How this calculator works
Fields store energy throughout space. In a uniform linear, nondispersive medium, electric energy density is half epsilon E squared and magnetic energy density is B squared divided by twice mu. These components add even when the fields do not form a travelling wave. Enter instantaneous fields for instantaneous density, or RMS fields for time-averaged sinusoidal density. Inverse modes use the selected component, not an unspecified total.
Formula
uE = epsilon E²/2; uB = B²/(2 mu); u = uE + uB. E = sqrt(2uE/epsilon), B = sqrt(2 mu uB).
Worked example
For epsilon = 2 F/m, E = 3 V/m, mu = 4 H/m and B = 4 T, uE = 9 J/m³ and uB = 2 J/m³, giving 11 J/m³ in total.
Frequently asked questions
Must electric and magnetic densities be equal?
Only for a plane travelling electromagnetic wave in a simple lossless medium. Static fields can have either component alone.
Can I use peak sinusoidal fields for average density?
Peak inputs give peak component density. Use RMS fields to obtain time-averaged component densities.
Does this cover ferromagnetic hysteresis?
No. Nonlinear, dispersive or hysteretic media require constitutive relations and an energy integral.