## Ampère's force law |

Part of a series of articles about |

In **Ampère's force law**. The physical origin of this force is that each wire generates a magnetic field, following the

- equation
- historical background
- derivation of parallel straight wire case from general formula
- notable derivations of ampère's force law
- see also
- references and notes
- external links

The best-known and simplest example of Ampère's force law, which underlies the definition of the

- ,

where *k*_{A} is the magnetic force constant from the *F _{m}/L* is the total force on either wire per unit length of the shorter (the longer is approximated as infinitely long relative to the shorter),

This is a good approximation if one wire is sufficiently longer than the other that it can be approximated as infinitely long, and if the distance between the wires is small compared to their lengths (so that the one infinite-wire approximation holds), but large compared to their diameters (so that they may also be approximated as infinitely thin lines). The value of *k*_{A} depends upon the system of units chosen, and the value of *k*_{A} decides how large the unit of current will be. In the ^{[1]}
^{[2]}

with μ_{0} the *defined* in SI units as^{[3]}^{[4]}

Thus, in vacuum,

*the force per*eachmeter of length between two parallel conductors – spaced apart by 1 m and*carrying a current of 1*A – is exactly

The general formulation of the magnetic force for arbitrary geometries is based on iterated ^{[5]}^{[6]}^{[7]}

- ,

where

- is the total magnetic force felt by wire 1 due to wire 2 (usually measured in
newtons ), *I*_{1}and*I*_{2}are the currents running through wires 1 and 2, respectively (usually measured inamperes ),- The double line integration sums the force upon each element of wire 1 due to the magnetic field of each element of wire 2,
- and are infinitesimal vectors associated with wire 1 and wire 2 respectively (usually measured in
metres ); seeline integral for a detailed definition, - The vector is the
unit vector pointing from the differential element on wire 2 towards the differential element on wire 1, and*|r|*is the distance separating these elements, - The multiplication
**×**is avector cross product , - The sign of
*I*_{n}is relative to the orientation (for example, if points in the direction ofconventional current , then*I*_{1}>0).

To determine the force between wires in a material medium, the

By expanding the ^{[8]}

In this form, it is immediately obvious that the force on wire 1 due to wire 2 is equal and opposite the force on wire 2 due to wire 1, in accordance with

Other Languages

azərbaycanca: Amper qanunu

беларуская: Сіла Ампера

čeština: Ampérův silový zákon

Deutsch: Ampèresches Kraftgesetz

eesti: Ampère'i jõud

Esperanto: Ampera forta leĝo

فارسی: قانون نیروی آمپر

français: Force d'Ampère

հայերեն: Ամպերի օրենք

latviešu: Ampēra spēks

македонски: Амперова сила

norsk: Ampères kraftlov

oʻzbekcha/ўзбекча: Amper qonuni

ភាសាខ្មែរ: ច្បាប់កំលាំងរបស់អំពែរ

русский: Закон Ампера

татарча/tatarça: Ампер кануны

українська: Закон Ампера

中文: 安培力定律