+ -. Visualization of scalar and vector fields of system of two positive point charges. The generalized potential function has the form φ(r)=Σqₖ*|rₖ –r|ᵐ, where m is a real number
The images below were created using an applet.
This applet illustrates the construction of various scalar fields φ for the selected parameters m=-1,1,0.4 and the corresponding gradient vector fields E using the example of a two-point system of identical 'charges' (designated as '++') located at a certain distance from each other.
The images below show:
Multifocal loci of points with:
a) equipotential lines φ=c and lines of the corresponding gradient vector fieldE;
c) lines of equal field strength modE(x,y) =c.
Graphs of distribution functions in the xy-plane:
b) potential -φ(x, y);
d) values of the vector field -modE(x,y).
Note that the gradient field lines are perpendicular to the equipotential lines.
m=-1. This is the case for a Coulomb or gravitational field.
m = 1. N-Ellipse - The case of multifocal curves (N≥2), the construction of which is a generalization of the construction of an ellipse-hyperbola.
m=0.4
