Formulas

With ra,b as distance from a point source situated at a,b in the xy plane, the basic potential formulas are (sqrt:  square root):

1 source at the origin of the xy-plane V = E/r0 = 1/sqrt( x2 + y2 + z2)

1 source at R on the y axis V = E/r0,R= 1/sqrt( x2 + (y - R)2 + z2)

1 source at a,b V = E/ra,b = 1/sqrt(( x - a)2 + ( y - b)2 + z2)

E defines polarity and magnitude of the influence on a trial body .

In the simulation E = +1 is set for the first object.

The potential equation for the dipole results as:

V = 1/r-R - 1/r+R = 1/sqrt(x2 + (y - R2) - 1/sqrt(x2 + (y + R2)

The formula for three objects contains a constant v =1/2*sqrt(3): it takes care that the three objects are situated symmetrically to the origin, with distance 2R between them.