Difference between revisions of "Function Conjunction"

From S.H.O.
Jump to: navigation, search
Line 1: Line 1:
−
==The Anatomy of a Physical Expression==
+
==The Anatomy of an Electromagnetic Expression==
  
 
{| class="wikitable"
 
{| class="wikitable"
Line 34: Line 34:
  
 
===Dislocations===
 
===Dislocations===
−
* <math>\mathbf{r'}</math> = position at which a light signal is emitted 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 time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>
−
* <math>\frac{d\mathbf{r'}}{dt}</math> = velocity of the source of the light signal at the retarded 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 the source of the light signal at the retarded 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>
  
 
==Functions Composed of Physical Expressions==
 
==Functions Composed of Physical Expressions==

Revision as of 12:29, 21 April 2016

The Anatomy of an Electromagnetic Expression

Constant Coefficient Quantity Proximity Dislocation Direction
Examples:
μ0,ϵ0
kB,α,c 		Examples:
μr,ϵr
N 		Examples:
q,λq,σq,ρq
m,ρ 		Examples:
1|r|,1|r|2 		Examples:
r,drdt,d2rdt2
r′,dr′dt,d2r′dt2
x,v,a,β 		Examples:
ˆr,ˆ˙r,ˆ¨r
^r′,^˙r′,^¨r′
ˆx,ˆv,ˆa

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

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

Dislocations

  • 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 = 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 = 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 = 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 = 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

Functions Composed of Physical Expressions

Electric scalar potential φ

φ of a point charge q:

φ(r,r′)=q4π ϵ0constant×1|r−r′|proximity

Magnetic vector potential A

A of a moving point charge q:

A(r,r′,v)=μ0 q4πconstant×1|r−r′|proximity×vdislocation

Retrieved from "http://www.sho.wiki/index.php?title=Function_Conjunction&oldid=417"