Magnetic Feild Mapping

Nope.
Visualize magnetic fields: electromagnetic finite element ...

Try FEMM on google. Here is a screenshot. Remember, there is no free lunch. What you get ≈ what you pay. Having said that, this is a pretty decent software, till you graduate to CEDRAT or something like that.

Quickfield. Its a free FEA program that can probably do it.

What you get ≈ what you pay.

...or in some cases "What you get=What you overpay." Ex.: Autocad.

There are freeware programs that are quite capable in many areas -- maybe not the particular one you are asking about. But sometimes we look for something that is so niche that no one who enjoys writing freeware code has thought of it. Also, a lot of freeware is written because the author couldn't find any other freeware to do exactly what s/he wanted.

i have actually modelled magnets (for electromagnetic contactors) in freeware on my own. And in $50k software belonging to a client.

i found the user interface easy in the expensive software which could import CAD models. In the freeware, i had to do it by giving XY coords to the nodes. Almost made me give up.

i used my first computer at age 49, now i am 66. Many young engineers may find it very easy to do what i found almost impossible.

In the event, i agree with you. A lot of freeware is superb and so well written that i am embarrassed not being able to pay.

Try Elmer or OpenFOAM. Both are included with CAELinux, and are pretty sophisticated.

http://www.keosoft90.downarchive.com/software/graphics__design/215627-ansoft-maxwell-v1300-2010.html

not free.