## Background

The electromagnetic force is the interaction between charged particles, through electric fields and magnetic fields. This section discusses the electric force, which is responsible for the electric field. The magnetic force is discussed separately.

Electricity is a good example of the electric force. Electrons are pushed through wires in electricity as they repel each other, continually forcing electrons down the wire. Force (F) is the measurement of how strong they repel or attract each other and is based on the charge of the particles (q) in Coulomb’s Law, a constant (k) and the distance between particles (r), shown below.

*Credit: hyperphysics.phy-astr.gsu.edu*

The electric force has a feature, unlike gravity, that allows particles to be attracted or repelled. At a subatomic particle level, two electrons are known to repel each other. However, an electron and positron will attract each other, as was shown in the Annihilation section. The electric force will be shown to be based on constructive or destructive wave interference of longitudinal waves.

**Explanation**

The energy wave explanation for the electric force, like all of the forces, is based on a difference in wave amplitude as particles move to minimize amplitude. When a particle’s standing wave structure breaks down and becomes a traveling wave, we see this as the particle’s radius. Beyond the radius, waves are traveling, spherical, **longitudinal waves** that have an amplitude that decreases with the square of the distance from the particle core – the inverse square law seen in the electric force.

### Constructive Wave Interference – Repel

Gabriel LaFreniere has modeled the wave mechanics of two electrons in proximity. Due to the phase shift at the electron core, the waves constructively add between the particles but destructively add beyond them. This is seen in the simulation as amplitude is much higher between the particles. As particles move to minimize amplitude, this forces them to repel.

### Destructive Wave Interference – Attract

In a similar animation, LaFreniere has also modeled the electron and positron interaction. However, these results are different because the positron is model as a phase difference from the electron. In this case, waves are destructive between the particles and constructive beyond them. The minimal amplitude between the particles causes an attraction effect as each particle moves to minimize its amplitude.

This is the electric force. Traveling, longitudinal waves that affect particles as they move to minimize their amplitude.

### Calculating the Force

The Force Equation was derived previously based on Longitudinal Wave Energy and related to a particle’s energy (in this example the electron). It is based on the a group of two particles (Q) at distance (r). The variable in the Force Equation is amplitude. Wave centers move to reduce amplitude. Thus, wave amplitude can be deduced based on the particle count and distance since it is a measurement of constructive or destructive wave interference. The electron’s movement is solely dependent on a difference in amplitude, based on other particles in its vicinity.

*Note: Particle count (Q) is similar to the variable used for Coulomb’s law (q), as it represents the number of particles. However, it is dimensionless, expressed in a numerical value as opposed to a Coulomb charge. Therefore it was given a capital letter (Q) as opposed to lower case (q).*

**Force Equation (Electric Force)**

**Proof**

Proof of the energy wave explanation for the electric force is the derivations of:

Further proof was also accomplished by using the Force Equation to accurately calculate various scenarios of charges particles at distance. Scenarios include single particles to groups of particles, at short ranges to very long ranges in separation distance. All have accuracy when compared to Coulomb’s law of 0.000%.

### Example Calculation

Two Electrons at Distance 1.40E-10:

In this example, two electrons are separated at a distance (r) of 1.40E-10 meters. Therefore Q_{1} and Q_{2} are both equal to -1 (electron). These values are inserted into the Force Equation (above). The remaining constants in the Force Equation are found under the energy wave constants section.

r = 1.40 x 10^{-10} m

Q_{1} = -1

Q_{2} = -1

**Calculated Force: **1.177E-8 newtons

**Difference vs Coulomb’s Law:** 0.000%

* Note: *A summary of various electromagnetic force calculations is found on this site; more detailed calculations with instructions to reproduce these calculations is found in the

*Forces*paper.