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

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* <math>\mathbf{\hat{a}}</math> = acceleration
 
* <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>\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\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 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>\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 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>
−
* <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\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{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>  
+
* <math>\frac{d^2\mathbf{r'}}{dt^2}</math> = <math>\mathbf{\dot{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 00:23, 24 April 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) × Coefficient (or 1) × Quantity (or 1) × Proximity (or 1) × Dislocation (or 1) × Direction (or 1)

Constants

  • μ0 = Magnetic Permeability of Free Space
  • ϵ0 = Electric Permittivity of Free Space
  • kB = Boltzmann's constant
  • α = Fine Structure constant
  • c = Speed of Light
  • G = Gravitational constant

Coefficients

  • μr = Relative Magnetic Permeability
  • ϵr = Relative Electric Permittivity

Quantities

  • q = point charge
  • λq = linear charge density (for continuous charge)
  • σq = surface charge density (for continuous charge)
  • ρq = volume charge density (for continuous charge)
  • m = mass
  • ρ = volume mass density

Proximities

  • 1|r−r′| = inverse of the magnitude of the separation between positions r and r′
  • 1|r−r′|2 = inverse square of the magnitude of the separation between positions r and r′

Dislocations

  • ˆx = position
  • ˆv = velocity
  • ˆa = acceleration
  • 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−|r−r′|/c
  • drdt = ˙r = velocity of a charge q at time t, when it receives a light signal from q′ that was emitted earlier at time t′=t−|r−r′|/c
  • d2rdt2 = ¨r = acceleration of a charge q at time t, when it receives a light signal from q′ that was emitted earlier at time t′=t−|r−r′|/c
  • r′ = position a charge q′ was at the retarded time t′=t−|r−r′|/c, when it emitted a light signal which has now reached q at position r and time t
  • dr′dt = ˙r′ = velocity a charge q′ was at the retarded time t′=t−|r−r′|/c, when it emitted a light signal which has now reached q at position r and time t
  • d2r′dt2 = ˙r″ = acceleration a charge q′ was at the retarded time t′=t−|r−r′|/c, when it emitted a light signal which has now reached q at position r and time t

Directions

  • ˆx = position unit vector
  • ˆv = velocity unit vector
  • ˆa = acceleration unit vector
  • ˆr = position unit vector of q
  • ˆ˙r = velocity unit vector of q
  • ˆ¨r = acceleration unit vector of q
  • ^r′ = position unit vector of q′
  • ^˙r′ = velocity unit vector of q′
  • ^¨r′ = acceleration unit vector of q′

Site map

HQ ● Glossary ● April 2016 Presentation

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