how to calculate the force on a charged conductive body (ball), when that body is between two parallel plates (+V, -V) (see image), ooh and I am calculating numerically. I would first calculate the surface charges on the conductive surfaces (2 disks + ball), then calculate the potential field from the two disks ONLY (with those surface charge configurations, where the charged ball also had a say), and from this field, go on to calculate E=-∇V. I think the ball can't exert the force on itself (kinda like trying to pick yourself up while standing in a basket and pulling up on the handles), that is why I think you would only need to calculate the field from the disks, and then with this field E, calculate the force on the body F=∫dQ*E. Would you agree, or am I missing something.
I get strange values of equipotential lines in the contour plot (see image).
PS: One more question, if you charge a ball to a potential +V (touch on of the disks) and then move the ball away from that disk (no longer touching) towards the second disk, would the potential of the ball change on its way??