A capacitor with square plates of width 'a separated by a distance 'd' with a filler of dielectric constant (relative permittivity) 'k' has a capacitance given by 'C'. Typical values are in the range of picofarads (pF). A voltage 'V' can hold positive and negative charges 'q' on the plates of the capacitor while producing an internal electric field 'E'. Assuming idealized geometry, the energy of a charged capacitor equals (CV^2)/2. This energy can be considered to be stored in the electric field.
Next consider an air-core inductor, again assuming idealized geometry. The relative permeability 'km' is approximated as 1. The inductance of a helical conducting coil, as shown in the graphic, is then given by 'L', where is the number of turns. Typical values can be in the range of microhenries. Considered as a solenoid, the inductor produces a magnetic field 'B', when carrying a current 'I'. The energy of the inductor equals '(LI^2)/2', 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.
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