Árpád Kurusa
mathematician, associate professor

Department of Geometry Bolyai Institute Faculty of Science University of Szeged 
The force field of three equally loaded point can be dynamically presented in HTML5 with Javascript.
High school job was to determine those points in the force field of three equally charged points where the force minimizes. For two points this is the midpoint of the segment of the points. If the charges are placed in the vertices of an equilateral triangle it is easy to see that the only point where the force of the field disappears is the center of the triangle. If the three charges had not been located so regular, then the problem becomes more difficult, but the force field can easily be made visible with a computer.
On the figure below the colors indicate the magnitude of the field (the borders of which are the lines of force), the small black vectors show the force itself (it is a vector filed!). It clearly shows that every line of the field is perpendicular to the force of the field at its every point.
To move the points you should move the appropriate sliders... :)
$A_x$ =  $B_x$ =  $C_x$ = 
$A_y$ =  $B_y$ =  $C_y$ = 
The HTML and JavaScript code was written by my son Levente. I was just encouraging him and a bit tailored the result for this page.
(Unfortunately on some compuzters the change may be very slow, but the Chrome works much faster than the other browsers we tried although Chrome shows mathematical formulae somewhat incorrectly.)