Attraction between a magnetic field and iron

[Anthony physics]

This seems simple but i cannot find an answer anywhere. First off: is iron attracted to a magnet because the field strength on the side of the iron object closest to the magnet is stronger than the one furthest? And if this is true, how can one use this "differential" magnetic field to calculate the force on the iron object? If this is not the way to do it, how can i calculate the force regardless? Is there an equation or something?
Thanks

 

[Simon Bridge]

is iron attracted to a magnet because the field strength on the side of the iron object closest to the magnet is stronger than the one furthest?

No.
The external field aligns the internal magnetic dipoles: the lump of iron becomes a magnet and then interacts with the external field like any magnet would.
https://en.wikipedia.org/wiki/Paramagnetism