EMG-11

Electric energy density

u = ½ ε0 E² in vacuum.

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EnergyMaxwell

Governing equation

u=\tfrac12\varepsilon_0 E^2

where

E: Electric field (V/m)
u: Energy density (J/m³)

Lecture brief

Historical brief

Coulomb, Gauss, Ampère, Faraday and Maxwell (1861–65) unified charge, current and light. The lab computes fields, induction, Poynting flux and the electromagnetic wave in SI. This sheet (EMG-11 — Electric energy density) is the form associated with Maxwell. Working symbols: $E$ $\rightarrow$ $u$ . The work to assemble a field configuration is stored locally as ½ E·D, reducing to ½ ε0 E² in vacuum.

Purpose

Purpose: compute

u

from

E

in Electromagnetism via

u=\tfrac12\varepsilon_0 E^2

u = ½ ε0 E² in vacuum. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E = 10000.000\,\mathrm{V/m}

, the governing relation

u=\tfrac12\varepsilon_0 E^2

yields

u = 4.427e-4\,\mathrm{J/m^{3}}

. Linear vacuum, uniform E. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Electric field E10000 V/m

Outputs

Energy density u0.0004 J/m³

Reading speed

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Narration of this film

Linear vacuum, uniform E.

The work to assemble a field configuration is stored locally as ½ E·D, reducing to ½ ε0 E² in vacuum.

Reading speed

Watch on YouTube