the field using cos θ.
• 💡Write the unit of flux as Wb and show that it is equivalent to T m² to avoid unit errors.
• 💡Sketch the area and mark the normal clearly, especially when the field is at an angle, to avoid using the wrong angle.
• 💡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.
• 💡Sketch the coil, field lines and normal clearly, label θ at the normal, and write NΦ = BANcosθ before substituting values.
• 💡When describing Required practical 11, state the independent variable (angle), dependent variable (oscilloscope voltage amplitude) and control variables such as AC frequency and primary coil current.
• 💡Link any oscilloscope observation to Faraday's law by stating that e.m.f. is proportional to the rate of change of flux linkage.
• 💡Always write the formula Φ = BA cosθ and define θ clearly in your answer to avoid ambiguity.
• 💡When calculating flux linkage, ensure you multiply by the number of turns N and use the correct unit (Wb turns).
• 💡In questions involving rotation, remember that flux linkage varies as cosθ, so sketch a graph to visualise the variation if helpful.

• Using the angle between B and the plane of the area instead of the angle between B and the normal to the area; the correction is to use θ measured from the normal, so Φ = BA cos θ.
• Forgetting to convert area to square metres when dimensions are given in centimetres or millimetres; the correction is to convert all lengths to metres before calculating area.
• Treating flux as a vector and attempting to add fluxes vectorially; the correction is to recognise that flux is a scalar and is added algebraically, taking account of sign conventions.
• Multiplying the area by N before calculating flux, which incorrectly changes the area rather than the number of turns; the correction is to 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; the correction is to 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; the correction is to use Φ = BA cos θ for each turn before multiplying by N.
• Measuring θ from the plane of the coil instead of from the normal to the coil; correct this by defining θ as the angle between the field direction and the normal.
• Treating flux linkage as a vector or adding N and A incorrectly; correct this by using the scalar product NΦ = BANcosθ and checking that the units reduce to weber-turns.
• Assuming the search coil must be rotated continuously to get a trace; correct this by explaining that the alternating field provides the changing flux, so a stationary coil at a fixed angle produces a steady AC trace.
• Students often think flux is a vector, but it is a scalar quantity. The direction of the field is accounted for by the angle θ in the cosine term.
• Many confuse flux density B with flux Φ. B is the magnetic field strength (in tesla), while Φ is the total field through an area (in weber).
• Students sometimes forget to convert area to square metres or to use the correct angle (between field and normal, not field and plane).

1. 1Day 1-2: Revise the definitions of magnetic flux and flux linkage, and learn the formula Φ = BA cosθ and NΦ = NBA cosθ. Practice simple calculations.
2. 2Day 3-4: Work through problems involving changing angle, area, or field strength. Focus on identifying θ correctly.
3. 3Day 5-6: Link flux linkage to Faraday's law and Lenz's law. Solve problems on induced emf.
4. 4Day 7-8: Attempt exam-style questions, including those with rotating coils and graphs of flux linkage against time.
5. 5Day 9-10: Review mistakes, create a summary sheet of key formulas and units, and test yourself with active recall.

• 📋Calculation of flux or flux linkage given B, A, N, and θ. Advice: always write the formula, substitute values with units, and give the answer to an appropriate number of significant figures.
• 📋Explanation of how flux linkage changes when a coil rotates in a magnetic field. Advice: describe the variation of cosθ and hence flux linkage, and relate to induced emf.
• 📋Graph interpretation: sketch or interpret graphs of flux linkage against time or angle. Advice: remember the sinusoidal shape and identify maximum and zero points.
• 📋Practical question: describe an experiment to investigate flux linkage, such as using a search coil and oscilloscope. Advice: include details of how to vary B or θ and measure the induced emf.