Inductor Energy⚠ unverified
Electrical / Basic · Compute the energy stored in an inductor
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| inductance | inductance | H | 1.0 | Inductance of the inductor |
| current | current | A | 1.0 | Current through the inductor |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | E | J | Stored energy, in joules (J) |
The science & history
Understanding the Parameters
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Inductance $L$ — the magnetic analogue of capacitance; it quantifies the flux linked per amp and the inductor's resistance to changes in current.
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Current $I$ — the through‑current. Energy grows with the square of current, so doubling $I$ quadruples the stored energy — which is why interrupting a large inductor current produces a large voltage spike ($v = L\,di/dt$).
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$E$ — the magnetic‑field energy, in joules; released when the current falls (the basis of boost converters, ignition coils, and flyback supplies).
Derivation (Approaching a Proof)
The instantaneous power delivered to an inductor is $p = v i = L\,\dfrac{di}{dt}\,i$. The energy stored while the current rises from $0$ to $I$ is the time integral of power, which changes variables cleanly to an integral over current:
$$E = \int p\,dt = \int_0^{I} L\,\frac{di}{dt}\,i \,dt = L\int_0^{I} i\,di = \frac{1}{2} L I^2.$$
The factor of $\tfrac12$ arises because the current builds up linearly, so the average is $I/2$. The energy physically resides in the magnetic field, with density $u = \dfrac{B^2}{2\mu}$ integrated over the field volume — the exact dual of the capacitor's $\tfrac12\varepsilon E^2$.
History
The relation follows from Faraday's law of induction (1831) and the concept of self‑inductance developed by Joseph Henry, after whom the SI unit of inductance (the henry) is named. It completes the energy‑storage duality with the capacitor and underpins all magnetic energy‑conversion devices.
Related Concepts: Capacitor Energy, Inductive Reactance, Watt's Law
Notes: Registry calculator basic-inductor-energy (unverified). Assumes a linear (constant‑$L$)
inductor; saturable magnetic cores require integrating $\int i\,d\lambda$ over the flux linkage.