Self-Inductance Calculator
Enter coil turns, flux per turn and current to compute self-inductance L=N·Φ/I. N=100, Φ=0.0001 Wb, I=0.5 A → L≈0.02 H.
Input Data
Results
At a glance:Self-inductance (henry, 1832): when a coil's current changes, the resulting change in its own magnetic flux induces a back-EMF in the coil. The coefficient is defined as L=N·Φ/I, where N is the number of turns, Φ is the flux per turn (Wb), I is the current (A), unit henry (H=Wb/A). By Faraday's law the back-EMF is ε=−L·dI/dt, the minus sign from Lenz's law (opposing the current change). History: Henry discovered self-inductance in the 1830s; Faraday proposed induction in 1831. Self-inductance depends on coil geometry (area A, length ℓ, turns N) and core permeability μ: solenoid L=μN²A/ℓ. Examples: N=100, Φ=1e-4 Wb, I=0.5 A → L=100×1e-4/0.5=0.02 H=20 mH; air-core solenoid 1000 turns, A=1 cm², ℓ=10 cm → L≈1.26 mH. Applications: (1) inductors — filtering, resonant circuits; (2) transformers — primary self-inductance sets magnetising current; (3) relays — coil inductance affects switching time; (4) induction cookers — heating coil; (5) ignition coils — high-voltage engine spark.
Formula
Definition: L = N·Φ/I (H = Wb/A)
Back-EMF: ε = −L·(dI/dt) (Lenz's law)
Solenoid: L = μ·N²·A/ℓ (μ = core permeability)
Total flux linkage: NΦ = L·I (Wb·turn)
Magnetic energy: U = L·I²/2 (J)
$$L = \frac{N\Phi}{I}, \quad \varepsilon = -L\frac{dI}{dt}, \quad L_{\text{solenoid}} = \frac{\mu N^2 A}{\ell}$$How to Use
- Enter coil turns N, flux per turn Φ (Wb) and current I (A).
- The tool computes L=N·Φ/I (H and mH) and total flux linkage NΦ.
- Common: N=100, Φ=1e-4, I=0.5 → L=0.02 H=20 mH; N=500, Φ=2e-4, I=1 → L=0.1 H.
Case Studies
Basic coil
N=100 turns, Φ=1e-4 Wb, I=0.5 A.
L = N·Φ/I = 100 × 1e-4 / 0.5 = 0.02 H.
= 20 mH; total flux linkage NΦ = 0.01 Wb·turn.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.