Definition:CGS Unrationalized System

Definition

The CGS unrationalized system of units is a system of measurement in the field of electromagnetism.

There are two versions:

CGS Unrationalised Electromagnetic System

This is obtained by taking as the basis the equation for the Force between Infinite Parallel Straight Conductors carrying Steady Current:

$\mathbf F \propto \dfrac {2 I_1 I_2} r$

where:

$\mathbf F$ denotes the force between two parallel infinitely long conductors in a vacuum carrying steady currents $I_1$ and $I_2$

$r$ denotes the distance between $s_1$ and $s_2$.

Let us arrange it such that:

$\mathbf F$ is expressed in dynes

$r$ is expressed in centimetres

the constant of proportion is taken to be $1$

the current is the same in both conductors: $I_1 = I_2 = I$

The base unit of electric current is defined to be the electromagnetic unit:

the electric current $I$ such as to produce a force of $1$ dyne between the two conductors when positioned $1$ centimetre apart.

The constant of proportion plays the same role in this equation as the vacuum permeability of the SI system.

As a consequence of this, the vacuum permittivity works out as being $\dfrac 1 {c^2}$.

CGS Unrationalised Electrostatic System

From Coulomb's Law of Electrostatics, the force between two stationary charged particles $a$ and $b$ is given by:

$\mathbf F_{a b} \propto \dfrac {q_a q_b {\mathbf r_{a b} } } {r^3}$

where:

$\mathbf F_{a b}$ is the force exerted on $b$ by the electric charge on $a$

$\mathbf r_{a b}$ is the displacement vector from $a$ to $b$

$r$ is the distance between $a$ and $b$.

the constant of proportion is defined as being positive.

Let us arrange it such that:

$\mathbf F$ is expressed in dynes

$r$ is expressed in centimetres

the constant of proportion is taken to be $1$

the charge is the same on both charged particles: $q_1 = q_2 = Q$

The base unit of electric charge is defined to be the electrostatic unit:

the electric charge $Q$ such as to produce a force of $1$ dyne between the $a$ and $b$ when positioned $1$ centimetre apart.

The constant of proportion plays the same role in this equation as the vacuum permittivity of the SI system.

As a consequence of this, the vacuum permeability works out as being $\dfrac 1 {c^2}$.

Sources

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $2$. Physical Constants and Conversion Factors