Mutual Inductance⚠ unverified
Physics / Electromagnetics · Compute the mutual inductance between two coupled coils
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| N1 | N1 | — | 1.0 | Number of turns in the primary coil |
| N2 | N2 | — | 1.0 | Number of turns in the secondary coil |
| Phi21 | Φ21 | Wb | 1.0 | Flux through one turn of the secondary coil due to the primary current |
| I1 | I1 | A | 1.0 | Current through the primary coil |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | M | H | Mutual inductance, in henries (H). Returns 0.0 when ``I1`` is zero |
The science & history
Understanding the Parameters
- $\Phi_{21}$, $N_2$, $I_1$ — define $M$ via flux linkage $\Lambda_2 = N_2\Phi_{21} = M I_1$.
- $N_1$ — appears in symmetric $M = N_1\Phi_{12}/I_2$; not used in the implemented expression.
- $M$ — also $M = k\sqrt{L_1 L_2}$ with coupling coefficient $k\le 1$.
Derivation (Approaching a Proof)
By definition of mutual inductance, $N_2\Phi_{21} = M I_1$. Neumann’s formula gives $M$ from geometry of the two circuits. Faraday: $\mathcal{E}_2 = -M\,dI_1/dt$.
History
Mutual inductance is the transformer coupling parameter; Faraday’s induction experiments are the physical root.
Related Concepts: Self Inductance, Inductance Solenoid, Induced Emf, Transformer Turns Ratio
Notes: Registry calculator mutual-inductance (unverified). Unused input: $N_1$. Confirm
whether $\Phi_{21}$ is per-turn or total flux.