The conservation of energy is one of the most basic physics laws, for the electromagnetic field, the energy conservation equation is as follows:
In which is the mass density, is the field velocity.
The mass density and energy density have the following relationship:
In which u is the electromagnetic field energy density.
From equation (14.15) and (14.16), we have:
Combine (15.6) and (15.7), thus:
Let us assume that the electromagnetic energy is conserved, therefore, we have:
Thus, we have:
As we know:
Let us define:
From the electromagnetic field energy conservation equation, then we can get the following equation:
Then we can rewrite the electromagnetic field as follows: