Magnetic Field Energy Density

Formula

Description

The energy stored per unit volume in a magnetic field grows with the square of the flux density. This is where an inductor or transformer actually stores its energy—in the field, mostly in the air gap of a gapped core because the low-permeability gap supports a high field. It sets the size of magnetic energy-storage components.

Variables

• u — Magnetic energy density (J/m³)
• B — Magnetic flux density (T)
• µ₀ = 4π×10⁻⁷ H/m —

Practical Notes

In a magnetic material replace µ₀ with µ₀·µr. Because high-µ core material supports little field for a given flux, most inductor energy is stored in the gap—this is why energy-storage inductors are gapped.