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 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:
