Ampère's force law

Ampère's force law

The force of attraction or repulsion between two current-carrying wires (see Figure 1) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field (according to the Biot-Savart law), and the other wire experiences a Lorentz force as a consequence.

The best-known and simplest example of Ampère's force law, which underlies the definition of the ampere, the SI unit of current, is as follows: For two thin, straight, stationary, parallel wires, the force per unit length one wire exerts upon the other in the vacuum of free space is

:: F_m = k_m frac {I_1 I_2 } {r} ,

where "k"m is the magnetic force constant, "r" is the separation of the wires, and "I"1, "I"2 are the DC currents carried by the wires. The value of "k"m depends upon the system of units chosen, and the value of "k"m decides how large the unit of current will be. In the SI system,cite book
author=Raymond A Serway & Jewett JW
title=Serway's principles of physics: a calculus based text
url=,M1 |publisher=Thompson Brooks/Cole
edition=Fourth Edition
location=Belmont, CA
page=p. 746
] cite book
author=Paul M. S. Monk
title=Physical chemistry: understanding our chemical world
url= |publisher=Chichester: Wiley
location=New York
page=p. 16

:: k_m overset{underset{mathrm{def{{=} frac {mu_0}{ 2 pi}

with μ0 the magnetic constant, "defined" in SI units as [ [ "BIPM definition"] ] cite web |url= |title=Magnetic constant |accessdate=2007-08-08 |work=2006 CODATA recommended values |publisher=NIST ]

:: mu_0 overset{underset{mathrm{def{{=} 4 pi imes 10^{-7} newtons / (ampere)2.

Thus, for two parallel wires carrying a current of 1 A, and spaced apart by 1 m in vacuum, [By "vacuum" is meant the unattainable vacuum of free space used as a reference state in electromagnetic theory.] the force on each wire per unit length is exactly 2 × 10-7 N/m.

A more general formulation of Ampère's force law for arbitrary geometries is based upon line integrals, and is as follows [The integrand of this expression appears in the official documentation regarding definition of the ampere [ BIPM SI Units brochure, 8th Edition, p. 105] ] cite book
author=Tai L. Chow
title=Introduction to electromagnetic theory: a modern perspective
url='s+law+of+force%22&source=web&ots=uZOFz9dWv7&sig=NJp3UQvbCOvcVm7eJN4IUdlC9bs |publisher=Jones and Bartlett
page=p. 153
] [ [ Ampère's Force Law] "Includes animated graphic of the force vectors. Scroll to bottom for formulas"] :

:: mathbf{F}_{12} = frac {mu_0} {4 pi} I_1 I_2 oint_{C_1} oint_{C_2} frac {d mathbf{s_2} mathbf{ imes} (d mathbf{s_1} mathbf{ imes } hat{mathbf{r_{12} )} {r_{12}^2} ,

where:F12 is the total force on circuit 2 exerted by circuit 1 (usually measured in newtons),:"I"1 and "I"2 are the currents running through circuits 1 and 2, respectively (usually measured in amperes),:The double line integration sums the force upon each element of circuit 2 due to each element of circuit 1,:"d"s1 and "d"s2 are infinitesimal vector elements of the paths "C"1 and "C"2, respectively, with the same direction as the conventional current (usually measured in metres),:The vector hat{mathbf{r_{12} is a vector of unit length along the line connecting the element pair [from s1 to s2] , and "r"12 is the distance separating these elements,:The multiplication × is a vector cross product.

To determine the force between wires in a material medium, the magnetic constant is replaced by the actual permeability of the medium.

References and notes

ee also

* Ampere
* Magnetic constant
* Lorentz force
* Ampère's circuital law
* Free space

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Ampère's circuital law — Ampère s law redirects here. For the law describing forces between current carrying wires, see Ampère s force law. Electromagnetism …   Wikipedia

  • Ampere — For other uses, see Ampere (disambiguation). Current can be measured by a galvanometer, via the deflection of a magnetic needle in the magnetic field created by the current. The ampere (SI symbol: A; non SI abbreviation: amp[1]) is the SI unit of …   Wikipedia

  • Law — /law/, n. 1. Andrew Bonar /bon euhr/, 1858 1923, English statesman, born in Canada: prime minister 1922 23. 2. John, 1671 1729, Scottish financier. 3. William, 1686 1761, English clergyman and devotional writer. * * * I Discipline and profession… …   Universalium

  • Ampere's law — Law Law (l[add]), n. [OE. lawe, laghe, AS. lagu, from the root of E. lie: akin to OS. lag, Icel. l[ o]g, Sw. lag, Dan. lov; cf. L. lex, E. legal. A law is that which is laid, set, or fixed; like statute, fr. L. statuere to make to stand. See… …   The Collaborative International Dictionary of English

  • Ampère's law — Physics. the law that a magnetic field induced by an electric current is, at any point, directly proportional to the product of the current intensity and the length of the current conductor, inversely proportional to the square of the distance… …   Universalium

  • Ampère , André Marie — (1775–1836) French physicist and mathematician Ampère was born in Lyons, France, where his father was a wealthy merchant. He was privately tutored, and to a large extent self taught. His genius was evident at an early age. He was particularly… …   Scientists

  • law — law1 lawlike, adj. /law/, n. 1. the principles and regulations established in a community by some authority and applicable to its people, whether in the form of legislation or of custom and policies recognized and enforced by judicial decision. 2 …   Universalium

  • Ampère, André Marie — born Jan. 22, 1775, Lyon, France died June 10, 1836, Marseille French physicist, founder of the science of electromagnetism. A prodigy who mastered the entire known field of mathematics by age 12, he became a professor of physics, chemistry, and… …   Universalium

  • law — 1. A principle or rule. 2. A statement of fact detailing a sequence or relation of phenomena that is invariable under given conditions. SEE ALSO: principle, rule, theorem. [A.S. lagu] Alexander l. states that a jerky nystagmus becomes worse when… …   Medical dictionary

  • Lorentz force — This article is about the equation governing the electromagnetic force. For a qualitative overview of the electromagnetic force, see Electromagnetism. For magnetic force of one magnet on another, see force between magnets. Electromagnetism …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.