Inductor Energy Storage

How an inductor stores energy

An inductor is a coil of wire — sometimes around an air core, more often around a ferromagnetic core that concentrates the field. When current flows through the wire it produces a magnetic field threading the coil's interior. That field stores energy in the same way a stretched spring stores it: invisibly, but recoverably.

The defining law is Faraday's. A changing current produces a changing magnetic flux, and that changing flux induces an opposing voltage:

V = L · (di/dt)

L (henries) is the proportionality constant — geometry-and-material in one number. For a solenoid of N turns, area A, length ℓ, with core relative permeability µᵣ:

L = µ₀ · µᵣ · N² · A / ℓ

The energy stored is the integral of v·i over time. Substitute v = L·di/dt:

W = ∫₀ᵗ v·i dt = ∫₀ᴵ L·i di = ½·L·I²

That energy lives in the magnetic field — specifically in the volume of space where B is non-zero, with energy density u = B²/(2µ). For a ferrite core operating at B = 0.25 T (just under saturation), u ≈ 25 kJ/m³ — about a thousand times what a high-voltage capacitor manages on a volume basis, but a thousand times worse than a battery.

Worked example: 100 µH carrying 5 A

A typical buck-converter inductor:

L = 100 µH = 100×10⁻⁶ H
I = 5 A
W = ½ · L · I²
  = 0.5 · 100×10⁻⁶ · 25
  = 1.25 × 10⁻³ J = 1.25 mJ

If the converter switches at 500 kHz, that 1.25 mJ is delivered to the load every cycle, equivalent to 1.25 mJ × 500,000 = 625 W of throughput. The inductor's job is not to store energy long-term but to bridge the on-time and off-time of the switch with current continuity.

Now flip the question. The same inductor sits in a flyback. The MOSFET interrupts 5 A in 100 ns:

V_spike = L · di/dt
        = 100×10⁻⁶ · (5 / 100×10⁻⁹)
        = 100×10⁻⁶ · 5×10⁷
        = 5000 V

5 kV across an unprotected MOSFET avalanche-clamps it instantly. The flyback diode or RCD snubber must conduct that current to a sink, dissipating ½LI² = 1.25 mJ as heat each cycle.

RL current curve

An inductor in series with a resistor R and a step voltage V₀ ramps current along an exponential curve, mirroring the capacitor's voltage curve:

i(t) = (V₀/R) · (1 − e^(-t/τ))     where τ = L/R

I/I_max
 1.0 ┤                          ╶─────── 100%
 0.99┤                    ╶─────              ← 5τ
     │              ╶─────
 0.86┤        ╶─────                          ← 2τ
     │     ╶─
 0.63┤   ╶─                                   ← 1τ
     │  ╱
 0.0 ┤─╱
     └──────────────────────────────── t/τ
     0    1    2    3    4    5    6

An RL filter has the dual behavior of an RC filter: voltage swaps for current, capacitance for inductance. The same 63.2% / 5τ engineering shorthand applies.

Inductor families compared

Core type	Permeability µᵣ	Q at 100 kHz	B_sat	Loss profile	Typical role
Air core	1	200–500	n/a (no sat)	Pure copper loss	RF tank circuits, antennas
Ferrite (MnZn)	2000–5000	50–150	0.30 T	Hysteresis dominant 100 kHz–1 MHz	SMPS chokes, EMI suppression
Ferrite (NiZn)	10–1500	40–100	0.20 T	Low loss above 1 MHz	RF transformers, baluns
Powdered iron	5–100	30–80	1.0–1.5 T	Soft saturation, distributed gap	DC-bias-tolerant chokes
Amorphous (Metglas)	15,000–100,000	100–300	1.5 T	Very low core loss	Common-mode chokes, EV inverters
Laminated silicon steel	4000–10,000	5–30	1.7–2.0 T	Eddy-current dominant >1 kHz	50/60 Hz transformers, large chokes

The selection driver: pick the core whose saturation flux you can stay below at peak current, whose loss profile sits below your operating frequency, and whose permeability gives the L you need at acceptable copper turns. Ferrite dominates the 50 kHz–1 MHz switching converter band; powdered iron handles DC-bias-heavy chokes; amorphous wins where lowest core loss matters at any cost.

Real-world numbers

• Transmission-line series reactor: 100s of µH per phase, carrying 1000s of amps to limit fault current. Energy in a 500 µH, 5000 A reactor is 6250 J — equivalent to a kilo of TNT in a single coil.
• Smartphone buck inductor: 1 µH wirewound shielded chip, 1.5 A saturation, footprint 2 mm × 2 mm × 1 mm. Switches at 6 MHz to deliver 1 W per output rail.
• EV traction motor stator: tens of mH effective at the controller switching frequency, 200 A peak. Field energy per PWM cycle is hundreds of joules, converted directly into shaft torque.
• Tokamak central solenoid: 5–10 H, 40 kA. Field energy 8 GJ — a tonne of high explosive in a magnet that costs more than most office buildings.
• RF coil for a 1 MHz tank: 25 µH air-core, Q ≈ 250. Drives ½LI² = 12.5 µJ at 1 A peak — develops 250× source voltage at the resonant cap.

Variants

• Iron-core vs gapped-core. Putting an air gap in a ferromagnetic core lowers µ_eff and the inductance per turn, but pushes saturation flux higher relative to ampere-turns — letting you carry far more DC current before B reaches B_sat. Buck inductors and flyback transformers always have a gap.
• Single-layer vs multi-layer windings. Single-layer (air-core RF) gives lowest interwinding capacitance and highest self-resonant frequency. Multi-layer (low-frequency choke) packs more turns and inductance into the same volume but rings at lower frequencies.
• Common-mode vs differential-mode. A common-mode choke has both lines wound in the same direction on a single core: differential current produces canceling fields and sees ~zero impedance, while common-mode current sees the full µ_r·N². EMI filters need both flavors.
• Coupled inductors (transformers). Two windings sharing a core couple energy from one circuit to another. Coupling coefficient k = M/√(L₁L₂), where M is mutual inductance. Tightly coupled (k → 1) is a transformer; loosely coupled (k ≈ 0.5) is a flyback or planar resonant converter.
• Variable inductors. Slug-tuned (movable ferrite core), saturable reactors (DC-controlled gain), or MEMS variable inductors. Used historically in radio tuning; now mostly displaced by varactor-tuned LC tanks.

Failure modes

• Saturation when DC bias exceeds rating. Once core flux reaches B_sat, inductance collapses. In a buck converter the slope di/dt = V/L blows up, peak current rockets past the MOSFET's SOA, and you smell magic smoke. Always check the I_sat curve, derate 30% for temperature.
• Open winding from thermal cycling. Magnet wire fatigues at stress points where the lead enters the core. The inductor goes open, breaking the circuit silently.
• Unprotected switch interruption. Open a switch in a current-carrying inductor without a freewheel path and V = L·di/dt rings to thousands of volts, arcing or destroying the switch. Every relay coil needs a flyback diode; every MOSFET driving an inductive load needs avalanche rating or an external clamp.
• Audible coil whine. Magnetostriction vibrates the core at the switching frequency. Drift into the 1–20 kHz audible band under light load and the inductor sings. Fixed-frequency control or potting compound fix it.
• Self-resonance. Interwinding capacitance forms a parasitic LC that resonates at SRF. Above SRF the part looks capacitive, not inductive. A 1 mH multilayer choke might have SRF of 200 kHz — useless above that.
• Core loss exceeding heat budget. Hysteresis and eddy losses scale with B²·f^n. High B and f raise temperature, µᵣ falls toward the Curie point (200–250 °C for MnZn), and the cycle runs away thermally.

Where the energy storage matters

• Switch-mode power supplies — the inductor bridges on/off cycles, transferring ½LI² each pulse.
• Boost converters — energy is built up at low voltage, dumped at higher voltage when the switch opens.
• Spark plugs and Tesla coils — abrupt interruption of primary current dumps coupled energy as a kilovolt arc.
• Pulsed power and railguns — capacitor banks discharge into low-resistance rails forming an inductive loop, briefly storing megajoules in field.
• Magnetic launch (maglev, mass drivers) — coils build field energy that propels conducting projectiles by Lenz reaction.
• Wireless charging — primary inductor stores ½LI² each cycle; resonant coupling siphons that energy through the coupled secondary.