Magnetic field distances

[MattM]

I was playing around with ferrous magnets and neos and noticed a huge difference in both strength and distances in the fields from the magnets.  The neos are about the size of American quarters (coins).  The ferrous magnets are the 3 for 99 cent flavors from the hardware store, each about 1.5 inches long.  The neos are stronger.  The ferrous magnets are considerably cheaper, but the magnetic field of ferrous magnets extend out about 4x as far.  Why the big differences in field distances?

[Mary B]

Bigger magnet larger field but much weaker for a ferro magnet. Try that with a neo that size, make sure to have all metal at least a foot away from it and don't get your fingers in front! They can pinch hard and even break bones.

[MattM]

My intuition would think weaker field, shorter distance.  The bigger magnet is only a fraction of the power, so that doesn't seem to make logical sense.

[Mary B]

You small magnet the field lines are going to curve out and back in a short distance,  large magnet has "wider" field area due to size of magnetic area...

https://www.kjmagnetics.com/blog.asp?p=surface-fields-101

[joestue]

you need to compare two identical magnets and actually measure the attractive forces with a scale sensitive enough.

I can assure you, the air is not saturating and the magnetic flux lines are identical in shape; once you account for the initial conditions, the attractive force between a magnet and an object (or another magnet) falls off with the 4th power of the distance.

this is because the magnetic flux density falls off with the square of the distance and the attractive force on an object is proportional to the flux density squared.