Ampère's Force Law: Force between Parallel Currents

Ampère's force law for parallel currents can be regarded as an analog of Coulomb's law for charges. The force per unit length between two current elements separated by a distance is given by , where is the permeability of free space. In contrast to Coulomb's law, parallel current elements attract (signified by the minus sign) while opposing currents repel. The formal SI definition of the ampere is "the constant current which will produce an attractive force of 2⨯10-7 newtons per meter of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one meter apart in a vacuum."


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Ampère's force law is a consequence of the Lorentz force on the moving charge in each current element acted upon by the magnetic field produced by the other current element: .
Wikipedia, "Ampère's Force Law," http://en.wikipedia.org/wiki/Ampère's_force_law.


    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+