Equilibrium Modeling for Forces in a Square-Circle System

[analysis001]

Homework Statement

I am trying to model an equilibrium for the attached picture. The picture is of a square with a small circle in the center of the square. There is a force from the sides of the square that attracts particles to the edges. There is also a force from the circle that attracts particles towards the circle. The two forces are the same value. I am trying to draw the equilibrium, where if a particle lands there, it stays in that place because the two forces are attracting it equally. It is a lot harder than I thought it would be because it is a circle inside of a square. Ideally I would like to mathematically model the equilibrium but I'm not really sure how to. Any thoughts or ideas would be greatly appreciated. Sources that you find would also be helpful. The second image I attached is just showing the direction a few particles move for reference.

 

[mfb]

The two forces are the same value.

Same magnitude everywhere?
What about the direction?

I am trying to draw the equilibrium, where if a particle lands there, it stays in that place because the two forces are attracting it equally.

Where is the problem? First you need some clear definition of your forces, but then you can check for points where the total force is zero.