Fields store energy. A capacitor’s energy is in the electric field between its plates; an inductor’s in its magnetic field. In an electromagnetic wave the energy is shared equally between the two.
How to use the Energy Density of Electric and Magnetic Fields Calculator
- Electric field E
- Magnetic field B
- Relative permittivity ε_r
- Relative permeability μ_r
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the electric field and magnetic field and the medium properties.
Inputs explained
| Field | What to enter |
|---|---|
| Electric field E | Units: V/m, kV/m, V/cm, MV/m, N/C |
| Magnetic field B | Units: T, mT, µT, G, nT |
| Relative permittivity ε_r | A number |
| Relative permeability μ_r | A number |
What each result means
- Electric energy density = 0.5×8.8541878128e-12×[Relative permittivity ε_r]×[Electric field E]^2
- Magnetic energy density = [Magnetic field B]^2÷(2×1.25663706212e-06×[Relative permeability μ_r])
- Total energy density = [Electric energy density] + [Magnetic energy density]
Example values
How the main result changes when Electric field E changes and everything else stays at the example values above:
| Electric field E (V/m) | Total energy density (J/m³) |
|---|---|
| 500,000 | 397,888.4643 |
| 750,000 | 397,889.8478 |
| 1,000,000 | 397,891.7846 |
| 1,250,000 | 397,894.2748 |
| 1,500,000 | 397,897.3185 |
| 2,000,000 | 397,905.0659 |
Formula
u = ½·ε₀·ε_r·E² + B²/(2·μ₀·μ_r)
Worked example
Inputs — Electric field E: 1,000,000 V/m; Magnetic field B: 1 T; Relative permittivity ε_r: 1; Relative permeability μ_r: 1.
Results — Electric energy density = 4.427094 J/m³; Magnetic energy density = 397,887.357513 J/m³; Total energy density = 397,891.784607 J/m³.
Key terms
- Energy density
- Energy per unit volume.
Frequently asked questions
Why do magnetic fields store so much energy?
μ₀ is tiny, so even 1 T stores about 400 kJ/m³.
What about an EM wave?
Electric and magnetic energy densities are equal.
Is energy density the same as pressure?
They have the same units (J/m³ = Pa).
How is energy stored in a capacitor?
In the electric field between the plates.