Magnetic Field Strength: Inverse Proportionality to Square or Cube?

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Discussion Overview

The discussion revolves around the nature of magnetic field strength and its relationship to distance, specifically whether it diminishes inversely proportional to the square or cube of the distance from a magnet. The scope includes theoretical considerations and practical implications related to magnetic fields from different sources.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants note that magnetic field strength is often described as diminishing inversely proportional to the square of the distance, particularly in the context of a monopole field.
  • Others argue that a dipole field, such as that from a bar magnet, diminishes inversely proportional to the cube of the distance when observed from a sufficient distance.
  • A participant mentions that the behavior of the magnetic field can depend on the proximity to the source, suggesting that close to one pole of a bar magnet, it may behave like a monopole.
  • There are inquiries about practical applications and the conditions under which a permanent magnet might exhibit monopole-like properties.
  • One participant raises the magnetic field of a single electron as a relevant consideration in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on whether the magnetic field strength diminishes with the square or cube of the distance, indicating that multiple competing views remain without a consensus.

Contextual Notes

Participants highlight that the definitions and behaviors of magnetic fields can vary based on the source and the distance from it, suggesting that assumptions about the context are important in understanding the claims made.

magnetics
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I have read a number of journal article that state that magnetic field strength diminishes inversely proportional to the square of the distance. BUT more than one has stated that the field strength is inversely proportional to the cube of the distance from the surface of the magnet.
Which one is correct?
 
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It depends on the source of the field and how close you are to it.

A "monopole" field goes like 1/r^2. Magnetic monopoles don't actually exist as far as we know to date, but some situations can produce a field which is approximately a monopole field over a limited region. For example, if you have a long bar magnet and you stay close to one pole.

A "dipole" field goes like 1/r^3. This is what you get from a current loop or a bar magnet, when you get far enough away that it appears "small."
 


Thank you jtbell, that makes a lot of sense now. Could you possibly point me to a reference book/article that defines this?

Also in practical terms for a permanent magnet, say rare Earth with Max. Energy Product of 40MGOe how long would it have to be before it's capable of taking on the properties of a monopole at each end?
 


dont forget about the magnetic field of a single electron moving through empty space
 


magnetics said:
Thank you jtbell, that makes a lot of sense now. Could you possibly point me to a reference book/article that defines this?

Also in practical terms for a permanent magnet, say rare Earth with Max. Energy Product of 40MGOe how long would it have to be before it's capable of taking on the properties of a monopole at each end?

That tends to be a matter of practical application. To be treated as a monopole, one need only be so close to one pole that the effects from the opposite pole are "negligable." Where that threshold lies is up to the individual and usually dictated by the purpose for which the magnet is being used or examined.
 

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