# Function Conjunction → The Anatomy of a Physical Expression

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Factors serve as The Anatomy of a Physical Expression. They come in several types as listed below, each characterized as having a distinct role in defining a property of a physical system. The following list items are partially underlined to make memorization easy:

1. Constants
2. Coefficients
3. Quantities
4. Proximities
5. Dislocations
6. Directions

## Definition

 Constant (or 1) $\times$ $\times$ $\times$ $\times$ $\times$ $=$

### Constants

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

### Coefficients

• $\mu_r$ = Relative Magnetic Permeability
• $\epsilon_r$ = Relative Electric Permittivity

### 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

• $\mathbf{x}$ = position
• $\mathbf{v}$ = velocity
• $\mathbf{a}$ = acceleration

#### Dislocations according to an inertial observer at time $t$

• $\mathbf{r}$ = position of a charge $q$ at time $t$, when it receives a light signal from $q'$ that was emitted earlier at the retarded time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
• $\frac{∂\mathbf{r}}{∂t}$ = $\mathbf{\dot{r}}$ = velocity of a charge $q$ at time $t$, when it receives a light signal from $q'$ that was emitted earlier at the retarded time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
• $\frac{∂^2\mathbf{r}}{∂t^2}$ = $\mathbf{\ddot{r}}$ = acceleration of a charge $q$ at time $t$, when it receives a light signal from $q'$ that was emitted earlier at the retarded time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
• $\mathbf{r'}$ = position a charge $q'$ had 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 $t$
• $\frac{∂\mathbf{r'}}{∂t}$ = $\mathbf{\dot{r}'}$ = velocity a charge $q'$ had 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 $t$
• $\frac{∂^2\mathbf{r'}}{∂t^2}$ = $\mathbf{\ddot{r}'}$ = acceleration a charge $q'$ had 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 $t$

### Directions

• $\mathbf{\hat{x}}$ = position unit vector
• $\mathbf{\hat{v}}$ = velocity unit vector
• $\mathbf{\hat{a}}$ = acceleration unit vector

#### Directions according to an inertial observer at time $t$

• $\mathbf{\hat{r}}$ = position unit vector of $q$ at time $t$
• $\mathbf{\hat{\dot{r}}}$ = velocity unit vector of $q$ at time $t$
• $\mathbf{\hat{\ddot{r}}}$ = acceleration unit vector of $q$ at time $t$
• $\mathbf{\hat{r'}}$ = position unit vector of $q'$ at retarded time $t'$
• $\mathbf{\hat{\dot{r'}}}$ = velocity unit vector of $q'$ at retarded time $t'$
• $\mathbf{\hat{\ddot{r'}}}$ = acceleration unit vector of $q'$ at retarded time $t'$

## Site map

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