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

From S.H.O.
Jump to: navigation, search
(→‎Dislocations)
 
(19 intermediate revisions by the same user not shown)
Line 1: Line 1:
 +
{{#seo:
 +
|title=The Anatomy of a Physical Expression @ The Function Conjunction [Sho Drives Wiki]
 +
|titlemode=replace
 +
|keywords=electricity,magnetism,motor,generator
 +
|description=Our own way to chop down a physical equation into building blocks.
 +
}}
 
{{DISPLAYTITLE:Function Conjunction → The Anatomy of a Physical Expression}}
 
{{DISPLAYTITLE:Function Conjunction → The Anatomy of a Physical Expression}}
 
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:
 
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:
Line 15: Line 21:
 
|-
 
|-
 
! Constant (or 1)
 
! Constant (or 1)
−
!rowspan=2 valign=top|<math>\times</math>
+
| <math>\times</math>
 +
|-
 
! Coefficient (or 1)
 
! Coefficient (or 1)
−
!rowspan=2 valign=top|<math>\times</math>
+
| <math>\times</math>
 +
|-
 
! Quantity (or 1)
 
! Quantity (or 1)
−
!rowspan=2 valign=top|<math>\times</math>
+
| <math>\times</math>
 +
|-
 
! Proximity (or 1)
 
! Proximity (or 1)
−
!rowspan=2 valign=top|<math>\times</math>
+
| <math>\times</math>
 +
|-
 
! Dislocation (or 1)
 
! Dislocation (or 1)
−
!rowspan=2 valign=top|<math>\times</math>
+
| <math>\times</math>
 +
|-
 
! Direction (or 1)
 
! Direction (or 1)
 +
| <math>=</math>
 +
|-
 +
!colspan=2| A Physical Expression
 
|}
 
|}
 
</div>
 
</div>
  
 
===Constants===
 
===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
 
* <math>c</math> = Speed of Light
 
* <math>G</math> = Gravitational constant
 
* <math>G</math> = Gravitational constant
 +
* <math>k_B</math> = Boltzmann's constant
 +
* <math>\alpha</math> = Fine Structure constant
 +
* <math>\mu_0</math> = Magnetic Permeability of Free Space
 +
* <math>\epsilon_0</math> = Electric Permittivity of Free Space
  
 
===Coefficients===
 
===Coefficients===
Line 42: Line 56:
 
===Quantities===
 
===Quantities===
 
* <math>q</math> = point charge
 
* <math>q</math> = point charge
−
* <math>\lambda_q</math> = linear charge density (for continuous charge)
+
* <math>\lambda_q</math> = linear charge density {{nobr|(for continuous charge)}}
−
* <math>\sigma_q</math> = surface charge density (for continuous charge)
+
* <math>\sigma_q</math> = surface charge density {{nobr|(for continuous charge)}}
−
* <math>\rho_q</math> = volume charge density (for continuous charge)
+
* <math>\rho_q</math> = volume charge density {{nobr|(for continuous charge)}}
 
* <math>m</math> = mass
 
* <math>m</math> = mass
 
* <math>\rho</math> = volume mass density
 
* <math>\rho</math> = volume mass density
Line 56: Line 70:
 
* <math>\mathbf{v}</math> = velocity
 
* <math>\mathbf{v}</math> = velocity
 
* <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 time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>
+
====Dislocations according to an inertial observer at time <math>t</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>\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>\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>\frac{∂\mathbf{r}}{∂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>
−
* <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{∂^2\mathbf{r}}{∂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>\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>\mathbf{r'}</math> = position a charge <math>q'</math> had 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{\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{∂\mathbf{r'}}{∂t}</math> = <math>\mathbf{\dot{r}'}</math> = velocity a charge <math>q'</math> had 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{∂^2\mathbf{r'}}{∂t^2}</math> = <math>\mathbf{\ddot{r}'}</math> = acceleration a charge <math>q'</math> had 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===
Line 67: Line 82:
 
* <math>\mathbf{\hat{v}}</math> = velocity unit vector
 
* <math>\mathbf{\hat{v}}</math> = velocity unit vector
 
* <math>\mathbf{\hat{a}}</math> = acceleration unit vector
 
* <math>\mathbf{\hat{a}}</math> = acceleration unit vector
−
* <math>\mathbf{\hat{r}}</math> = position unit vector of <math>q</math>
+
====Directions according to an inertial observer  at time <math>t</math>====
−
* <math>\mathbf{\hat{\dot{r}}}</math> = velocity unit vector of <math>q</math>
+
* <math>\mathbf{\hat{r}}</math> = position unit vector of <math>q</math> at time <math>t</math>
−
* <math>\mathbf{\hat{\ddot{r}}}</math> = acceleration unit vector of <math>q</math>
+
* <math>\mathbf{\hat{\dot{r}}}</math> = velocity unit vector of <math>q</math> at time <math>t</math>
−
* <math>\mathbf{\hat{r'}}</math> = position unit vector of <math>q'</math>
+
* <math>\mathbf{\hat{\ddot{r}}}</math> = acceleration unit vector of <math>q</math> at time <math>t</math>
−
* <math>\mathbf{\hat{\dot{r'}}}</math> = velocity unit vector of <math>q'</math>
+
* <math>\mathbf{\hat{r'}}</math> = position unit vector of <math>q'</math> at retarded time <math>t'</math>
−
* <math>\mathbf{\hat{\ddot{r'}}}</math> = acceleration unit vector of <math>q'</math>
+
* <math>\mathbf{\hat{\dot{r'}}}</math> = velocity unit vector of <math>q'</math> at retarded time <math>t'</math>
 +
* <math>\mathbf{\hat{\ddot{r'}}}</math> = acceleration unit vector of <math>q'</math> at retarded time <math>t'</math>
  
 
==See also==
 
==See also==
  
 +
* [[Magnetic Energy]]
 
* [[Functions composed of Physical Expressions]]
 
* [[Functions composed of Physical Expressions]]
 +
* [[Electromagnetic Potentials]]
  
 
{{Site map}}
 
{{Site map}}
 +
 +
[[Category:Function Conjunction]]

Latest revision as of 21:18, 4 July 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) =
A Physical Expression

Constants

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

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

  • x = position
  • v = velocity
  • a = acceleration

Dislocations according to an inertial observer at time t

  • r = position of a charge q at time t, when it receives a light signal from q′ that was emitted earlier at the retarded time t′=t−|r−r′|/c
  • ∂r∂t = ˙r = velocity of a charge q at time t, when it receives a light signal from q′ that was emitted earlier at the retarded time t′=t−|r−r′|/c
  • ∂2r∂t2 = ¨r = acceleration of a charge q at time t, when it receives a light signal from q′ that was emitted earlier at the retarded time t′=t−|r−r′|/c
  • r′ = position a charge q′ had 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
  • ∂r′∂t = ˙r′ = velocity a charge q′ had 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
  • ∂2r′∂t2 = ¨r′ = acceleration a charge q′ had 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

Directions according to an inertial observer at time t

  • ˆr = position unit vector of q at time t
  • ˆ˙r = velocity unit vector of q at time t
  • ˆ¨r = acceleration unit vector of q at time t
  • ^r′ = position unit vector of q′ at retarded time t′
  • ^˙r′ = velocity unit vector of q′ at retarded time t′
  • ^¨r′ = acceleration unit vector of q′ at retarded time t′

See also

Site map

HQ ● Glossary ● April 2016 Presentation

Retrieved from "http://www.sho.wiki/index.php?title=The_Anatomy_of_a_Physical_Expression&oldid=949"