Magnetic Field and Magnetic Induction in a Cylindrical Bar Magnet

This Demonstration shows the quantitative magnetic field and magnetic induction for a cylindrical bar magnet. The magnetization is assumed to be in the direction and uniform within a magnet of diameter and length . Colors on a logarithmic scale show field intensity and arrows show its direction. The field and induction outside the magnet satisfy , so the field patterns are identical (the same color is used for both fields). They are different inside the magnet, since there . While vectors go from the north pole to the south pole (top to bottom) in all regions, vectors return to the north pole through the magnetized body.


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


The magnetic field can be regarded as originating from two parallel, oppositely charged monopolar disks situated at the ends of the magnet. Since the effective surface magnetic charge densities are equal to , the magnetic field of any point in the - plane, a 2D vector, can be calculated by integrating on those surfaces:
Mathematica finds a function after integrating with respect to (i.e. in radial direction) that can be written as:
Snapshot 1: example of field; all vectors go from north pole to south pole
Snapshot 2 : example of field; vectors circulate between north pole and south pole
Snapshot 3 : example of field of thin bar magnet; the field resembles that of two point charges
    • 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+