Faraday's law

From his observations Faraday concluded that:

1. A relative motion between a conductor and a magnetic field that changes the magnetic flux linked with the conductor induces an emf in it. Its direction depends on the direction of the relative motion.
2. The magnitude of the induced emf is proportional to the rate of change of the magnetic flux (the rate at which the conductor cuts the flux lines): emf ∝ ΔΦ_m / Δt.
3. It is also proportional to the number of turns N of the coil that link the flux (each turn contributes the same emf, and they are in series): emf ∝ N.

Combining these:

emf = − N ΔΦ_m / Δt

Φ_m = B A cos(angle) is the magnetic flux (weber, Wb = T·m²); Δt in seconds. The flux is the product of the field and the area that is perpendicular to it, so the flux can change in three ways: B changes, the area A changes, or the angle between the coil and the field changes. The factors that increase the induced emf: more turns, a stronger magnet (or field), a faster motion (smaller Δt), an iron core.

• Practical check of Faraday's law (the usual essay): connect a coil of N turns to a galvanometer and move a magnet through it.
• (i) Move the magnet slowly, then quickly: the quicker motion (greater rate of change of flux) gives a larger deflection.
• (ii) Repeat with coils of different numbers of turns, keeping the speed constant: the deflection is proportional to N.
• (iii) Use a stronger magnet: the deflection increases.

Example 1a. A coil of 120 turns and area 0.01 m² has the field through it (perpendicular to the coil) fall from 0.5 T to 0.1 T in 0.04 s. ΔΦ = (0.5 − 0.1) × 0.01 = 4×10⁻³ Wb. |emf| = 120 × 4×10⁻³ / 0.04 = 12 V. If the circuit resistance is 24 Ω the induced current is 12 / 24 = 0.5 A.

Example 1b. A coil of 60 turns and area 0.05 m² is turned in a 0.4 T field from the position where its plane is perpendicular to the field to the position where it is parallel, in 0.1 s. The flux falls from BA = 0.02 Wb to zero, so |emf| = 60 × 0.02 / 0.1 = 12 V.