Suppose three finite line charges with positive linear charge densities , , are located on the sides opposite the vertices of the triangle . It can be shown that the electric field is zero at the point with trilinear coordinates that are in the same ratios as .
You can drag the vertices , , and vary the charge densities with the controls. The graphic shows a stream plot of the resulting electric field within the triangle.
Check "show trilinear coordinates" to see the point where the three contributions to the field cancel (where ); it has trilinear coordinates , , . The ratios of the densities to the trilinear coordinates then become equal: , as shown in the inset table.