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

Revision as of 22:44, 23 April 2016

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

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

Definition

Constants

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

Coefficients

• $\mu_r$ = Relative Magnetic Permeability of Free Space
• $\epsilon_r$ = Relative Electric Permittivity of Free Space

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

• $\mathbf{\hat{x}}$ = position
• $\mathbf{\hat{v}}$ = velocity
• $\mathbf{\hat{a}}$ = acceleration
• $\mathbf{r}$ = position of a charge $q$ at time $t$, when it receives a light signal from $q'$ that was emitted earlier at time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
• $\frac{d\mathbf{r}}{dt}$ = velocity of a charge $q$ at time $t$, when it receives a light signal from $q'$ that was emitted earlier at time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
• $\frac{d^2\mathbf{r}}{dt^2}$ = acceleration of a charge $q$ at time $t$, when it receives a light signal from $q'$ that was emitted earlier at time $t' = t - |\mathbf{r}-\mathbf{r'}|/c$
• $\mathbf{r'}$ = position a charge $q'$ was 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 $t$
• $\frac{d\mathbf{r'}}{dt}$ = velocity a charge $q'$ was 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 $t$
• $\frac{d^2\mathbf{r'}}{dt^2}$ = acceleration a charge $q'$ was 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
• $\mathbf{\hat{r}}$ = position unit vector of $q$
• $\mathbf{\hat{\dot{r}}}$ = velocity unit vector of $q$
• $\mathbf{\hat{\ddot{r}}}$ = acceleration unit vector of $q$
• $\mathbf{\hat{r'}}$ = position unit vector of $q'$
• $\mathbf{\hat{\dot{r'}}}$ = velocity unit vector of $q'$
• $\mathbf{\hat{\ddot{r'}}}$ = acceleration unit vector of $q'$

Site map

HQ ● Glossary ● April 2016 Presentation