Physics simulation with variable gravity field

Hello

I have a question regarding some blender trouble I am having, and I hope some kind soul here can illuminate me.

What I am trying to do is conceptually very simple.

I add to plane a force field with variable gravity field let say 0.1*g to g and simulate rotating disc as rigid body.

1.I have a plane,with dimensions x=20 m, y=20 m,z=0 m.
2.In edit mode I subdivide 10 times.
3. In weight paint ,I painted a half plane. it’s blue and red color.
4.I object data propierties i rename vertex Group to Gravity field.
5 In scene propierites i uncheck Gravity.
6.I add to plane a Force field. Shape every Point. Strength: -9.81

and I don’t see my vertex Groupe ( with name Gravity field) to check ?

Can we control intensity strength of gravity field by texture (white-black) ?

It can be done i Blender ?

Added blend file to this question.Projekt.blend (1.5 MB)

In brief:

I have a plane, e.g. 10 meters by 10 meters. On this plane, I want to simulate some physical phenomena.

Half of the surface (10 m by 5 m) has an acceleration due to gravity of 9.81 m / s ^ 2 and the other half of the surface (10 m by 5 m) for example 5 m / s ^ 2.

Addition:

We assume that the Earth’s acceleration does not change with altitude.