Difference between revisions of "Function Conjunction"

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''<math>\mathbf{A}</math> at <math>\left(\mathbf{r},t\right)</math> due to a point charge <math>q'</math> which had a velocity <math>\mathbf{v'}</math> at <math>\left(\mathbf{r'},t'\right)</math>'':
 
''<math>\mathbf{A}</math> at <math>\left(\mathbf{r},t\right)</math> due to a point charge <math>q'</math> which had a velocity <math>\mathbf{v'}</math> at <math>\left(\mathbf{r'},t'\right)</math>'':
  
−
<math>\mathbf{A}\left(\mathbf{r},\mathbf{r'},\mathbf{v}\right) = \underset{constant}{\frac{q'}{4\pi\ \epsilon}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v'}/c^2} = \underset{constant}{\frac{\mu_0\ q'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v'}}</math>
+
<math>\mathbf{A}\left(\mathbf{r},\mathbf{r'},\mathbf{v}\right) = \underset{constant}{\frac{q'}{4\pi\ \epsilon_0}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v'}/c^2} = \underset{constant}{\frac{\mu_0\ q'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v'}}</math>

Revision as of 12:44, 21 April 2016

The Anatomy of an 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 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 at (r,t) due to a point charge q′ at (r′,t′):

φ(r,r′)=q′4π ϵ0constant×1|r−r′|proximity

Magnetic vector potential A

A at (r,t) due to a point charge q′ which had a velocity v′ at (r′,t′):

A(r,r′,v)=q′4π ϵ0constant×1|r−r′|proximity×v′/c2dislocation=μ0 q′4πconstant×1|r−r′|proximity×v′dislocation

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