Energy Electric Field⚠ unverified
Physics / Electromagnetics · Compute the energy stored in an electric field over a volume
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| E | E | V/m | 1.0 | Electric field magnitude |
| V | V | m**3 | 1.0 | Volume occupied by the field |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | U | J | Stored electric energy, in joules (J) |
The science & history
Understanding the Parameters
- $E$ — stronger field stores more energy ($E^{2}$).
- $V$ — geometric volume of the field region (e.g. gap volume of a parallel-plate capacitor).
- $U$ — equals $\tfrac12 C V_{\mathrm{volt}}^{2}$ for a capacitor with the same field energy (Capacitor Energy).
Derivation (Approaching a Proof)
Capacitor energy $U = \tfrac12 C\Phi^{2}$ with $C = \varepsilon_0 A/d$ and $\Phi = E d$ gives $U = \tfrac12\varepsilon_0 E^{2} (A d)$. Identifying volume $V = A d$ yields $U = \tfrac12\varepsilon_0 E^{2} V$. Locally, Maxwell stress / field Lagrangian density gives the same $u_E = \tfrac12\varepsilon_0 E^{2}$ in free space.
History
Field energy is central to Maxwell’s theory and to capacitor/RF design energy budgets.
Related Concepts: Energy Magnetic Field, Capacitor Energy, Parallel-Plate Capacitance, Electric Field point charge
Notes: Registry calculator energy-electric-field (unverified). Uniform field, free space
$\varepsilon_0$ in the formula as written.