Mutual Inductance

M = k × √(L1 × L2)

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Formula

M = k × √(L₁ × L₂)

Description

Mutual inductance M quantifies the magnetic coupling between two inductors. When current changes in one inductor, the changing magnetic flux links to the second inductor and induces a voltage: V₂ = M × dI₁/dt. The coupling coefficient k ranges from 0 (no coupling) to 1 (perfect coupling). Power transformers on ferrite cores achieve k = 0.95-0.99. Air-core coils used for wireless power transfer typically have k = 0.1-0.5 depending on distance and alignment. RFID and NFC systems rely on mutual inductance for energy and data transfer.

Variables

  • M — Mutual inductance (H)
  • k — Coupling coefficient (0 to 1, dimensionless)
  • L₁ — Self-inductance of coil 1 (H)
  • L₂ — Self-inductance of coil 2 (H)

Practical Notes

The total inductance of two coupled inductors in series is L_total = L1 + L2 ± 2M, where + applies when fluxes aid and − when they oppose. For transformers, the leakage inductance is L_leak = L × (1 − k²). Tight coupling (high k) is desired for power transformers to minimize leakage inductance and improve regulation.

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