Difference between revisions of "Function Conjunction"

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(→‎Functions Composed of Physical Expressions)
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|valign=top| '''Examples:'''<br><math>q,\lambda_q,\sigma_q,\rho_q</math><br><math>m,\rho</math>
 
|valign=top| '''Examples:'''<br><math>q,\lambda_q,\sigma_q,\rho_q</math><br><math>m,\rho</math>
 
|valign=top| '''Examples:'''<br><math>\frac{1}{|\mathbf{r}|}, \frac{1}{|\mathbf{r}|^2}</math>
 
|valign=top| '''Examples:'''<br><math>\frac{1}{|\mathbf{r}|}, \frac{1}{|\mathbf{r}|^2}</math>
−
|valign=top| '''Examples:'''<br><math>\mathbf{r}, \frac{d^2\mathbf{r}}{dt^2}, \frac{d^3\mathbf{r}}{dt^3}</math><br><math>\mathbf{r'}, \frac{d^2\mathbf{r'}}{dt^2}, \frac{d^3\mathbf{r'}}{dt^3}</math><br><math>\mathbf{x}, \mathbf{v}, \mathbf{a}, \beta</math>
+
|valign=top| '''Examples:'''<br><math>\mathbf{r}, \frac{d\mathbf{r}}{dt}, \frac{d^2\mathbf{r}}{dt^2}</math><br><math>\mathbf{r'}, \frac{d\mathbf{r'}}{dt}, \frac{d^2\mathbf{r'}}{dt^2}</math><br><math>\mathbf{x}, \mathbf{v}, \mathbf{a}, \beta</math>
−
|valign=top| '''Examples:'''<br><math>\mathbf{\hat{r}},\mathbf{\hat{\dot{r}}},\mathbf{\hat{\ddot{r}}}</math><br><math>\mathbf{\hat{x}}, \mathbf{\hat{v}}, \mathbf{\hat{a}}</math>
+
|valign=top| '''Examples:'''<br><math>\mathbf{\hat{r}},\mathbf{\hat{\dot{r}}},\mathbf{\hat{\ddot{r}}}</math><br><math>\mathbf{\hat{r'}},\mathbf{\hat{\dot{r'}}},\mathbf{\hat{\ddot{r'}}}</math><br><math>\mathbf{\hat{x}}, \mathbf{\hat{v}}, \mathbf{\hat{a}}</math>
 
|}
 
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 +
 +
===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
 +
 +
===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
 +
 +
===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>\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^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>
  
 
==Functions Composed of Physical Expressions==
 
==Functions Composed of Physical Expressions==

Revision as of 12:06, 21 April 2016

The Anatomy of a Physical 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 at which a light signal is emitted at the retarded time t′=t−|r−r′|/c
  • dr′dt = velocity of the source of the light signal at the retarded time t′=t−|r−r′|/c
  • d2r′dt2 = acceleration of the source of the light signal at the retarded time t′=t−|r−r′|/c

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

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