Magnetism of a bar magnet - maximum rate of change?

[Gatsby51]

Magnetism of a bar magnet -- maximum rate of change?

If a bar magnet is placed along the x-axis with (0,0) at its center, along which axis does the magnetic field fall off faster and why?

 

[berkeman]

If a bar magnet is placed along the x-axis with (0,0) at its center, along which axis does the magnetic field fall off faster and why?

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http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/imgmag/bar.gif