Key Equations
Magnetic Flux & Flux Linkage — AQA A-Level Physics
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.