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)	[math]\times[/math]	Coefficient (or 1)	[math]\times[/math]	Quantity (or 1)	[math]\times[/math]	Proximity (or 1)	[math]\times[/math]	Dislocation (or 1)	[math]\times[/math]	Direction (or 1)

Constants

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

Coefficients

[math]\mu_r[/math] = Relative Magnetic Permeability of Free Space
[math]\epsilon_r[/math] = Relative Electric Permittivity of Free Space

Quantities

[math]q[/math] = point charge
[math]\lambda_q[/math] = linear charge density (for continuous charge)
[math]\sigma_q[/math] = surface charge density (for continuous charge)
[math]\rho_q[/math] = volume charge density (for continuous charge)
[math]m[/math] = mass
[math]\rho[/math] = volume mass density

Proximities

= inverse of the magnitude of the separation between positions [math]\mathbf{r}[/math] and [math]\mathbf{r'}[/math]
= inverse square of the magnitude of the separation between positions [math]\mathbf{r}[/math] and [math]\mathbf{r'}[/math]

Dislocations

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

Directions

[math]\mathbf{\hat{x}}[/math] = position unit vector
[math]\mathbf{\hat{v}}[/math] = velocity unit vector
[math]\mathbf{\hat{a}}[/math] = acceleration unit vector
[math]\mathbf{\hat{r}}[/math] = position unit vector of [math]q[/math]
[math]\mathbf{\hat{\dot{r}}}[/math] = velocity unit vector of [math]q[/math]
[math]\mathbf{\hat{\ddot{r}}}[/math] = acceleration unit vector of [math]q[/math]
[math]\mathbf{\hat{r'}}[/math] = position unit vector of [math]q'[/math]
[math]\mathbf{\hat{\dot{r'}}}[/math] = velocity unit vector of [math]q'[/math]
[math]\mathbf{\hat{\ddot{r'}}}[/math] = acceleration unit vector of [math]q'[/math]