The Anatomy of a Physical Expression

The Anatomy of a Physical Expression, is simply put, a product of factors.

More specifically, a physical expression is a product of factors, each with their own distinct role in defining a property of a physical system. These factors come in several types:

Constants
Coefficients
Quantities
Proximities
Dislocations
Directions

Definition

Constant (or 1)	$\times$	Coefficient (or 1)	$\times$	Quantity (or 1)	$\times$	Proximity (or 1)	$\times$	Dislocation (or 1)	$\times$	Direction (or 1)

Constants

$\mu_0$ = Magnetic Permeability of Free Space
$\epsilon_0$ = Electric Permittivity of Free Space
$k_B$ = Boltzmann's constant
$\alpha$ = Fine Structure Constant
$c$ = Speed of Light
$G$ = Gravitational Constant

Coefficients

$\mu_r$ = Relative Magnetic Permeability of Free Space
$\epsilon_r$ = Relative Electric Permittivity of Free Space

Quantities

$q$ = point charge
$\lambda_q$ = linear charge density (for continuous charge)
$\sigma_q$ = surface charge density (for continuous charge)
$\rho_q$ = volume charge density (for continuous charge)
$m$ = mass
$\rho$ = volume mass density

Proximities

$\frac{1}{|\mathbf{r}-\mathbf{r'}|}$ = inverse of the magnitude of the separation between positions $\mathbf{r}$ and $\mathbf{r'}$
$\frac{1}{|\mathbf{r}-\mathbf{r'}|^2}$ = inverse square of the magnitude of the separation between positions $\mathbf{r}$ and $\mathbf{r'}$

Dislocations

$\mathbf{\hat{x}}$ = position
$\mathbf{\hat{v}}$ = velocity
$\mathbf{\hat{a}}$ = acceleration
$\mathbf{r}$ = position of a charge $q$ at time $t$ , when it receives a light signal from $q'$ that was emitted earlier at time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
$\frac{d\mathbf{r}}{dt}$ = velocity of a charge $q$ at time $t$ , when it receives a light signal from $q'$ that was emitted earlier at time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
$\frac{d^2\mathbf{r}}{dt^2}$ = acceleration of a charge $q$ at time $t$ , when it receives a light signal from $q'$ that was emitted earlier at time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
$\mathbf{r'}$ = position a charge $q'$ was at the retarded time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$ , when it emitted a light signal which has now reached $q$ at position $\mathbf{r}$ and time $t$
$\frac{d\mathbf{r'}}{dt}$ = velocity a charge $q'$ was at the retarded time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$ , when it emitted a light signal which has now reached $q$ at position $\mathbf{r}$ and time $t$
$\frac{d^2\mathbf{r'}}{dt^2}$ = acceleration a charge $q'$ was at the retarded time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$ , when it emitted a light signal which has now reached $q$ at position $\mathbf{r}$ and time $t$