Array of magnets around a sphere

  • Context: Graduate 
  • Thread starter Thread starter intervoxel
  • Start date Start date
  • Tags Tags
    Array Magnets Sphere
Click For Summary

Discussion Overview

The discussion revolves around the equilibrium configuration of an array of magnets distributed uniformly around a spherical surface, focusing on the minimum energy state of the system. Participants explore the theoretical implications and potential numerical solutions related to this configuration.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the equilibrium configuration of N magnets that can rotate freely in 3D space on a spherical surface and asks for existing work on the topic.
  • Another participant questions the meaning of "uniformly" in the context of magnet distribution, noting that N discrete magnets cannot achieve a truly uniform distribution without specific locations.
  • A third participant asserts that creating a spherical magnet with one pole inside and the other outside is not feasible, suggesting limitations in the proposed configuration.
  • A participant references simulation software related to the Ising model on curved surfaces, providing links to relevant work that may align with the original inquiry.
  • One participant reiterates the need for specific initial conditions to derive quantitative results, mentioning a cubic lattice arrangement near a spherical surface as a potential configuration.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of uniform distribution and the nature of the magnet configuration, indicating that multiple competing perspectives exist without a clear consensus.

Contextual Notes

Participants highlight the need for precise definitions and initial conditions to advance the discussion, indicating that the lack of these elements may limit the exploration of the problem.

intervoxel
Messages
192
Reaction score
1
An array of N magnets which can turn freely about their centers in any direction in 3d space is distributed uniformly around a spherical surface (their centers). What is the configuration of equilibrium of the system after some time? (minimum energy)

Do you know of any work showing that?

Thanks.
 
Physics news on Phys.org
How much 'uniformly' do you mean? You know, N discrete magnets cannot be in a uniform distribution.

What are the exact locations of the magnets? To get quantitative result, we need more specific information than just that they are on a sphere. I think I can get some numerical solutions once I have an idea about the initial conditions.
 
It's not possible to make a spherical magnet with one pole inside and the other outside. If you try you won't get the result you might hope for.
 
  • Like
Likes   Reactions: 1 person
This post refers to simulation software that can be used to study the Ising model on curved surfaces:

https://www.physicsforums.com/showthread.php?t=409671

This work treats 'sphere-like' lattices, such as a pillow-shaped one and a cube projected onto a sphere:

http://arxiv.org/pdf/hep-lat/9602025.pdf

Is this the kind of work you are looking for?
 
  • Like
Likes   Reactions: 1 person
j824h said:
How much 'uniformly' do you mean? You know, N discrete magnets cannot be in a uniform distribution.

What are the exact locations of the magnets? To get quantitative result, we need more specific information than just that they are on a sphere. I think I can get some numerical solutions once I have an idea about the initial conditions.

Thanks for your reply, j824h. I was thinking of points belonging to a cubic lattice nearest to a spherical surface of integer radius.
 
Last edited:

Similar threads

Undergrad Magnetic Resonance physics question: RF pulse role and 'in-phase'
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Charging a small metal ball from a charged hollow sphere
  • · Replies 4 ·
Replies
4
Views
2K
Magnetization of a paramagnetic sphere
  • · Replies 11 ·
Replies
11
Views
2K
High School Experiment issues (electromagnetism)
  • · Replies 42 ·
2
Replies
42
Views
3K
Graduate A sphere radiating charges isotropically
  • · Replies 5 ·
Replies
5
Views
1K
Graduate Current flow on the surface of a permeability bigger than 1
  • · Replies 1 ·
Replies
1
Views
1K
Graduate PPMT, Magnetic Flux Switch, electro-permanent magnet generator
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Electric Field & Interplay between Coordinate Systems | DJ Griffiths
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Effect of time on density distribution+shape of uniformly dense sphere
  • · Replies 58 ·
2
Replies
58
Views
4K
Graduate Electric potential energy between charge and moving magnet
  • · Replies 7 ·
Replies
7
Views
2K