Key Equations
Electromagnetic Induction — AQA A-Level Physics
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Faraday's law
$$\varepsilon = -N\frac{\Delta\Phi}{\Delta t}$$
- Where:
- $ε$ = induced EMF (V)
- $N$ = number of turns
- $ΔΦ$ = change in magnetic flux (Wb)
- $Δt$ = time interval (s)
The minus sign is Lenz's law. For magnitude calculations, use the absolute value.
EMF in a straight moving conductor
$$\varepsilon = BLv$$
- Where:
- $ε$ = induced EMF (V)
- $B$ = magnetic flux density (T)
- $L$ = length of conductor in field (m)
- $v$ = velocity perpendicular to B (m s⁻¹)
Derived from Faraday's law by considering the area swept out: ΔΦ/Δt = B × L × v.
EMF in a rotating coil
$$\varepsilon = BAN\omega\sin(\omega t)$$
- Where:
- $ε$ = instantaneous EMF (V)
- $B$ = magnetic flux density (T)
- $A$ = area of coil (m²)
- $N$ = number of turns
- $ω$ = angular velocity (rad s⁻¹)
- $t$ = time (s)
Obtained by differentiating the flux linkage NΦ = BAN cos(ωt) with respect to time.
Peak EMF (rotating coil)
$$\varepsilon_0 = BAN\omega$$
- Where:
- $ε₀$ = peak (maximum) EMF (V)
- $B$ = magnetic flux density (T)
- $A$ = area of coil (m²)
- $N$ = number of turns
- $ω$ = angular velocity (rad s⁻¹)
Maximum value of ε = BANω sin(ωt) when sin(ωt) = 1. The coil is edge-on to the field at this instant.
Flux linkage (rotating coil)
$$N\Phi = BAN\cos(\omega t)$$
- Where:
- $NΦ$ = flux linkage (Wb turns)
- $B$ = magnetic flux density (T)
- $A$ = area of coil (m²)
- $N$ = number of turns
- $ω$ = angular velocity (rad s⁻¹)
- $t$ = time (s)
Cosine because at t = 0 the coil is face-on to the field (maximum flux linkage). Quarter cycle ahead of the EMF.