Calculate magnetic flux and flux linkage
Define magnetic flux through a surface, use Φ = BA and relate flux through one turn to total flux linkage.
Section 20 · Magnetic fields
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 20. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use current, charge, force, velocity, vectors, area and SI units; distinguish conventional current from electron flow.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
For a uniform field perpendicular to a flat surface, what is the magnetic flux?
What you will learn
- Define flux using field strength and area perpendicular to the field
- Use Φ = BA
- Calculate flux linkage for a coil of N turns
Flux counts field through a perpendicular area
Magnetic flux Φ through a surface is the product of magnetic flux density B and the cross-sectional area perpendicular to the field. For a uniform field normal to a flat area, Φ = BA. Its unit is the weber (Wb), with 1 Wb = 1 T m².
If a surface is tilted, only its projected area perpendicular to B contributes; equivalently Φ = BA cos θ when θ is the angle between B and the surface normal. Use the perpendicular-area wording to avoid confusing this angle with the plane of the surface.
A coil links the flux through its turns
For a coil of N turns with the same flux Φ through each turn, the magnetic flux linkage is NΦ. Its unit is Wb-turn. A change in flux linkage is what matters for electromagnetic induction in a coil.
When calculating flux, use the component of B normal to the area and convert area to square metres. A field parallel to the plane has zero perpendicular component and therefore zero flux through that ideal surface.
Pause and explain
A 100-turn coil has flux 0.004 Wb through each turn. What is its flux linkage?
Worked example
A 0.020 m² coil is in a 0.50 T uniform field perpendicular to its plane. Find the flux through one turn and the linkage for 200 turns.
Show the worked solution
- The field is normal to the plane, so the full area is perpendicular to B.
- Use Φ = BA.
- Multiply by the number of turns for flux linkage.
Answer Φ = 0.50 × 0.020 = 0.010 Wb; linkage = 200 × 0.010 = 2.0 Wb-turn.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A 0.030 m² surface is in a 0.40 T field normal to its plane. Calculate Φ.
Give me a hint
Use Φ = BA with SI area.
Compare my reasoning
- The field is normal, so A⊥ = 0.030 m².
- Φ = 0.40 × 0.030.
- State webers.
Φ = 0.012 Wb.
Look for these in your work
- Perpendicular area identified
- Product calculated
- Weber unit stated
A 250-turn coil has 0.0060 Wb through each turn. Find its flux linkage.
Give me a hint
Multiply the flux per turn by N.
Compare my reasoning
- NΦ = 250 × 0.0060.
- NΦ = 1.5.
- State Wb-turn.
Flux linkage = 1.5 Wb-turn.
Look for these in your work
- Turn count applied
- Product calculated
- Linkage unit stated
A uniform field lies parallel to the plane of a flat loop. What is the magnetic flux through the loop, and why?
Give me a hint
Use the area component perpendicular to B.
Compare my reasoning
- If B is parallel to the plane, the area normal is perpendicular to B.
- The projected area perpendicular to B is zero.
- Thus Φ = BA⊥ = 0.
The flux is zero because no area component is perpendicular to the field.
Look for these in your work
- Surface orientation interpreted
- Perpendicular area found
- Flux conclusion stated
Common mistakes
- Using area in cm² without conversion
- Using the angle to the plane instead of the surface normal
- Confusing flux Φ with flux linkage NΦ
- Multiplying by turns when asked for flux through one turn
What can you explain now?
For a uniform field perpendicular to a flat surface, what is the magnetic flux?
Compare with the explanation
Φ = BA
Use field strength times the area perpendicular to B.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do surface orientation and number of turns distinguish flux from flux linkage?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.