Magnetic Field Strength: Inverse Proportionality to Square or Cube?

[magnetics]

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?

 

[jtbell]

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."

 

[granpa]

http://en.wikipedia.org/wiki/Biot–Savart_law#Point_charge_at_constant_velocity

 

[magnetics]

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?

 

[granpa]

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

 

[LURCH]

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.