Energies and powers (magnetic system)
Introduction
This section discusses the stored energy and the power dissipated in a magnetic system.
Electro-magnetic energy: definition (IEC)
The electromagnetic energy is the energy associated with the presence of an electromagnetic field.
Note: In a linear medium the electromagnetic energy is given by the volume integral
where; E, D, H and B are the four vector quantities determining the electromagnetic field.
Starting from the Poynting vector …
It is convenient to define the electromagnetic energy by means of the Poynting vector:
(according to …)
The vector analysis associated with the Maxwell equations then gives:
- The first term describes the energy stored as magnetic energy
- The second term describes the energy dissipated by the Joule effect
- The third term describes the energy stored as electric energy
Stored magnetic energy
To create a magnetic field in a region we must supply some energy, which will be stored as magnetic energy.
The volume density of the stored magnetic energy can be expressed by means of the vector quantities B and H in the relationship:
which in a linear homogeneous isotropic region can be equally written as:
Dissipated power / Power losses by Joule effect
The volume density of the dissipated power (or the volume density of power losses by
Joule effect) is expressed by means of E and J in the relationship: 
In a linear homogeneous isotropic region the
corresponding equality is: 