Magnetic field



Magnetic field - a region in space, in which magnetic forces are observable. Magnetic forces are mechanical forces acting as a result of magnetic interactions. Magnetic field is always generated around electric current, or more generally by varying electric field. The existence of magnetic field is responsible for magnetism.

Difficulty with definition of magnetic field
It is difficult to give a simple and exact definition of magnetic or electromagnetic field. Progress of science and technology is based on some quantities which so far cannot be defined precisely. For example, the fundamental electric charge q or time t are referred to without defining what they are. Scientists can describe, but cannot explain what exactly is time or electric charge. The assumption is that they exist, have some physical meaning and are measurable within the system of units.

Magnetic field can be produced by electric current, which itself is defined as the flow of electric charge in time. It is empirically known that magnetic field acts with mechanical force on moving charged particles in specific ways described by Maxwell's equations. Therefore, the acting of such specific mechanical force ultimately defines the presence or absence of magnetic field. Or in other words, the detection of magnetic field can be reduced to analysis of such mechanical forces acting on moving electrically charged particles. This is the reason for the opening definition in this article which refers only to magnetic forces (mechanical forces caused by magnetic field). Such definition seems somewhat circular, but as stated above due to the so far inexplicable nature of underlying physics it cannot be made more precise.

Medium in which magnetic and electromagnetic field propagates
Mathematical equations can be used to describe electromagnetic field either as a wave (electromagnetic waves) or as particles (e.g. photons), and both representations were proved to be correct from experimental point of view. If electromagnetic field is a wave then it is unknown in what medium such wave should exist, because it propagates equally well through free space or vacuum.

In all quantum field theories like quantum chromodynamics (QCD) the absence of elementary particles does not necessarily have to mean the lack of any medium. For instance, it is possible to analyse the effect of electromagnetic field on the vacuum in various energy regimes. As a result of such analysis the vacuum is no longer "free space" and theoretically particles can be continuously created and annihilated. Such property can be therefore responsible for allowing the electromagnetic energy to propagate in a seemingly "empty" medium. However, this is only a theoretical treatment and with the current state of science and technology cannot be proved or disproved.

Quantities and units, H and B
Magnetic field is a concept of a kind of energy contained in a given volume of space. This energy can be physically and mathematically described by various means or quantities. There are several magnetic units, which refer to such measurable quantities. However, the two basic ones are magnetic field strength H, and magnetic flux density B (also referred to as magnetic induction).

These two quantities are defined separately in the International System of Units (SI), with H having the unit of ampere per metre (A/m), and B the unit of tesla (T).

There are also magnetisation M and polarisation J, which are related to B and H through other quantities like permeability μ and susceptibility χ.

Magnetic field strength H


A current I produces around itself magnetic field strength H, whose amplitude is independent of the type of a uniform medium (regardless if it is non-magnetic, magnetic, non-linear, etc.)

As an example, in order to produce H = 1 A/m it would be required to have a single circular loop with diameter of 1 m and to pass a current of 1 A through it. Alternatively, an infinitely long, cylindrical conductor with a current of 1 A generates H = 1 A/m around itself in a circle whose circumference is 1 m (which translates to a radius of 1/(2&pi;) &asymp; 0.159 m).

The direction of generated magnetic field is such that it follows the right-hand rule, so that if the thumb points towards the direction of current flow then the fingers show direction of the generated magnetic field strength (see the image on the right).

If the medium is not uniform, or there are several different materials then the field distribution is affected by demagnetising field caused by magnetic poles. These poles become new sources of magnetic field which change distribution of the original applied field.

Magnetic flux density B
Application of H to a given medium causes it to respond with flux density B. The amplitude of B depends both on the applied excitation as well as the material properties. Constant H (e.g. generated by a DC current) produces constant B, whose value depends on the magnetic permeability &mu; of the material.

For free space (vacuum) the B-H relationship is fully linear, with the proportionality factor being the physical constant $$\mu_0 = 4 \cdot \pi \cdot 10^{-7}$$ (H/m):

$$B = \mu_0 \cdot H$$

Permeability of a medium different than free space can be defined as a product of dimensionless number relative to and the value of  itself. Hence, μ = ·. So for instance, relative permeability = 2 means that the given material has permeability twice the value of.

For uniform materials permeability can be expressed as scalar, even though H and 'B are vectors. For anistoropic materials permeability is different in various directions and tensor approach has to be used for more correct representation.

When excitation H varies in time then additional effects are introduced, like for instance eddy currents, which affect the apparent permeability.

Maxwell's equations
Maxwell's equations fully describe mathematically the interrelation between electric and magnetic fields. The early version of these equations were first collated by Scottish physicist James Clerk Maxwell. Subsequently they were simplified and unified so that today four fundamental equations are used, whose physical meaning can be summarised as follows:
 * Gauss's law for electrostatics relates distribution of electric charge to electric field
 * Gauss's law for magnetism states that there are no magnetic monopoles
 * Faraday's law of electromagnetic induction states that electric fields are produced by varying magnetic fields
 * Ampère's circuital law states that magnetic fields are produced by electric currents or changing magnetic fields

The equations can be mathematically written in many ways (e.g. differential or integral form) or different units (e.g. CGS or MKS). They can also be formulated on the basis of more fundamental theory of quantum electrodynamics.