How this calculator works
The inverse-square electric force acts along the line joining stationary charges. In a uniform linear dielectric, the vacuum force is divided by relative permittivity. This page preserves the sign of the product of the charges so attraction and repulsion remain visible. It uses k = 1/(4 pi epsilon0), with CODATA 2022 vacuum permittivity; finite-size charge distributions need a field calculation.
Formula
F = q1 q2/(4 pi epsilon0 epsilonr r²). r = sqrt(k q1 q2/(epsilonr F)); q1 = F epsilonr r²/(k q2).
Worked example
Charges of +1 microcoulomb and -1 microcoulomb separated by 1 m in vacuum attract with force -0.00898755 N. Charges 2 and 3 microcoulombs at 2 m in a dielectric with epsilonr = 3 repel with 0.00449378 N.
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Frequently asked questions
Can the charges be negative?
Yes. Opposite signs give attraction; equal signs give repulsion.
What does the equal-charge inverse return?
It returns a positive magnitude. Both charges could be positive or both negative, which the force alone cannot distinguish.
Why is zero separation rejected?
The point-charge expression is singular there. Overlapping extended charges require a different physical model.