Functions composed of Physical Expressions - Revision history

S.H.O.: Undo revision 1706 by S.H.O. (talk)

2017-07-15T02:26:00Z

Undo revision 1706 by S.H.O. (talk)

S.H.O. at 02:25, 15 July 2017

2017-07-15T02:25:49Z

S.H.O. at 04:18, 5 July 2016

2016-07-05T04:18:52Z

S.H.O.: /* See also */

2016-06-30T02:18:57Z

‎See also

S.H.O.: /* See also */

2016-06-20T06:07:09Z

‎See also

S.H.O. at 00:09, 16 May 2016

2016-05-16T00:09:59Z

S.H.O. at 21:47, 15 May 2016

2016-05-15T21:47:30Z

S.H.O.: /* Lorentz Force for (q,q') */

2016-05-15T08:59:34Z

‎Lorentz Force for (q,q')

S.H.O.: /* Functions for an ordered pair of point charges (q,q') */

2016-05-15T08:56:40Z

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

S.H.O.: /* Lorentz Force for (q,q') */

2016-05-15T08:55:32Z

‎Lorentz Force for (q,q')

@@ Line 8: / Line 8: @@
 Math can be hard and physics can be even harder. But if that is your thing, continue on for more about '''Functions composed of Physical Expressions'''. For experts!
 :Or, if you want to the see the S.H.O. Drive [[Presentation]], check it out '''[[Presentation|here]]'''.
 ==Preface==

@@ Line 8: / Line 8: @@
 Math can be hard and physics can be even harder. But if that is your thing, continue on for more about '''Functions composed of Physical Expressions'''. For experts!
 :Or, if you want to the see the S.H.O. Drive [[Presentation]], check it out '''[[Presentation|here]]'''.
 ==Preface==

@@ Line 1: / Line 1: @@
 {{#seo:
-|title=Functions composed of Physical Expressions @ The Function Conjunction [Sho Drive Wiki]
+|title=Functions composed of Physical Expressions @ The Function Conjunction [Sho Drives Wiki]
 |titlemode=replace
 |keywords=electricity,magnetism,motor,generator

@@ Line 93: / Line 93: @@
 ==See also==
 * [[The Anatomy of a Physical Expression]]
 * [[Electromagnetic Potentials]]

@@ Line 94: / Line 94: @@
 * [[The Anatomy of a Physical Expression]]
 {{Site map}}
 [[Category:Function Conjunction]]

← Older revision		Revision as of 00:09, 16 May 2016
Line 1:		Line 1:
		+	{{#seo:
		+	\|title=Functions composed of Physical Expressions @ The Function Conjunction [Sho Drive Wiki]
		+	\|titlemode=replace
		+	\|keywords=electricity,magnetism,motor,generator
		+	\|description=Visit http://sho.wiki/ for tips, hints, and whys for all things Sho Drives related!
		+	}}
	{{DISPLAYTITLE:Function Conjunction → Functions composed of Physical Expressions}}		{{DISPLAYTITLE:Function Conjunction → Functions composed of Physical Expressions}}
		+	Math can be hard and physics can be even harder. But if that is your thing, continue on for more about '''Functions composed of Physical Expressions'''. For experts!
		+
		+	:Or, if you want to the see the S.H.O. Drive [[Presentation]], check it out '''[[Presentation\|here]]'''.
		+	==Preface==
		+
		+	Physics can be a challenging subject, especially in more difficult areas such as in quantum mechanics and string theory. However, the physics involved in classical electromagnetism is an intermediate level of difficulty. It's harder than Newtonian dynamics, but all of it exists in three dimensions of space + one dimension of time. No wormholes or hyper-dimensions here! Just classical electromagnetism. ''[[User:S.H.O.\|S.H.O.]] <sup>[[User_talk:S.H.O.\|talk]]</sup>'' 17:09, 15 May 2016 (PDT)
		+
	==Functions for a point charge <math>q'</math>==		==Functions for a point charge <math>q'</math>==

@@ Line 50: / Line 50: @@
 * <math>\mathbf{v} \times \left( \nabla \times \mathbf{A} \right)</math> = the cross product of the velocity <math>\mathbf{v}</math> of the charge <math>q</math> and the curl of the magnetic vector potential <math>\nabla \times \mathbf{A} = \mathbf{B}</math> due to charge <math>q'</math>.
-To restate from a previous section, the magnetic vector potential from a charge <math>q'</math> at the position <math>r</math> at <math>q</math> is:
+To restate from a previous section, the magnetic vector potential from a charge <math>q'</math> at the position <math>\mathbf{r}</math> at <math>q</math> is:
 : <math>\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) \quad = \quad \underset{constant}{\frac{\mu_0\ q'}{4\pi}} \quad \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \quad \underset{dislocation}{\frac{∂\mathbf{r'}}{∂t}}</math>
@@ Line 58: / Line 58: @@
 : <math>\frac{d}{dt}(xy) = \dfrac{dx}{dt}y + x\dfrac{dy}{dt}</math>.
-Therefore, the partial derivative of the magnetic vector potential at <math>r</math> due to <math>q'</math> with respect to time <math>t</math> is:
+Therefore, the partial derivative of the magnetic vector potential at <math>\mathbf{r}</math> due to <math>q'</math> with respect to time <math>t</math> is:
 : <math>\frac{∂\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right)}{∂t} \quad = \quad \underset{constant}{\frac{\mu_0\ q'}{4\pi}} \left[ \underset{proximity}{ \frac{ ∂\left[ \frac{1}{|\mathbf{r}-\mathbf{r'}|} \right] }{∂t}} \quad \underset{dislocation}{\frac{∂\mathbf{r'}}{∂t}} + \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \quad \underset{dislocation}{ \frac{ ∂\left[ \frac{∂\mathbf{r'}}{∂t} \right] }{∂t}} \right]</math>
@@ Line 67: / Line 67: @@
 |+ First term in the brackets
 |-
-|width=240 valign=top align=center| <math>\frac{ ∂\left[ \frac{1}{|\mathbf{r}-\mathbf{r'}|} \right] }{∂t}</math><br>The partial derivative, with respect to time <math>t</math>, of the proximity of the position <math>r</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t'</math>.
+|width=240 valign=top align=center| <math>\frac{ ∂\left[ \frac{1}{|\mathbf{r}-\mathbf{r'}|} \right] }{∂t}</math><br>The partial derivative, with respect to time <math>t</math>, of the proximity of the position <math>\mathbf{r}</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>.
 |width=240 valign=top align=center| <math>\frac{∂r'}{∂t}</math><br>According to an observer at time <math>t</math>: the 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>
 |}
@@ Line 74: / Line 74: @@
 |+ Second term in the brackets
 |-
-|width=240 valign=top align=center| <math>\frac{1}{|\mathbf{r}-\mathbf{r'}|}</math><br>The proximity of the position <math>r</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t'</math>.
+|width=240 valign=top align=center| <math>\frac{1}{|\mathbf{r}-\mathbf{r'}|}</math><br>The proximity of the position <math>\mathbf{r}</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t' = t - |\mathbf{r}-\mathbf{r'}|/c</math>.
 |width=240 valign=top align=center| <math>\frac{∂^2r'}{∂t^2}</math><br>According to an observer at time <math>t</math>: the 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>
 |}

@@ Line 67: / Line 67: @@
 |+ First term in the brackets
 |-
-|width=240 valign=top align=center| <math>\frac{ ∂\left[ \frac{1}{|\mathbf{r}-\mathbf{r'}|} \right] }{∂t}</math><br>= the partial derivative, with respect to time <math>t</math>, of the proximity of the position <math>r</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t'</math>.
+|width=240 valign=top align=center| <math>\frac{ ∂\left[ \frac{1}{|\mathbf{r}-\mathbf{r'}|} \right] }{∂t} =</math><br>The partial derivative, with respect to time <math>t</math>, of the proximity of the position <math>r</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t'</math>.
-|width=240 valign=top align=center| <math>\frac{∂r'}{∂t}</math><br>= According to an observer at time <math>t</math>: the 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>
+|width=240 valign=top align=center| <math>\frac{∂r'}{∂t} =</math><br>According to an observer at time <math>t</math>: the 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>
 |}
@@ Line 74: / Line 74: @@
 |+ Second term in the brackets
 |-
-|width=240 valign=top align=center| <math>\frac{1}{|\mathbf{r}-\mathbf{r'}|}</math><br>= the proximity of the position <math>r</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t'</math>.
+|width=240 valign=top align=center| <math>\frac{1}{|\mathbf{r}-\mathbf{r'}|} =</math><br>The proximity of the position <math>r</math> of <math>q</math> at time <math>t</math> to the position <math>r'</math> of <math>q'</math> at the retarded time <math>t'</math>.
-|width=240 valign=top align=center| <math>\frac{∂^2r'}{∂t^2}</math><br>= According to an observer at time <math>t</math>: the 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>
+|width=240 valign=top align=center| <math>\frac{∂^2r'}{∂t^2} =</math><br>According to an observer at time <math>t</math>: the 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>
 |}