10176

# Magnetic Fields for a Pair of Parallel Currents and for a Ring Current

This Demonstration calculates magnetic fields for a pair of oppositely directed parallel currents and also for the cross-section of a ring current passing through the plane. The currents are assumed to be filamentary in either case.
For a pair of parallel currents, the magnetic field pattern depends on the separation distance .
For a ring current, the magnetic field is calculated using a complete elliptic integral. The pattern depends on the ring radius .
In both cases, you can vary the current and length . The magnetic field and energy intensities are indicated by variations in color.

### DETAILS

Snapshot 1: pair of opposing parallel currents , separated by a small distance
Snapshot 2: ring current of for ring of diameter 1 m
Snapshot 3: a ring current with small diameter; the field resembles that of a magnetic dipole
In the both cases, the magnetic fields are calculated from vector potential using .
The energy density is given by .
The vector potential is determined as follows.
Pair of Opposing Parallel Currents
Designating the line current vector by and the separation length by , we find , where , are the distances to the currents.
Ring Current
Using cylindrical coordinates with current and radius , we find , , , where is the distance to the center, and .
In the actual calculation, Cartesian coordinates are used and the symmetry axis is changed from to .
Reference
[1] G. Lehner, Electromagnetic Field Theory for Engineers and Physicists, 1st ed. (M. Horrer, trans.), New York: Springer, 2009.

### PERMANENT CITATION

 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.