Difference between revisions of "Function Conjunction"

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<math>\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) =  \underset{constant}{\frac{\mu_0\ q'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}</math>
 
<math>\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) =  \underset{constant}{\frac{\mu_0\ q'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}</math>
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Revision as of 21:58, 23 April 2016

The Anatomy of a Physical Expression

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

Coefficients

  • μr = Relative Magnetic Permeability of Free Space
  • ϵr = Relative Electric Permittivity of Free Space

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 = 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

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′

Functions Composed of Physical Expressions

Functions for a point charge q′

The electric scalar potential φ at (r,t) due to a point charge q′ at (r′,t′) is:

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

The magnetic vector potential A at (r,t) due to a point charge q′ which had a velocity v′ at (r′,t′) is:

A(r,r′)=φ(r,r′)×1c2constant×dr′dtdislocation

A(r,r′)=μ0 q′4πconstant×1|r−r′|proximity×dr′dtdislocation

Site map

HQ ● Glossary ● April 2016 Presentation

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