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

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* <math>\mathbf{a}</math> = acceleration
 
* <math>\mathbf{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 the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</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>
βˆ’
* <math>\frac{d\mathbf{r}}{dt}</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{βˆ‚\mathbf{r}}{βˆ‚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>
βˆ’
* <math>\frac{d^2\mathbf{r}}{dt^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>\frac{βˆ‚^2\mathbf{r}}{βˆ‚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> 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>\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>
βˆ’
* <math>\frac{d\mathbf{r'}}{dt}</math> = <math>\mathbf{\dot{r}'}</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{βˆ‚\mathbf{r'}}{βˆ‚t}</math> = <math>\mathbf{\dot{r}'}</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>
βˆ’
* <math>\frac{d^2\mathbf{r'}}{dt^2}</math> = <math>\mathbf{\ddot{r}'}</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>
+
* <math>\frac{βˆ‚^2\mathbf{r'}}{βˆ‚t^2}</math> = <math>\mathbf{\ddot{r}'}</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===
 
===Directions===

Revision as of 01:06, 15 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

Constant (or 1) Γ—
Coefficient (or 1) Γ—
Quantity (or 1) Γ—
Proximity (or 1) Γ—
Dislocation (or 1) Γ—
Direction (or 1) =
A Physical Expression

Constants

  • c = Speed of Light
  • G = Gravitational constant
  • kB = Boltzmann's constant
  • Ξ± = Fine Structure constant
  • ΞΌ0 = Magnetic Permeability of Free Space
  • Ο΅0 = Electric Permittivity of Free Space

Coefficients

  • ΞΌr = Relative Magnetic Permeability
  • Ο΅r = Relative Electric Permittivity

Quantities

  • q = point charge
  • Ξ»q = linear charge density (for continuous charge)
  • Οƒq = surface charge density (for continuous charge)
  • ρq = volume charge density (for continuous charge)
  • m = mass
  • ρ = volume mass density

Proximities

  • 1|rβˆ’rβ€²| = inverse of the magnitude of the separation between positions r and rβ€²
  • 1|rβˆ’rβ€²|2 = inverse square of the magnitude of the separation between positions r and rβ€²

Dislocations

  • x = position
  • v = velocity
  • a = acceleration
  • r = position of a charge q at time t, when it receives a light signal from qβ€² that was emitted earlier at the retarded time tβ€²=tβˆ’|rβˆ’rβ€²|/c
  • βˆ‚rβˆ‚t = Λ™r = velocity of a charge q at time t, when it receives a light signal from qβ€² that was emitted earlier at the retarded time tβ€²=tβˆ’|rβˆ’rβ€²|/c
  • βˆ‚2rβˆ‚t2 = Β¨r = acceleration of a charge q at time t, when it receives a light signal from qβ€² that was emitted earlier at the retarded time tβ€²=tβˆ’|rβˆ’rβ€²|/c
  • rβ€² = position a charge qβ€² was at the retarded time tβ€²=tβˆ’|rβˆ’rβ€²|/c, when it emitted a light signal which has now reached q at position r and time t
  • βˆ‚rβ€²βˆ‚t = Λ™rβ€² = velocity a charge qβ€² was at the retarded time tβ€²=tβˆ’|rβˆ’rβ€²|/c, when it emitted a light signal which has now reached q at position r and time t
  • βˆ‚2rβ€²βˆ‚t2 = Β¨rβ€² = acceleration a charge qβ€² was at the retarded time tβ€²=tβˆ’|rβˆ’rβ€²|/c, when it emitted a light signal which has now reached q at position r and time t

Directions

  • Λ†x = position unit vector
  • Λ†v = velocity unit vector
  • Λ†a = acceleration unit vector
  • Λ†r = position unit vector of q at time t
  • Λ†Λ™r = velocity unit vector of q at time t
  • Λ†Β¨r = acceleration unit vector of q at time t
  • ^rβ€² = position unit vector of qβ€² at retarded time tβ€²
  • ^Λ™rβ€² = velocity unit vector of qβ€² at retarded time tβ€²
  • ^Β¨rβ€² = acceleration unit vector of qβ€² at retarded time tβ€²

See also

Site map

HQ ● Glossary ● April 2016 Presentation

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