## Description

Named after Charles-Augustin de Coulomb, **Coulomb’s Law (F=kqq/r ^{2})** is an equation that represents the attractive or repulsive electric force (F) of two point charges (q). The force is proportional to the square of the distance (r) between charges. The proportionality constant that relates force to charge and distance is given the letter k, or k

_{e}, and is known as Coulomb’s constant.

In energy wave theory, particles experience constructive or destructive longitudinal wave interference based on their position on standing wave nodes. Constructive wave interference leads to a repulsion of two particles as a result of increased wave amplitude between them; destructive wave interference leads to an attraction of two particles. This causes the motion of particles and is measured as the electric force. Note, when the energy is stored, such as the electron’s position in an atom, it may result in a photon as explain in the Planck relation (E=hf).

## Derivation – Classical Constants

Coulomb’s Law can be derived using only Planck constants (classical constants), and the electron’s energy at distance (r). The derivation is very similar to the Planck relation as they are both related to the electron’s energy at distance. Energy is conserved, yet wave formation (geometry) changes, as explained in the geometry of spacetime page. The geometries (α_{1 }and α_{2}) are described in Eq. 1.4.3. When all of the variables in the α_{2} ratio are the electron’s classical radius (r_{e}), with the exception of slant length (l), which is πr_{e}, it resolves to be the fine structure constant (described in Eq. 1.4.6). Further details can be found in the *Geometry of Spacetime* paper.

## Proof

**Coulomb’s constant: **From Eq. 1.4.13, Coulomb’s constant matches in numerical value.

## Derivation – Wave Constants

This derivation begins from a classical form of the electron’s force. It uses a dimensionless particle count (Q) which needs to be converted to charge (q) to be consistent with Coulomb’s law. Charge is based on each particle having an elementary charge (e). In other words, q=Qe.

In this derivation, the elementary charge (e) is found, in addition to Coulomb’s constant (k). Both of these constants are no longer necessary when using energy wave constants. Their values were found to match CODATA values in the Constants section, thus with this proof they can be substituted below. Further details, including the reference to Eq. 1.11, can be found in the *Key Physics Equations and Experiments* paper.** **.

## Proof

**Coulomb’s constant: **From Eq. 2.4.7, Coulomb’s constant matches in numerical value. In wave theory, Coulombs (C) is measured in amplitude (meters). Coulomb’s constant is therefore a force, in terms of units.

**Elementary charge: **From Eq. 2.4.4, the elementary charge was accurately calculated on this site and in the *Fundamental Physical Constants* paper. It matches in numerical value. In wave theory, Coulombs (C) is measured in amplitude (meters).

The equations use wave constants explained here.

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