Electromagnetic Energy
The electric and magnetic energies are defined as
The time derivatives of these expressions are the electric and magnetic power:
These quantities are related to the resistive and radiative energy, or energy loss, through Poynting’s theorem (
Ref. 1
):
where
V
is the computation domain and
S
is the closed boundary of
V
.
The first term on the right-hand side represents the resistive losses,
which result in heat dissipation in the material. (The current density
J
in this expression is the one appearing in Maxwell–Ampère’s law.)
The second term on the right-hand side of Poynting’s theorem represents the radiative losses
The quantity
S
=
E
×
H
is called the Poynting vector.
Under the assumption that the material is linear and isotropic, it holds that
By interchanging the order of differentiation and integration (justified by the fact that the volume is constant and the assumption that the fields are continuous in time), the result is
The integrand of the left-hand side is the total electromagnetic energy density:
