Energy in Inductor

Stored magnetic energy from inductance and current

Calculation
Quick Introduction

An inductor stores energy in its magnetic field. Stored energy increases linearly with inductance and quadratically with current, so current peaks strongly impact energy levels.

The formula \(W=\frac{1}{2}LI^2\) is central to chokes, switched-mode power stages, and pulsed magnetic systems.

Sizing schema:
1) derive target energy from application
2) match L and I range against saturation/losses
3) validate magnetic, thermal, and dynamic margins
Formulas (MathJax)
\[W=\frac{1}{2}LI^2\]
\[L=\frac{2W}{I^2}\]
\[I=\sqrt{\frac{2W}{L}}\]
\[P=\frac{dW}{dt}\quad\text{(for dynamic analysis)}\]
Symbol Legend
  • \(W\): stored energy [J]
  • \(L\): inductance [H]
  • \(I\): inductor current [A]
  • \(P\): instantaneous power change [W]


Examples
Example 1: \(L=22mH\), \(I=3.5A\) ⇒ \(W=0.13475J\) (\(134.75mJ\)).
Example 2: \(W=0.5J\), \(I=5A\) ⇒ \(L=40mH\).
Example 3: \(W=0.2J\), \(L=10mH\) ⇒ \(I\approx6.325A\).
Detailed Documentation & Summary

Magnetic energy storage in inductors is a core mechanism of modern power electronics. In buck, boost, and flyback topologies, energy is cyclically stored in the magnetic field and transferred to the load. The achievable energy level strongly influences core, winding, and switching strategy.

Real-world design extends beyond the ideal equation: core losses, copper losses, temperature rise, saturation limits, leakage inductance, and tolerance spread must be considered. The quadratic current dependency means peak currents can quickly push operation toward saturation.

Robust engineering typically compares computed energy against allowable operating margins with safety factors. This calculator provides fast first-order predesign support for energy-storage inductors and pulsed magnetic applications.

Summary
  • Computes energy, inductance, or current in three modes
  • Highlights the quadratic current effect on stored energy
  • Useful for early-stage inductor and magnetic energy storage sizing

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