# Magnetic field

In physics, a **magnetic field** (commonly denoted by **H** and sometimes referred to as *magnetic intensity*) describes a magnetic force (a vector) on a magnetic probe (for instance a piece of iron) at every point in space; it is a vector field. In non-relativistic physics, the space in question is the three-dimensional Euclidean space 𝔼^{3}—the infinite world that we live in.

In general **H** is seen as an auxiliary field useful when a magnetizable medium is present. The magnetic flux density **B** is usually seen as the fundamental magnetic field, see the article about **B** for more details about magnetism.

The SI unit of magnetic field strength is ampere⋅turn/meter; a unit that is based on the magnetic field of a solenoid. In the Gaussian system of units |**H**| has the unit oersted, with one oersted being equivalent to (1000/4π)⋅A⋅turn/m.

## [edit] Relation between **H** and **B**

The magnetic field **H** is closely related to the magnetic induction **B** (also a vector field). It is the vector **B** that gives the magnetic force on moving charges (Lorentz force). Historically, the theory of magnetism developed from Coulomb's law, where **H** played a pivotal role and **B** was an auxiliary field, which explains its historic name "magnetic induction". At present the roles have swapped and some authors give **B** the name magnetic field (and do not give a name to **H** other than "auxiliary field").

The relation between **B** and **H** is for the most common case of linear materials^{[1]} in SI units,

where **1** is the 3×3 unit matrix, **χ** the magnetic susceptibility tensor of the magnetizable medium, and μ_{0} the magnetic permeability of the vacuum (also known as magnetic constant).
In Gaussian units the relation is

Most non-ferromagnetic materials are linear and isotropic; in the isotropic case the susceptibility tensor is equal to χ_{m}**1**, and **H** can easily be solved (in SI units)

with the *relative magnetic permeability* μ_{r} = 1 + χ_{m}.

For example, at standard temperature and pressure (STP) air, a mixture of paramagnetic oxygen and diamagnetic nitrogen, is paramagnetic (i.e., has positive χ_{m}), the χ_{m} of air is 4⋅10^{−7}. Argon at STP is diamagnetic with χ_{m} = −1⋅10^{−8}. For most ferromagnetic materials χ_{m} depends on **H**, with a non-linear relation between **H** and **B** and is large (depending on the material) from, say, 50 to 10000 and strongly varying as a function of **H**.

Both magnetic fields, **H** and **B**, are solenoidal (divergence-free, transverse) vector fields because of one of Maxwell's equations

This equation denies the existence of magnetic monopoles (magnetic charges) and hence also of magnetic currents.

## [edit] Note

- ↑ For non-linear materials, or very strong fields, second and higher powers of
**H**appear in the relation between**B**and**H**.