Energy Density of Fields Calculator

Energy density is the amount of energy stored per unit volume of a substance or field. For electromagnetic fields, it represents how much energy is contained within a given volume of space occupied by electric and magnetic fields. A higher energy density means more energy is packed into the same volume.

The energy density of an electromagnetic field in a vacuum is given by u = (ε₀/2)E² + B²/(2μ₀), where ε₀ is the permittivity of free space (8.854 × 10⁻¹² F/m), E is the electric field strength in V/m, B is the magnetic flux density in Tesla, and μ₀ is the permeability of free space (4π × 10⁻⁷ H/m).

For a pure electric field of 50 N/C (V/m) with no magnetic field, u = (ε₀/2) × E² = (8.854 × 10⁻¹²/2) × 50² ≈ 1.107 × 10⁻⁸ J/m³. This is the energy stored in the electric field per cubic metre.

The permittivity of free space (ε₀) is approximately 8.854 × 10⁻¹² F/m, and the permeability of free space (μ₀) is 4π × 10⁻⁷ H/m (approximately 1.2566 × 10⁻⁶ H/m). These are fundamental physical constants that define how electric and magnetic fields propagate in a vacuum.

Electromagnetic field energy density is important in the study of light and electromagnetic waves, capacitor and inductor design, plasma physics, and MRI machines. In electromagnetic waves such as light, energy is shared equally between the electric and magnetic field components.

Classical electromagnetism does not impose an upper limit on field energy density. However, in practice, material breakdown limits (such as dielectric breakdown in capacitors) and quantum electrodynamic effects set practical boundaries. For extremely intense fields, non-linear effects and pair production begin to play a role.

In a propagating electromagnetic wave in vacuum, the energy is carried equally by the electric and magnetic field components — u_E equals u_B. The total energy density fluctuates with the wave, and the time-averaged total energy density is related to the intensity (power per unit area) of the wave by I = u_avg × c, where c is the speed of light.

The result is given in joules per cubic metre (J/m³), which is the SI unit for volumetric energy density. This tells you how many joules of energy are stored in every cubic metre of space occupied by the electromagnetic field.