Difference between revisions of "Magnetic field"
From Encyclopedia of Mathematics
(Importing text file) |
m (AUTOMATIC EDIT (latexlist): Replaced 13 formulas out of 13 by TEX code with an average confidence of 2.0 and a minimal confidence of 2.0.) |
||
| Line 1: | Line 1: | ||
| − | + | <!--This article has been texified automatically. Since there was no Nroff source code for this article, | |
| + | the semi-automatic procedure described at https://encyclopediaofmath.org/wiki/User:Maximilian_Janisch/latexlist | ||
| + | was used. | ||
| + | If the TeX and formula formatting is correct, please remove this message and the {{TEX|semi-auto}} category. | ||
| − | + | Out of 13 formulas, 13 were replaced by TEX code.--> | |
| − | where | + | {{TEX|semi-auto}}{{TEX|done}} |
| + | 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==== | ====References==== | ||
| − | <table>< | + | <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> |
Latest revision as of 17:01, 1 July 2020
A vector-valued function of 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., [a1], Sect. 1). However, quite often $\overset{\rightharpoonup} { B }$ is considered as a vector of magnetic induction (see, e.g., [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.
References
| [a1] | R. Feynman, R. Leighton, M. Sands, "The Feynman lectures on physics" , 2 , Addison-Wesley (1964) |
| [a2] | L.D. Landau, Ye.M. Lifshits, "Course of theoretical physics: Electrodynamics of continuous media" , VIII , Nauka (1992) (In Russian) (English transl.: Pergamon) |
How to Cite This Entry:
Magnetic field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Magnetic_field&oldid=19112
Magnetic field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Magnetic_field&oldid=19112
This article was adapted from an original article by V.V. Kravchenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article