Function Conjunction

The Anatomy of a Physical Expression

Constant	Coefficient	Quantity	Proximity	Dislocation	Direction
Examples: $\mu_0, \epsilon_0$ $k_B, \alpha, c$	Examples: $\mu_r, \epsilon_r$ $N$	Examples: $q,\lambda_q,\sigma_q,\rho_q$ $m,\rho$	Examples: $\frac{1}{|\mathbf{r}|}, \frac{1}{|\mathbf{r}|^2}$	Examples: $\mathbf{r}, \frac{d^2\mathbf{r}}{dt^2}, \frac{d^3\mathbf{r}}{dt^3}$ $\mathbf{r'}, \frac{d^2\mathbf{r'}}{dt^2}, \frac{d^3\mathbf{r'}}{dt^3}$ $\mathbf{x}, \mathbf{v}, \mathbf{a}, \beta$	Examples: $\mathbf{\hat{r}},\mathbf{\hat{\dot{r}}},\mathbf{\hat{\ddot{r}}}$ $\mathbf{\hat{x}}, \mathbf{\hat{v}}, \mathbf{\hat{a}}$

Functions Composed of Physical Expressions

Electric scalar potential $\mathbf{\varphi}$

$\mathbf{\varphi}$ of a point charge $q$:

$\mathbf{\varphi}\left(\mathbf{r},\mathbf{r'}\right) = \underset{constant}{\frac{q}{4\pi\ \epsilon_0}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}}$

Magnetic vector potential $A$

$\mathbf{A}$ of a moving point charge $q$:

$\mathbf{A}\left(\mathbf{r},\mathbf{r'},\mathbf{v}\right) = \underset{constant}{\frac{\mu_0\ q}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v}}$