# 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: