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Magnetic field is a vector field in space, and is a kind of energy whose full quantification requires the knowledge of the vector fields of both magnetic field strength $H$ and flux density $B$ (or other values correlated with them, like magnetisation or polarisation). In vacuum, at each point the $H$ and $B$ vectors are oriented along the same direction and are directly proportional through permeability of free space, but in other media they can be misaligned (especially in non-uniform or anisotropic materials).
The requirement of two quantities is analogous for example to electricity. Both electric voltage $V$ and electric current $I$ are required to fully quantify the effects of electricity, e.g. the amount of transferred energy.3)
The name magnetic flux density and the symbol $B$ are defined by International Bureau of Weights and Measures (BIPM) as a one of the coherent derived physical units.4) Therefore, strictly speaking, other names like induction or B field which can be encountered in everyday technical jargon5) are incorrect.
It is difficult to give a concise definition of such a basic quantity like magnetic field, but various authors give at least a descriptive version. The same applies to magnetic flux density, as well as the other basic quantity - magnetic field strength.
The table below shows some examples of definitions of $H$ given in the literature (exact quotations are shown).
|Publication||Definition of magnetic field||Definition of magnetic field strength $H$||Definition of magnetic flux density $B$|
| Richard M. Bozorth |
|A magnet will attract a piece of iron even though the two are not in contact, and this action-at-a-distance is said to be caused by the magnetic field, or field of force.||The strength of the field of force, the magnetic field strength, or magnetizing force H, may be defined in terms of magnetic poles: one centimeter from a unit pole the field strength is one oersted.||Faraday showed that some of the properties of magnetism may be likened to a flow and conceived endless lines of induction that represent the direction and, by their concentration, the flow at any point. […] The total number of lines crossing a given area at right angles is the flux in that area. The flux per unit ara is the flux density, or magnetic induction, and is represented by the symbol B.|
| David C. Jiles |
Introduction to Magnetism and Magnetic Materials7)
|One of the most fundamental ideas in magnetism is the concept of the magnetic field. When a field is generated in a volume of space it means that there is a change of energy of that volume, and furthermore that there is an energy gradient so that a force is produced which can be detected by the acceleration of an electric charge moving in the field, by the force on a current-carrying conductor, by the torque on a magnetic dipole such as a bar magnet or even by a reorientation of spins of electrons within certain types of atoms.||There are a number of ways in which the magnetic field strength H can be defined. In accordance with the ideas developed here we wish to emphasize the connection between the magnetic field H and the generating electric current. We shall therefore define the unit of magnetic field strength, the ampere per meter, in terms of the generating current. The simplest definition is as follows. The ampere per meter is the field strength produced by an infinitely long solenoid containing n turns per metre of coil and carrying a current of 1/n amperes.||When a magnetic field H has been generated in a medium by a current, in accordance with Ampere's law, the response of the medium is its magnetic induction B, also sometimes called the flux density.|
|Magnetic field, Encyclopaedia Britannica8)||Magnetic field, region in the neighbourhood of a magnetic, electric current, or changing electric field, in which magnetic forces are observable.||The magnetic field H might be thought of as the magnetic field produced by the flow of current in wires […]9)||[…] the magnetic field B [might be thought of] as the total magnetic field including also the contribution made by the magnetic properties of the materials in the field.10)|
| V.A.Bakshi, A.V.Bakshi |
Electromagnetic Field Theory11)
|The region around a magnet within which the influence of the magnet can be experienced is called magnetic field.||The quantitative measure of strongness or weakness of the magnetic field is given by magnetic field intensity or magnetic field strength. The magnetic field intensity at any point in the magnetic field is defined as the force experienced by a unit north pole of one weber strength, placed at that point.||The total magnetic lines of force i.e. magnetic flux crossing a unit area in a plane at right angles to the direction of flux is called magnetic flux density. It is denoted as B and it is a vector quantity.|