In physics, a magnetic field is a vector field that permeates space and which can exert a magnetic force on moving electric charges and on magnetic dipoles (such as permanent magnets). When placed in a magnetic field, magnetic dipoles tend to align their axes to be parallel with the magnetic field, as can be seen when iron filings are in the presence of a magnet (see picture at right). In addition, a changing magnetic field can induce an electric field. Magnetic fields surround and are created by electric currents, magnetic dipoles, and changing electric fields. Magnetic fields also have their own energy, with an energy density proportional to the square of the field intensity.

There are some notable specific instances of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. For magnetic fields created by changing electric fields, see electromagnetism.

The electric field and the magnetic field are tightly interlinked, in two senses. First, changes in either of these fields can cause ("induce") changes in the other, according to Maxwell's equations. Second, according to Einstein's theory of special relativity, a magnetic force in one inertial frame of reference may be an electric force in another, or vice-versa (see relativistic electromagnetism for examples). Together, these two fields make up the electromagnetic field, which is best known for underlying light and other electromagnetic waves.

B and H

There are two quantities that physicists may refer to as the magnetic field, notated $\backslash mathbf\{H\}$ and $\backslash mathbf\{B\}$. Although the term "magnetic field" was historically reserved for $\backslash mathbf\{H\}$, with $\backslash mathbf\{B\}$ being termed the "magnetic induction", $\backslash mathbf\{B\}$ is now understood to be the more fundamental entity. Modern writers vary in their usage of $\backslash mathbf\{B\}$ as the magnetic field. See: The standard graduate textbook by J. D. Jackson "Classical Electrodynamics" specifically follows the historical tradition, specifically, "In the presence of magnetic materials the dipole tends to align itself in a certain direction. That direction is by definition the direction of the magnetic flux density, denoted by $\backslash mathbf\{B\}$, provided the dipole is sufficiently small and weak that it does not perturb the existing field". Similarly, in Section 5 of Jackson, $\backslash mathbf\{H\}$ is referred to as the magnetic field. Hence, Edward Purcell, in Electricity and Magnetism, McGraw-Hill, 1963, writes, Even some modern writers who treat $\backslash mathbf\{B\}$ as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field," not "magnetic induction." You will seldom hear a geophysicist refer to the earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling $\backslash mathbf\{B\}$ the magnetic field. As for $\backslash mathbf\{H\}$, although other names have been invented for it, we shall call it "the field$\backslash mathbf\{H\}$" or even "the magnetic field $\backslash mathbf\{H\}$". This article will follow the convention of referring to $\backslash mathbf\{B\}$ as the magnetic field and will discuss the more fundamental $\backslash mathbf\{B\}$ magnetic field, before treating the $\backslash mathbf\{H\}$ field. But the reader is cautioned that the literature is inconsistent. A technical paper may fail to make a distinction between the magnetic field and magnetic induction, knowing that the audience may know the difference, but as can be seen in the case of a textbook such as Jackson, the distinction is made precisely.