In physics, a magnetic field is the relativistic part of an electric field (as explained by Einstein in 1905). When an electric charge is moving from the perspective of an observer, the electric field of this charge due to space contraction is no longer seen by the observer as spherically symmetric (and due to time dilation not radial) and must be computed using the Lorentz transformations. One of the products of these transformations is the part of electric field which only acts on moving charges - and we call it "magnetic field".

The quantum-mechanical motion of electrons in atoms produces magnetic fields of permanent ferromagnets. Spinning charged particles also have magnetic moment. Some electrically neutral particles (like neutron) with non-zero spin also have magnetic moment due to charge distribution in their inner structure. Spin-zero particles never have magnetic moment.

A magnetic field is a vector field: it associates with every point in space a (pseudo-)vector that may vary in time. The direction of the field is the equilibrium direction of a magnetic dipole (like compass needle) placed in the field.