Mutual Inductance

Two coils nearby: a changing current in one induces an EMF in the other through shared flux. The constant is the mutual inductance M.

Defining relation: ε₂ = −M · dI₁/dt (and symmetrically ε₁ = −M · dI₂/dt).

Unit: henry (H), same as self-inductance.

Two coaxial solenoids (outer = primary, inner = secondary, same area A and length ℓ): M = μ₀·N₁·N₂·A/ℓ.

M depends only on geometry and core material — never on currents.

M is SYMMETRIC: M₁₂ = M₂₁. EMF induced in coil 2 per dI/dt in coil 1 equals EMF induced in coil 1 per dI/dt in coil 2.

Mutual inductance is the basic principle of transformers, induction cookers, and wireless charging.

Coupling coefficient k = M/√(L₁L₂), with 0 ≤ k ≤ 1. Perfect coupling (k=1) means ALL flux links both coils.