## 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. However, since we can’t measure individual electrons in the wire, electricity is a measurement of a collection of electrons. The force that moves electrons is referred to as a voltage (V), the flow of electrons as a current (I), and its opposition is called resistance (R). Georg Ohm established the relationship between these as V=IR, known as Ohm’s law. Since electricity is the study of a collection of particles, it is described separately on this site, including a relationship between Ohm’s law and Newton’s 2nd law. Refer to the What is Electricity page.

The electric force has a feature, unlike gravity, that allows particles to be attracted or repelled. At a subatomic particle level, two electrons or two positrons are known to repel each other. However, an electron and positron will attract each other, described in more detail in the annihilation page.

**Electric Force**

Force (F) is the measurement of how charged particles repel or attract each other and is based on the total charge of the particles (q), a constant (k) and the distance between particles (r), shown below – Coulomb’s law. The law works perfectly to describe the electric force, yet it has two issues: 1) reconciling the property of charge (q) with mass (m) to unify forces for particles with forces for large objects (Newton’s laws), and 2) explaining the proportionality constant (k).

**Coulomb’s Law**

**Explanation**

Like all motion, the electric force is based on a difference in wave amplitude as particles move to minimize amplitude. When a particle reflects longitudinal waves (out-waves), it is a standing wave structure as it combines with in-waves of the same frequency. This forms a particle. Beyond the particle’s perimeter, the standing wave structure transitions back to traveling waves. These waves are spherical, traveling longitudinal waves that decrease in amplitude from the source and will have an effect on other particles based on constructive or destructive wave interference. The electric force is simply the calculation of this wave interference of two particle groups (Q), separated at a distance, and proportional to the electron’s energy as seen in the equation in the next section of this page.

**Electric Force** – Longitudinal wave interference between two particle groups (Q) separated at distance (r)

### Wave Interference

Particles are formed at one of two nodes in a standing wave where amplitude is zero, leading to two types of particles of opposite wave phase: matter and antimatter (e.g. electron and positron). This difference in wave phase between these two types of particles leads to either constructive or destructive wave interference. The motion of particles is to minimize amplitude.

**Constructive wave interference**– particles at same wave phase (e.g. two electrons) increase amplitude between particles, forcing particles apart.**Destructive wave interference**– particles of opposite wave phase (e.g. electron and positron) decrease amplitude between particles, attracting the particles.

The following are simulations of particles with longitudinal waves of same phase and opposite phase, modeled by Gabriel LaFreniere.

**Repelling Force** – Two electrons of same wave phase increasing amplitude between particles

**Attractive Force** – Electron and positron of opposite wave phase decreasing amplitude between particles

### Why Particle Group Count (Q)?

To unify force equations. Measurements are rarely a single particle affecting another particle. More often, it is a group of particles separated at distance that are being calculated for their force, typically based on size, and based on the properties of:

**Charge**– calculating forces of particles as seen in the electric force and magnetic force**Mass**– calculating forces of objects formed from atoms (e.g. people, cars, planets) as seen in the gravitational force and Newton’s laws of motion

What’s common in these variables for charge and mass? They are both based on the number of particles in a group. Charge is based on the total number of particles with elementary charge in a group. Mass is based on the sum of all particle masses in a group. These variables are simply measurements of particles with different wave properties and different units, as explained in further detail here. The common item in both variables is the count of particles (Q). When this is used, all force equations can be unified.

*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).*

**Equation**

In simple terms using two groups (Q) of particles separated at distance (r), and the properties of the electron’s energy and radius (E_{e }and r_{e}), the electric force of an electron is shown below. It is the “fundamental” force.

**Electric Force**

Using classical constants | Using energy wave constants |

**Proof**

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

- Derived the electron’s mass and energy –
*from the energy form of the force equation* - Derived Coulomb’s Law and Coulomb’s constant.
- Calculations of electric forces –
*see example calculation below*

### Single Proton and Electron at Bohr Radius (*Hydrogen*) – Calculation

The calculation is shown with the electric force equation in **two formats** (classical constants and wave constants). Both result in the same solution.

**Variables:**

- Q
_{1}**=**1 (*proton*) - Q
_{2}**= –**1 (*electron*) - r = a
_{0}= 5.2918E-11 m (*Bohr radius*)

**Equation #1: **Electric Force Equation – Classical Format**Result: –**8.239E-8 newtons (kg m/s^{2})

**Equation #2: **Electric Force Equation – Wave Format**Result: –**8.239E-8 newtons (kg m/s^{2})

**Comments:** There is no difference (0.000%) from the Coulomb force calculation using either formats. Also, the value is equal to the orbital force at this location, for the electron’s position in hydrogen.

A summary of various electric force calculations is found on this site; more detailed calculations with instructions to reproduce these calculations is found in the *Forces* paper.