## Introduction

Heaviside-Lorentz units (named for O. Heaviside and H.A. Lorentz) constitute a particular extension of CGS units which are most often useful in theoretical electrodynamics. As a practical system of units, Heaviside-Lorentz falls short due to most measureable quantities being excessively small or big for intuition. Neverless, Heaviside-Lorentz showcases the simplicity and beauty of the electromagnetic equations more than both SI and CGS systems.

The primary motivation behind Heaviside-Lorentz units is the setting of the vacuum permittivity and vacuum permeability both to 1 while retaining factors of found in the SI equations. Factors of (the speed of light) are included as needed to fix units (just as with CGS units).

## Units of Primary Electromagnetic Quantities

### Fields

The units of , , , , , and are the same in Heaviside-Lorentz. Units for these quantities are:

- In order to obtain units of and : multiply by units of length
- In order to obtain units of , , and : multiply by units of length squared

### Charge and Flux

The units of , , and are also the same in Heaviside-Lorentz. Units for these quantities are:

- In order to obtain units of and : divide by units of length
- In order to obtain units of , , , , , and : divide by units of length squared

### Potentials

In like fashion, the units of and are the same in Heaviside-Lorentz. Units for these quantities are:

- In order to obtain units of , , and : multiply by units of length
- In order to obtain units of , , , , , and : divide by units of length

## The Maxwell Equations

The Maxwell equations (microscopic form) can be written elegantly in Heaviside-Lorentz units.

## The Lorentz Force Law

There is a minor modification to the Lorentz force law compared to the well-known SI version. We must include a factor of in the magnetic force term in order to obtain proper Heaviside-Lorentz units. For a particle with trajectory we write:

## Other Electromagnetic Quantities

Force:

Energy:

Power:

Electric Diploe Moment:

Magnetic Diploe Moment:

Electric Susceptibility:

(unitless)

Magnetic Susceptibility:

(unitless)

Resistivity:

Conductivity:

Voltage:

Current:

Resistance:

Capacitance:

Inductance:

Bulk Current Density:

Volume Charge Density:

Surface Charge Density:

Line Charge Density:

This is not intended to be a full exploration of every electromagnetic quantity in Heaviside-Lorentz units. Rather, this is a starting point for further study and use of this unit system. NASA has produced a useful resource for help determining the units of other quantities of interest.

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