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

Revision as of 21:20, 23 April 2016

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:

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

Definition

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

• [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{\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]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math]
• [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]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math]
• [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]t' = t - |\mathbf{r}-\mathbf{r'}|/c[/math]
• [math]\mathbf{r'}[/math] = position a charge [math]q'[/math] was 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{d\mathbf{r'}}{dt}[/math] = velocity a charge [math]q'[/math] was 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{d^2\mathbf{r'}}{dt^2}[/math] = acceleration a charge [math]q'[/math] was 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
• [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]

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