charge particles attracted to a dielectric

[danielemateriale]

hello an electric field forms a dipole moment of a dielectric material and if the field is not constant, the dielectric or the source of the field can be drawn between them.

The simulation speaks of an electric charge that is attracted by a thin layer of alumina. I produced the expressions, which are shown in the world file, which I have attached. A force is repulsive is another attractive. the repulsive force arises from charges that have been positioned on the dielectric at a distance from the particle and forming a field opposite to that of the particle.

in the file d is the vertical distance of the particle from the dielectric. all forces are parallel to the direction of the velocity of the particle

I would like to know if the particle is trapped on the surface of the dielectric or if she runs away from Dielectric.

typical charge of particles =e or n*e n=1,2,3
typical d =4*10^-4m
typical v= from 400 to 2000 m/s
d minimum tipical=120 pm N2 radius (120*10^-12 m)

[danielemateriale]

the minus sign on a is wrong!!!

[danielemateriale]

I have no more need the simulation I solved alone

[AimeeSantana]

the minus sign on a is wrong!!!

If the minus sign is wrong, what is the best thing to put in?