Close to the magnet, that depends on the detailed shape of the magnet.
Farther away (say at distances more than a few times the size of the
magnet) the magnetic field will generally fall off as the cube of the
distance from the magnet. If you have a small magnet, the field two
feet away will only be 1/8 as strong as the field one foot away.
There are special magnets for which the field falls off even
faster, but in general the 1/distance cubed law holds at large
distances.
Mike W.
That's the magnetic field strength Mike's talking about. The force
something feels in a magnetic field depends on how the magnetic field
changes with distance (paradoxically, objects would feel no net force
in a perfectly uniform magnetic field! This is one reason why the
shapes of the pole tips of magnets is important). So in fact, the force
another magnet will feel will fall off with the distance to the fourth
power. If the object which feels the force isn't a magnet but needs to
have its magnetization induced by the presence of the magnetic field,
the force gets weaker still with increasing distance. The field falls
off with 1/distance cubed, the rate of change falls off with 1/distance
to the fourth power, and if the induced magnetization is proportional
to the field strength, the force felt falls off with 1/distance to the
seventh power.
This is one of the reasons why we are reluctant to answer
questions about how strong the force is between two magnets or between
magnets and other stuff. The detailed shapes of the magnets are really
important, and tiny changes in distance make a big change in the forces
you feel, as you can tell with real magnets.
Tom
(published on 10/22/2007)
