$2D$ Box

The calculation done on rectangular magnet with constant magnetization and the result represented in AViz:
Adirondack Stream
The magnet is placed in the middle, the calculation is done only ouside it. Red colors correspond to strong magnetic field and blue to weaker (the calculation is done in a.u., the result depend on overall constant magnetization which is 1 for the calculation).
Closer look with different orientation:
Adirondack Stream
Magnetic Field lines look like closed loops as expected. Now lets take a look on real demonstration of rectangular magnet field using iron filings (it have slightly different geometry):
Adirondack Stream

$2D$ Horseshoe

The calculation is done on Horseshoe magnet with constant magnetization and the result represented in AViz:
Adirondack Stream
Closer look:
Adirondack Stream
Magnetic Field lines look like closed loops as expected. Black region is a magnet and again the calculation is done outside the magnet.
Expreimental result using iron fillings:
Adirondack Stream