Electromagnetic Field Energies in Capacitors and Inductors

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.



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