Electrostatic Potential

The force vector field produced from electrostatic potential between two points with opposite charges.

In[1]:=

ElectroStaticPotential[ql_, pl_, r_] := Sum[ ql[[i]]/Norm[r - pl[[i]]], {i, Length[ql]}]

In[2]:=

v = Simplify[ ElectroStaticPotential[{1, -1}, {{-1, -1, 0}, {1, 1, 0}}, {x, y, z}], {x, y, z} \[Element] Reals];

In[3]:=

field = -Grad[v, {x, y, z}];

In[4]:=

SliceVectorPlot3D[Clip[field], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, PlotTheme -> "Scientific", ImageSize -> 500]

Out[4]=

Looking at the field around isosurfaces of the potential, the field is stronger between the points.

In[5]:=

SliceVectorPlot3D[ Clip[field], {v == -0.5, v == 0.5}, {x, -2.5, 2.5}, {y, -2.5, 2.5}, {z, -2.5, 2.5}, PlotTheme -> "Scientific", ImageSize -> 500]

Out[5]=