A capacitor with square plates of width

separated by a distance

with a filler of dielectric constant (relative permittivity)

has a capacitance given by

. Typical values are in the range of picofarads (pF). A voltage

can hold positive and negative charges

on the plates of the capacitor while producing an internal electric field

. Assuming idealized geometry, the energy of a charged capacitor equals

. This energy can be considered to be stored in the electric field, which implies a corresponding energy density

(with

).

Next consider an air-core inductor, again assuming idealized geometry. The relative permeability

is approximated as 1. The inductance of a helical conducting coil, as shown in the graphic, is then given by

, where

is the number of turns. Typical values can be in the range of microhenries (

H). Considered as a solenoid, the inductor produces a magnetic field

, when carrying a current

. The energy of the inductor equals

, which implies a magnetic-field energy density

.

Combining the above results gives the well-known formula for the energy density of an electromagnetic field in a vacuum:

. This is valid for electric and magnetic fields from any sources, notably for electromagnetic radiation.