Magnetic Flux & Flux Linkage

How magnetic field, area, and coil turns combine to create flux linkage — the key to electromagnetic induction.

Spec Points Covered
  • Define magnetic fluxThe product of magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³. and the area perpendicular to the field. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area. (Wb). and state its unit.
  • Apply $\Phi = BA \cos \theta$ to calculate flux through a coil at an angle to the field.
  • Define flux linkageThe product of magnetic flux and the number of turns of a coil. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area.-turns (Wb turns). and explain why the number of turns matters.
  • Identify the angle θ correctly as the angle between the field and the normal to the coil.
  • Describe four ways to change the flux linkageThe product of magnetic flux and the number of turns of a coil. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area.-turns (Wb turns). through a coil.
  • Sketch and interpret graphs of flux linkageThe product of magnetic flux and the number of turns of a coil. Measured in weber-turns (Wb turns). and induced EMFElectromotive force. The energy transferred per unit charge by a source in driving charge around a complete circuit. Measured in volts (V). against angle for a rotating coil.
Notes
01 Magnetic flux measures the total field passing through an area Magnetic flux (Φ) 3.7.5.3 → 02 One weber is one tesla through one square metre The weber (Wb) 3.7.5.3 → 03 The angle θ is between the field and the normal — not the coil face $\Phi = BA \cos \theta$ 3.7.5.3 → 04 Flux linkage multiplies flux by the number of turns Flux linkage (NΦ) 3.7.5.3 → 05 Four ways to change the flux linkage through a coil 3.7.5.3 → 06 A rotating coil produces sinusoidal flux linkage $N\Phi = BAN \cos(\omega t)$ 3.7.5.3 → 07 Worked example: pulling it all together 3.7.5.3 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Magnetic flux (perpendicular field)
$$\Phi = BA$$
  • Where:
    • $Φ$ = magnetic flux (Wb)
    • $B$ = magnetic flux density (T)
    • $A$ = cross-sectional area perpendicular to the field (m²)
Special case when field is perpendicular to area (θ = 0°). Given on the AQA data sheet.
Magnetic flux (at angle θ)
$$\Phi = BA \cos \theta$$
  • Where:
    • $Φ$ = magnetic flux (Wb)
    • $B$ = magnetic flux density (T)
    • $A$ = area of coil (m²)
    • $θ$ = angle between field and normal to coil (°)
General form. θ is measured from the normal, not the coil face. Reduces to Φ = BA when θ = 0°.
Flux linkage
$$N\Phi = BAN \cos \theta$$
  • Where:
    • $NΦ$ = flux linkage (Wb turns)
    • $B$ = magnetic flux density (T)
    • $A$ = area of each turn (m²)
    • $N$ = number of turns
    • $θ$ = angle between field and normal to coil (°)
Flux linkage = N × flux. This is what appears in Faraday's law. When θ = 0°, NΦ = BAN.
Flux linkage for a rotating coil
$$N\Phi = BAN \cos(\omega t)$$
  • Where:
    • $NΦ$ = flux linkage at time t (Wb turns)
    • $B$ = magnetic flux density (T)
    • $A$ = area of coil (m²)
    • $N$ = number of turns
    • $ω$ = angular speed (rad s⁻¹)
    • $t$ = time (s)
For a coil rotating at constant ω, θ = ωt. Produces a cosine wave. EMF (from Faraday's law) is BANω sin(ωt), which is 90° out of phase.
Q Retrieval Practice All 10 Questions →
Q1. Define magnetic fluxThe product of magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³. and the area perpendicular to the field. Measured in weber (Wb)..
  • The product of magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³.The strength of a magnetic field. The force per unit length per unit currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). on a currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).-carrying conductor perpendicular to the field. Measured in teslaThe SI unit of magnetic flux density. One tesla is the flux density when a force of 1 N acts on a 1 m conductor carrying 1 A perpendicular to the field. (T). and the cross-sectional area perpendicular to the field. Φ = BA.
  • Unit: weber (Wb).
Q2. State the unit of magnetic fluxThe product of magnetic flux density and the area perpendicular to the field. Measured in weber (Wb). and express it in terms of base SI units of flux density and area.
The weber (Wb). 1 Wb = 1 T m².
Q3. Write the equation for magnetic flux through a coil at angle θ to the field, and define θ.
Φ = BA cos θ, where θ is the angle between the magnetic field direction and the normal to the plane of the coil.
Q4. When is the flux through a coil (a) maximum and (b) zero?
(a) Maximum when θ = 0° — the field is perpendicular to the coil face (normal parallel to field). Φ = BA. (b) Zero when θ = 90° — the field is parallel to the coil face (normal perpendicular to field). cos 90° = 0.
Q5. Define flux linkage.
  • The product of the number of turns on a coil and the magnetic flux through each turn.
  • NΦ = BAN cos θ.
  • Unit: Wb turns.