How it works
Faraday's Law: emf = −dΦ/dt = −d/dt ∮ B · dA. The negative sign expresses Lenz's Law — the induced EMF drives a current whose magnetic field opposes the change in flux. In differential (Maxwell) form: ∇×E = −∂B/∂t. Transformer EMF involves a stationary loop with time-varying B (transformer action); motional EMF involves a moving conductor in a static B field, given by emf = ∮(v × B)·dl. For a conductor of length L moving at velocity v perpendicular to field B: emf = BLv. In a transformer, E2 = 4.44·f·N2·Φm (RMS), where Φm is peak flux — this formula must be memorised exactly.
Key points to remember
The EMF formula E = 4.44·f·N·Φm is valid only for sinusoidal flux, and the factor 4.44 is actually the product of √2, π, and 1/√2 combined — knowing its origin prevents sign and factor errors. Lenz's Law is a consequence of energy conservation: if the induced current reinforced the flux change, a perpetual motion machine would result. Faraday's Law ∇×E = −∂B/∂t is the third of Maxwell's equations and couples the electric and magnetic fields, enabling electromagnetic wave propagation. The concept of flux linkage λ = NΦ accounts for a coil with N turns, giving emf = −dλ/dt. Self-inductance L = λ/I = NΦ/I follows directly.
Exam tip
Every university EMT paper asks you to apply Faraday's Law to a coil rotating in a uniform field B — derive the expression for instantaneous EMF e = NBAω·sin(ωt) step by step, starting from Φ = NBA·cos(ωt).