Coulomb’s Constant


Named after Charles-Augustin de Coulomb, this constant is the electric force constant. When charged particles interact, a force repels or attracts the particles. For example, two electrons will repel and travel in opposite directions; a proton and electron will be attracted to each other. The force is modeled based on the charge and distance, and Coulomb’s constant (k) is known as a proportionality constant in the equation F=k qq/r2.

When particles are present, wave amplitude changes as a result of wave interference between particles. Wave interference may be constructive or destructive, causing either a repelling of two particles of the same wave phase or attracting two particles of opposite wave phase. Wave amplitude declines with distance, therefore the force becomes F=ke(q1q2/r2), where variables in the equation are separated by parentheses.


Coulomb's Constant Explained

In the section on spacetime, the Coulomb force was found to be at the Planck level, as the force between two granules.  The Coulomb force is modeled classically as a spring-mass system in the paper, and thus pictured in the next illustration as a spring in a spring-mass system.

Coulomb force of spring mass system


See also: electric constant, magnetic constant



Derivation – Coulomb’s Constant

Coulomb’s constant can be derived classically from the four fundamental Plancks: Planck mass, Planck length, Planck time and Planck charge. In wave constant form, it is a complex proportionality constant derived in the Forces paper; a summary is found on this site at F=kqq/r2. It is the combination of constants in a wave equation, where the remaining variables are wave amplitude and distance.


Classical Constant Form

Coulomb's constant derived by Planck constants

Wave Constant Form

Coulomb Constant Wave Constant Form

Using classical constants Using energy wave constants


Calculated Value: 8.9876E+9
Difference from CODATA: 0.000%
Calculated Units: kg m / s2
G-Factor: gλ  gA2



The equation for Coulomb’s constant in energy wave theory has units that are based in kg * m/s2. By comparison Coulomb’s constant (k) is measured in N * m2/C2. However, in wave theory, C (Coulombs) are measured in m (meters) as charge is based on amplitude. N (Newtons) can be expressed in kg * m/s2, so when N is expanded and C is represented by meters, it resolves to the correct units expected for the Coulomb constant. The derivation of units from the current Coulomb constant to the wave theory version is as follows:

Coulomb Constant Units


Coulomb Energy

An alternative derivation in classical form is shown with the magnetic constant and speed of light. This version shows the consistency of energy and mass equations in classical format, as explained further below.

Coulomb's Constant Derived

Many of the energy and mass equations are shown with an alternative derivation to show the consistency of the Coulomb energy across all equations (e.g. Electron energy, electron mass, Planck mass, Rydberg energy, etc).  The Coulomb energy is constant across particles, photons and forces.  The components of the Coulomb constant from above is found in the next equation as it is expanded to be an energy equation by multiplying amplitude (squared) and dividing by the distance (radius).

Energy equation expressed as magnetic constant and wave amplitude

Coulomb Energy Equation


Three example using this simple equation to demonstrate the electric properties of the universe:

1) Electron Energy – In the Coulomb energy equation, replace amplitude with elementary charge; replace radius with electron radius.  Energy of a single electron. For the electron’s mass, simply remove c2.

Electron energy


2) Electric Force – The only difference between this energy and a force, is that radius is squared in a force.  In the Coulomb energy equation, replace amplitude with elementary charge; radius is now a variable distance r at which two electrons are measured.  It is the force of two electrons.

Electric force of two electrons


3) Rydberg Energy – The Rydberg energy, which is for an electron at the Bohr radius (a0), illustrates that the energy continues from the electron’s core as traveling waves (now ½ as it will eventually need two electrons in an orbit to be stable).  Other than the factor of ½, only the distance changes in the denominator from the electron’s radius, to the Bohr radius for the electron in an orbit of hydrogen.

Rydberg unit of energy in magnetic constant terms


Its value was calculated and shown to match the known value in the Summary of Calculations table. The derivation of this constant is available in the Fundamental Physical Constants paper.