Difference between revisions of "Functions composed of Physical Expressions"

From S.H.O.
Jump to: navigation, search
(→‎Functions for an ordered pair of point charges (q,q'))
Line 20: Line 20:
 
A charge <math>q</math> subject to a magnetic vector potential <math>A</math> at <math>\left(\mathbf{r},t\right)</math> due to a point charge <math>q'</math> which had a velocity <math>\frac{d\mathbf{r'}}{dt}</math> at <math>\left(\mathbf{r'},t'\right)</math> has a potential momentum of:
 
A charge <math>q</math> subject to a magnetic vector potential <math>A</math> at <math>\left(\mathbf{r},t\right)</math> due to a point charge <math>q'</math> which had a velocity <math>\frac{d\mathbf{r'}}{dt}</math> at <math>\left(\mathbf{r'},t'\right)</math> has a potential momentum of:
  
−
<math>q\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) = \mathbf{\varphi}\left(\mathbf{r},\mathbf{r'}\right) \times \underset{constant}{\frac{1}{c^2}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}</math>
+
<math>q\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) = \mathbf{q\varphi}\left(\mathbf{r},\mathbf{r'}\right) \times \underset{constant}{\frac{1}{c^2}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}</math>
  
 
<math>q\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) =  \underset{constant}{\frac{\mu_0\ qq'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}</math>
 
<math>q\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) =  \underset{constant}{\frac{\mu_0\ qq'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}</math>

Revision as of 23:02, 14 May 2016

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 dr′dt 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

Functions for an ordered pair of point charges (q,q′)

A charge q subject to an electric scalar potential φ at (r,t) due to a point charge q′ at (r′,t′) has an electric potential energy of:

qφ(r,r′)=qq′4π ϵ0constant×1|r−r′|proximity

A charge q subject to a magnetic vector potential A at (r,t) due to a point charge q′ which had a velocity dr′dt at (r′,t′) has a potential momentum of:

qA(r,r′)=qφ(r,r′)×1c2constant×dr′dtdislocation

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

See also

Site map

HQ ● Glossary ● April 2016 Presentation

Retrieved from "http://www.sho.wiki/index.php?title=Functions_composed_of_Physical_Expressions&oldid=709"