9860

Magnetic Shielding Effect of a Spherical Shell

Consider a spherical shell of linear magnetic material with relative permeability placed in a uniform magnetic field . The magnetic fields in this region can be described by a magnetic potential . Selecting the direction of as the axis of spherical coordinates , is given by , where is a Legendre function. The magnetic field at any point is . The coefficients , in the regions with (1) , (2) , and (3) are determined by considering the boundary conditions at and , taking into account the permeability in each region: (1) and (3) and (2) . As the result, the field in (1) is that of superimposed with the contribution of a magnetic dipole. The field in (3) turns out to be uniform, with magnitude considerably lower than . The magnetic induction or B field is obtained by , where or depending on the region.

SNAPSHOTS

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

DETAILS

The direction of is chosen as the axis. The fields are displayed on the cross section through the center of the spherical shell. The color represents the field intensity normalized by . The field lines are calculated from equally distributed points. You can vary the shell's relative permeability and its configuration parameters , . It is observed that the field intensity in the inner space is greatly reduced relative to that in the outer space, especially for a large . This is shown in snapshots 1 and 2. Since the E and B fields are shown in normalized bases, the two fields are equal in free space, but the E field is much smaller in the shell (magnetic medium), as shown in snapshot 3.
    • 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.









 
RELATED RESOURCES
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 © 2014 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+