Coulomb's law

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Coulomb's law is the inverse-square rule that describes the electrostatic force between stationary electric charges. For two point charges q1 and q2 separated by a distance r, the force magnitude is
F = ke |q1 q2| / r^2,
and it acts along the straight line between the charges. Like charges repel, opposite charges attract. The constant ke is 1/(4π ε0) and is about 8.99 × 10^9 N·m^2·C^−2.

A single charge Q creates an electric field E in vacuum given by
E = ke Q / r^2,
pointing away from Q if Q is positive. The force on a small test charge q at a position r is F = q E.

For many charges, the total field is found by superposition:
E(r) = ke ∑ qi r_hat_i / ri^2,
and the total force on a test charge q is F(r) = q E(r). This can also be written using the standard form
E(r) = (1/4π ε0) ∑ qi r_hat_i / ri^2.

Coulomb's law is foundational to electromagnetism and is consistent with Gauss's law. It best describes static charges; when charges move, magnetic effects arise and a full treatment requires Maxwell's equations and relativity. In slow-motion situations, Coulomb's law remains a good approximation.

Historically, the idea of electrical forces grew from early observations of static electricity, and Charles-Augustin de Coulomb published his law in 1785, using a torsion balance to measure the forces between charged bodies.