Electromagnetic Potentials - Revision history

S.H.O.: /* A New Idea: The Makerarc */

2017-07-15T02:55:06Z

‎A New Idea: The Makerarc

S.H.O. at 02:33, 15 July 2017

2017-07-15T02:33:15Z

S.H.O.: /* Deriving James Paul Wesley's additional force term in the case of co-linear current elements */

2017-03-26T21:44:14Z

‎Deriving James Paul Wesley's additional force term in the case of co-linear current elements

S.H.O.: /* Deriving James Paul Wesley's additional force term in the case of fixed current elements */

2017-03-26T19:22:15Z

‎Deriving James Paul Wesley's additional force term in the case of fixed current elements

S.H.O.: /* Deriving James Paul Wesley's additional force term in the case of fixed current elements */

2017-03-26T19:20:25Z

‎Deriving James Paul Wesley's additional force term in the case of fixed current elements

S.H.O. at 19:14, 26 March 2017

2017-03-26T19:14:56Z

S.H.O.: /* Deriving James Paul Wesley's additional force term in the case of fixed current elements */

2017-03-24T07:21:39Z

‎Deriving James Paul Wesley's additional force term in the case of fixed current elements

S.H.O.: /* Deriving James Paul Wesley's additional force term in the case of fixed current elements */

2017-03-24T07:20:48Z

‎Deriving James Paul Wesley's additional force term in the case of fixed current elements

S.H.O.: /* Deriving James Paul Wesley's additional force term in the case of fixed current elements */

2017-03-24T07:17:51Z

‎Deriving James Paul Wesley's additional force term in the case of fixed current elements

S.H.O. at 07:08, 24 March 2017

2017-03-24T07:08:56Z

← Older revision		Revision as of 02:55, 15 July 2017
Line 569:		Line 569:

	<youtube>https://www.youtube.com/watch?v=hFAOXdXZ5TM</youtube>		<youtube>https://www.youtube.com/watch?v=hFAOXdXZ5TM</youtube>
		+
		+	An attempt to produce the Makerarc back in March 2017<ref>https://www.facebook.com/Sho.Drives/videos/790278744462849/</ref> failed to demonstrate the predictions of the term <math>\mathbf{F}_r = \left( - Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} \right)_r</math><ref>https://www.facebook.com/Sho.Drives/videos/791514291005961/</ref> where I assumed that an external vector potential <math>\mathbf{A}</math> would lead to a force co-linear to current elements. This may be due to the supercurrent nature of electrons bounded to atoms, allowing atoms to be capable of preserving or "fixing" the amount of magnetic flux that passes through them, just as "macroscopic" superconducting currents do for superconductors, and therefore, by extension be capable of resisting changes in the magnetic vector potential. This does not negate the possibility of a Marinov Generator, as designed by Cyril Smith, because in his case the currents receiving power were inside a conductor where an externally applied vector potential is not fully shielded against, permitting <math>\mathbf{F}_r = \left( - Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} \right)_r</math> to yield a force. At the moment, I am still trying to decide on the correct model, but hopefully the surviving concept is similar to what I have developed so far in this page. Sincerely, ''[[User:S.H.O.\|S.H.O.]] <sup>[[User_talk:S.H.O.\|talk]]</sup>'' 19:55, 14 July 2017 (PDT)

	==Explaining "Altered" Lenz' Law Devices==		==Explaining "Altered" Lenz' Law Devices==

@@ Line 29: / Line 29: @@
 ==Novel Force laws proposed by various researchers==
-===James Paul Wesley's proposal===
+===James Wesley's proposal===
-James Paul Wesley proposed adding the "motional induction" on charge q. In SI Units, this can be expressed as:<ref name="Marinov Motor"/>
+James Wesley proposed adding the "motional induction" on charge q. In SI Units, this can be expressed as:<ref name="Marinov Motor"/>
 : <math>-q(\mathbf{v}\cdot\nabla)\mathbf{A}</math>
@@ Line 63: / Line 63: @@
 Consider the vector potential due a current-carrying wire on the x-axis. Both the current and the vector potential of this current point in the <math>+x</math> direction. Now have a charge approaching this wire perpendicularly. Both the magnetic Lorentz force and the additional Wesley term predict the same force. The proposed additional term is superfluous and would double the force of deflection if added.
-===Cyril William Smith's proposal===
+===Cyril Smith's proposal===
 Cyril Smith proposed adding the following gradient to the Lorentz force:<ref name="Marinov Generator"/>
@@ Line 266: / Line 266: @@
 :<math>\mathbf{E}_- = \frac{\mathbf{\hat{r}}}{r^2} \frac{1}{2c^2} \left( q_- \left(v_{x--}^2 + v_{y--}^2 - 2 v_{r--}^2\right) + q_+ \left(v_{x+-}^2 + v_{y+-}^2 - 2 v_{r+-}^2\right) \right)</math>
 :<math>\mathbf{E}_+ = \frac{\mathbf{\hat{r}}}{r^2} \frac{1}{2c^2} \left( q_- \left(v_{x-+}^2 + v_{y-+}^2 - 2 v_{r-+}^2\right) + q_+ \left(v_{x++}^2 + v_{y++}^2 - 2 v_{r++}^2\right) \right)</math>
 ===The Forces due to the Liénard–Wiechert electric fields for electrically-neutral currents===
@@ Line 483: / Line 483: @@
 :<math>d^2\mathbf{F} = \frac{\mu_0 \mathbf{\hat{r}}}{4\pi r^2} \left( 2 \mathbf{I}_r \cdot \mathbf{i}_r - \mathbf{I}_\theta \cdot \mathbf{i}_\theta \right)</math>
-===Deriving James Paul Wesley's additional force term in the case of co-linear current elements===
+===Deriving James Wesley's additional force term in the case of co-linear current elements===
-As pointed out above in the sub-section titled "James Paul Wesley's proposal", James Paul Wesley proposed adding the "motional induction" on charge <math>q</math>. In SI Units, this can be expressed as:<ref name="Marinov Motor"/>
+As pointed out above in the sub-section titled "James Wesley's proposal", James Wesley proposed adding the "motional induction" on charge <math>q</math>. In SI Units, this can be expressed as:<ref name="Marinov Motor"/>
 : <math>-q(\mathbf{v}\cdot\nabla)\mathbf{A}</math>
@@ Line 547: / Line 547: @@
 This is based on the directional derivative of vector potential <math>\mathbf{A}</math> along <math>Id\mathbf{L}</math>.
-It is important to note that the total force <math>\mathbf{F}_r</math> in <math>r</math> remains unaffected by the relative motion between the target current element <math>I_rd\mathbf{L}_r</math> and the source current element <math>i_rd\mathbf{l}_r</math> responsible for vector potential <math>\mathbf{A}_r</math>. However, forces <math>\mathbf{F}_{r-}</math> and <math>\mathbf{F}_{r+}</math> are affected by the relative speed <math>(v_{rel})_r</math> between the current elements in <math>r</math>, which leads to a kind of electromagnetic induction acting between co-linear current elements in relative motion in <math>r</math>. This feature may help to explain Cyril William Smith's "Marinov Generator"<ref name="Marinov Generator"/>.
+It is important to note that the total force <math>\mathbf{F}_r</math> in <math>r</math> remains unaffected by the relative motion between the target current element <math>I_rd\mathbf{L}_r</math> and the source current element <math>i_rd\mathbf{l}_r</math> responsible for vector potential <math>\mathbf{A}_r</math>. However, forces <math>\mathbf{F}_{r-}</math> and <math>\mathbf{F}_{r+}</math> are affected by the relative speed <math>(v_{rel})_r</math> between the current elements in <math>r</math>, which leads to a kind of electromagnetic induction acting between co-linear current elements in relative motion in <math>r</math>. This feature may help to explain Cyril Smith's "Marinov Generator"<ref name="Marinov Generator"/>.
 ==A New Idea: The Makerarc==
@@ Line 580: / Line 580: @@
 ==Explaining the Newman Motor==
-{{See also|Memory Lane#The Energy Machine of Joseph Newman}}
+{{See also|Memory Lane}}
 A Newman Motor-style coil and magnet arrangement, like that shown in the video below, have been simulated by me using JavaScript and THREE.js.

@@ Line 491: / Line 491: @@
 How may we derive the same result for current elements located and oriented along the same line? Equation 2b of the paper titled "Observations of the Marinov Motor"<ref name="Marinov Motor"/> can be adapted to the form above, resulting in:
-: <math>\mathbf{F} = -Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = Q_- \left(-\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = I \left( d\mathbf{L} \cdot \nabla \right) \mathbf{A} </math>
+: <math>\mathbf{F} = -Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = Q_- \left(-\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = - I \left( d\mathbf{L} \cdot \nabla \right) \mathbf{A} </math>
 In the case that we are dealing only with co-linear current elements, the result can be expressed as:
-: <math>\mathbf{F}_r = \left( -Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = Q_- \left(-\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = I \left( d\mathbf{L} \cdot \nabla \right) \mathbf{A} \right)_r</math>
+: <math>\mathbf{F}_r = \left( -Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = Q_- \left(-\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = - I \left( d\mathbf{L} \cdot \nabla \right) \mathbf{A} \right)_r</math>
 As stated in the parent section, the force on <math>Q_-</math> depends on:

@@ Line 483: / Line 483: @@
 :<math>d^2\mathbf{F} = \frac{\mu_0 \mathbf{\hat{r}}}{4\pi r^2} \left( 2 \mathbf{I}_r \cdot \mathbf{i}_r - \mathbf{I}_\theta \cdot \mathbf{i}_\theta \right)</math>
-===Deriving James Paul Wesley's additional force term in the case of fixed current elements===
+===Deriving James Paul Wesley's additional force term in the case of co-linear current elements===
 As pointed out above in the sub-section titled "James Paul Wesley's proposal", James Paul Wesley proposed adding the "motional induction" on charge <math>q</math>. In SI Units, this can be expressed as:<ref name="Marinov Motor"/>
@@ Line 489: / Line 489: @@
 : <math>-q(\mathbf{v}\cdot\nabla)\mathbf{A}</math>
-How may we derive the same result for current elements located and oriented along the same line which are effectively stationary? Equation 2b of the paper titled "Observations of the Marinov Motor"<ref name="Marinov Motor"/> can be adapted to the form above, resulting in:
+How may we derive the same result for current elements located and oriented along the same line? Equation 2b of the paper titled "Observations of the Marinov Motor"<ref name="Marinov Motor"/> can be adapted to the form above, resulting in:
 : <math>\mathbf{F} = -Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = Q_- \left(-\mathbf{V}_d \cdot \nabla \right) \mathbf{A} = I \left( d\mathbf{L} \cdot \nabla \right) \mathbf{A} </math>

@@ Line 547: / Line 547: @@
 This is based on the directional derivative of vector potential <math>\mathbf{A}</math> along <math>Id\mathbf{L}</math>.
-It is important to note that the total force <math>\mathbf{F}_r</math> in <math>r</math> remains unaffected by the relative motion between the target current element <math>Id\mathbf{L}</math> and the source current element <math>id\mathbf{l}</math> responsible for vector potential <math>\mathbf{A}</math>. However, forces <math>\mathbf{F}_{r-}</math> and <math>\mathbf{F}_{r+}</math> are affected by the relative speed <math>(v_{rel})_r</math> between the current elements in <math>r</math>, which leads to a kind of electromagnetic induction acting between co-linear current elements in relative motion in <math>r</math>. This feature may help to explain Cyril William Smith's "Marinov Generator"<ref name="Marinov Generator"/>.
+It is important to note that the total force <math>\mathbf{F}_r</math> in <math>r</math> remains unaffected by the relative motion between the target current element <math>I_rd\mathbf{L}_r</math> and the source current element <math>i_rd\mathbf{l}_r</math> responsible for vector potential <math>\mathbf{A}_r</math>. However, forces <math>\mathbf{F}_{r-}</math> and <math>\mathbf{F}_{r+}</math> are affected by the relative speed <math>(v_{rel})_r</math> between the current elements in <math>r</math>, which leads to a kind of electromagnetic induction acting between co-linear current elements in relative motion in <math>r</math>. This feature may help to explain Cyril William Smith's "Marinov Generator"<ref name="Marinov Generator"/>.
 ==A New Idea: The Makerarc==

@@ Line 154: / Line 154: @@
 The variables <math>v_x</math>, <math>v_y</math>, and <math>v_r</math> are mutually independent from each other. Therefore, the electric field <math>\mathbf{E}</math> can be split into three co-radial contributions:
-:<math>\mathbf{E}_x = q\ \frac{\mathbf{\hat{r}}}{r^2} \frac{v_x^2}{2c^2}</math>
+:<math>\mathbf{E}_x = + q\ \frac{\mathbf{\hat{r}}}{r^2} \frac{v_x^2}{2c^2}</math>
-:<math>\mathbf{E}_y = q\ \frac{\mathbf{\hat{r}}}{r^2} \frac{v_y^2}{2c^2}</math>
+:<math>\mathbf{E}_y = + q\ \frac{\mathbf{\hat{r}}}{r^2} \frac{v_y^2}{2c^2}</math>
-:<math>\mathbf{E}_r = q\ \frac{\mathbf{\hat{r}}}{r^2} \frac{v_r^2}{c^2}</math>
+:<math>\mathbf{E}_r = - q\ \frac{\mathbf{\hat{r}}}{r^2} \frac{v_r^2}{c^2}</math>
 Consider the existence of four charges:
@@ Line 514: / Line 514: @@
 As stated in the section "The Forces due to the Liénard–Wiechert electric fields for electrically-neutral currents", the electric forces on charges <math>Q_-</math> and <math>Q_+</math> are:
-:<math>\mathbf{F}_r- = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( v_{--}^2 - v_{+-}^2  \right)_r</math>
+:<math>\mathbf{F}_{r-} = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( v_{--}^2 - v_{+-}^2  \right)_r</math>
-:<math>\mathbf{F}_r+ = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( v_{++}^2 - v_{-+}^2  \right)_r</math>
+:<math>\mathbf{F}_{r+} = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( v_{++}^2 - v_{-+}^2  \right)_r</math>
 From this and above, it follows that:
-:<math>\mathbf{F}_r- = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d)  \right)_r</math>
+:<math>\mathbf{F}_{r-} = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d)  \right)_r</math>
-:<math>\mathbf{F}_r+ = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d)  \right)_r</math>
+:<math>\mathbf{F}_{r+} = + \frac{Q_+ q_+ \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d)  \right)_r</math>
 Therefore:
-:<math>\mathbf{F}_r- = + \frac{Q_- q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d) \right)_r</math>
+:<math>\mathbf{F}_{r-} = + \frac{Q_- q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d) \right)_r</math>
-:<math>\mathbf{F}_r+ = + \frac{Q_+ q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( + (v_d)(V_d) \right)_r</math>
+:<math>\mathbf{F}_{r+} = + \frac{Q_+ q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( + (v_d)(V_d) \right)_r</math>
 The effective electric fields experience by each charge is:
-:<math>\mathbf{E}_r- = + \frac{q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d) \right)_r</math>
+:<math>\mathbf{E}_{r-} = + \frac{q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( - (v_d)(V_d) \right)_r</math>
-:<math>\mathbf{E}_r+ = + \frac{q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( + (v_d)(V_d) \right)_r</math>
+:<math>\mathbf{E}_{r+} = + \frac{q_- \mathbf{\hat{r}}}{r^2} \frac{1}{c^2} \left( + (v_d)(V_d) \right)_r</math>
 Given that:

@@ Line 541: / Line 541: @@
 It can be shown that:
-:<math>\mathbf{F}_r_+ = \left( - Q_+ \left((-\mathbf{U}) \cdot \nabla \right) \mathbf{A} \right)_r</math>
+:<math>\mathbf{F}_{r+} = \left( - Q_+ \left((-\mathbf{U}) \cdot \nabla \right) \mathbf{A} \right)_r</math>
-:<math>\mathbf{F}_r_- = \left( - Q_- \left((+\mathbf{U}) \cdot \nabla \right) \mathbf{A} \right)_r</math>
+:<math>\mathbf{F}_{r-} = \left( - Q_- \left((+\mathbf{U}) \cdot \nabla \right) \mathbf{A} \right)_r</math>
-:<math>\mathbf{F}_r = \left( - Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} \right)_r = \mathbf{F}_r_- + \mathbf{F}_r_+</math>
+:<math>\mathbf{F}_r = \left( - Q_- \left(\mathbf{V}_d \cdot \nabla \right) \mathbf{A} \right)_r = \mathbf{F}_{r-} + \mathbf{F}_{r+}</math>
 This is based on the directional derivative of vector potential <math>\mathbf{A}</math> along <math>Id\mathbf{L}</math>.
-It is important to note that the total force in <math>r</math> remains unaffected by the relative motion between the target current element <math>Id\mathbf{L}</math> and the source current element <math>id\mathbf{l}</math> responsible for vector potential <math>\mathbf{A}</math>.
+It is important to note that the total force <math>\mathbf{F}_r</math> in <math>r</math> remains unaffected by the relative motion between the target current element <math>Id\mathbf{L}</math> and the source current element <math>id\mathbf{l}</math> responsible for vector potential <math>\mathbf{A}</math>. However, forces <math>\mathbf{F}_{r-}</math> and <math>\mathbf{F}_{r+}</math> are affected by the relative speed <math>v_{rel}_r</math> between the current elements in <math>r</math>, which leads to a kind of electromagnetic induction acting between co-linear current elements in relative motion in <math>r</math>.
 ==A New Idea: The Makerarc==