Single Point Charge ("Monopole")

A function to calculate the potential energy of a monopole (unit charge):
(The .00001 offset is to overcome divide-by-zero problems.)

The electric field of a monopole:

The electric potential of a monopole:
(The contours represent factors of 10 difference in energy.)

Both the electric field and electric potential of monopole on the same plot:
(Note how the field is always perpendicular to the equipotential lines.)

A 3-D view of the electric potential of a monopole:

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