The law

The scalar form of Coulomb's law is an expression for the magnitude and

sign of the electrostatic force between two point charges, small in

size compared to their separation. This force (F) acting simultaneously on point charges (q ₁) and (q ₂), is given by:

where r- is the separation distance and k _e- is a proportionality constant.

A positive force implies it is repulsive, while a negative force implies it is

attractive. The proportionality constant k _e, called the Coulomb constant

(sometimes called the Coulomb force constant), is related to defined properties of space and can be calculated based on the speed of light to be exactly

Coulomb's law states that: "The magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them."

In the more useful vector-form statement, the force in the equation is a vector force acting on either point charge, so directed as to push it away from the other point charge; the right-hand side of the equation, in this case, must have an additional product term of a unit vector pointing in one of two opposite directions, e.g., from q ₁ to q ₂ if the force is acting on q ₂; the charges may have either sign and the sign of their product determines the ultimate direction of that force. Thus, the vector force pushing the charges away from each other (pulling towards each other if negative) is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The square of the distance part arises from the fact that the force field due to an isolated point charge is uniform in all directions and gets "diluted" with distance as much as the area of a sphere centered on the point charge expands with its radius.

The law of superposition allows this law to be extended to include any number of point charges, to derive the force on any one point charge by a vector addition of these individual forces acting alone on that point charge. The resulting vector happens to be parallel to the electric field vector at that point, with that point charge (or "test charge") removed.

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