Difference between revisions of "The Anatomy of a Physical Expression"

Revision as of 13:16, 22 May 2016

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

Constants

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

Coefficients

• [math]\mu_r[/math] = Relative Magnetic Permeability
• [math]\epsilon_r[/math] = Relative Electric Permittivity

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

• [math]\frac{1}{|\mathbf{r}-\mathbf{r'}|}[/math] = inverse of the magnitude of the separation between positions [math]\mathbf{r}[/math] and [math]\mathbf{r'}[/math]
• [math]\frac{1}{|\mathbf{r}-\mathbf{r'}|^2}[/math] = inverse square of the magnitude of the separation between positions [math]\mathbf{r}[/math] and [math]\mathbf{r'}[/math]

Dislocations

• [math]\mathbf{x}[/math] = position
• [math]\mathbf{v}[/math] = velocity
• [math]\mathbf{a}[/math] = acceleration

Dislocations according to an inertial observer at time [math]t[/math]

• [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 the retarded time [math]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math]
• [math]\frac{∂\mathbf{r}}{∂t}[/math] = [math]\mathbf{\dot{r}}[/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 the retarded time [math]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math]
• [math]\frac{∂^2\mathbf{r}}{∂t^2}[/math] = [math]\mathbf{\ddot{r}}[/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 the retarded time [math]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math]
• [math]\mathbf{r'}[/math] = position a charge [math]q'[/math] had at the retarded time [math]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math], 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{∂\mathbf{r'}}{∂t}[/math] = [math]\mathbf{\dot{r}'}[/math] = velocity a charge [math]q'[/math] had at the retarded time [math]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math], 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{∂^2\mathbf{r'}}{∂t^2}[/math] = [math]\mathbf{\ddot{r}'}[/math] = acceleration a charge [math]q'[/math] had at the retarded time [math]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math], 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

Directions according to an inertial observer at time [math]t[/math]

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

See also

• Functions composed of Physical Expressions

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