Inductance Solenoid⚠ unverified
Physics / Electromagnetics · Compute the inductance of a solenoid
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| N | N | — | 1.0 | Number of turns in the solenoid |
| A | A | m**2 | 1.0 | Cross-sectional area of the solenoid |
| l | l | m | 1.0 | Length of the solenoid |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | L | H | Inductance, in henries (H). Returns 0.0 when ``l`` is not positive |
The science & history
Understanding the Parameters
- $N$ — $L$ scales as $N^{2}$ (flux linkage $N\Phi$).
- $A$ — larger area → more flux per amp.
- $\ell$ — longer solenoid (fixed $N$) lowers turn density $n = N/\ell$ and lowers $L$.
- $\mu_0$ — free-space permeability (air-core model).
Derivation (Approaching a Proof)
Interior $B = \mu_0 n I = \mu_0 (N/\ell) I$ (infinite-solenoid approximation). Flux per turn $\Phi = B A$; total linkage $\Lambda = N\Phi = \mu_0 N^{2} A I / \ell$. By definition $L = \Lambda/I$:
$$L = \mu_0\frac{N^{2} A}{\ell}.$$
History
Solenoid inductance is the workhorse formula for air-core coils and a starting point for gapped-core inductor design.
Related Concepts: Self Inductance, Mutual Inductance, Magnetizing Inductance, Energy Magnetic Field, Inductor Energy
Notes: Registry calculator inductance-solenoid (unverified). Long-solenoid, air-core idealisation.