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A vector-valued function of [[Space-time|space-time]] variables describing a force acting on a moving electrical charge and proportional to the charge velocity in the following sense. The total force $\overset{\rightharpoonup} { F }$ which acts on a charge $q$ moving with velocity $\overset{\rightharpoonup }{ v }$ is given by the Lorentz force law

\begin{equation*} \vec { F } = q ( \vec { E } + \vec { v } \times \vec { B } ), \end{equation*}

where $\overset{\rightharpoonup }{ E }$ is the electric intensity field. The vector $\overset{\rightharpoonup} { B }$ is called the magnetic field (see, e.g., [[#References|[a1]]], Sect. 1). However, quite often $\overset{\rightharpoonup} { B }$ is considered as a vector of magnetic induction (see, e.g., [[#References|[a2]]], Sect. 29), while the vector $\overset{\rightharpoonup }{ H }$ related to $\overset{\rightharpoonup} { B }$ by the material equation $\overset{\rightharpoonup} { B } = \mu \overset{\rightharpoonup}{ H }$ is named magnetic intensity field or simply magnetic field. Here, $\mu$ denotes the material permeability. Together with the electric intensity field $\overset{\rightharpoonup }{ E }$, the vector $\overset{\rightharpoonup} { B }$ satisfies the [[Maxwell equations|Maxwell equations]].

====References====
<table><tr><td valign="top">[a1]</td> <td valign="top">  R. Feynman,   R. Leighton,   M. Sands,   "The Feynman lectures on physics" , '''2''' , Addison-Wesley  (1964)</td></tr><tr><td valign="top">[a2]</td> <td valign="top">  L.D. Landau,   Ye.M. Lifshits,   "Course of theoretical physics: Electrodynamics of continuous media" , '''VIII''' , Nauka  (1992)  (In Russian)  (English transl.: Pergamon)</td></tr></table>