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  1. #1 Maxwell's equations 
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    MAXWELL EQUATIONS



    Maxwell's electric curl equation is derived using Faraday's wire loop induction effect represented with the magnetic flux (fig 24),





    emf = - ʃʃ (dB/dt) dA...........................................93





    A second wire loop emf equation is used that represents the internal electric field E that forms the wire loop emf,





    emf = ʃ E dl................................................ .......94





    Equating equations 89 and 90,





    ʃ E dl = - ʃʃ (dB/dt) dA.......................................95




    Using Stokes' theorem (Hecht, p. 649),





    ʃ E dl = - ʃʃ (∇ x E) dA......................................96





    Equating equations 91 and 92,




    - ʃʃ(dB/dt) dA = ʃʃ (∇ x E) dA.............................97





    Maxwell electric curl equation is derived using equation 93,





    ∇ x E = - dB/dt................................................ ...98





    Faraday's induction effect depicts an internal electric current that only forms within the conduction wire represented in equation 90 yet Maxwell's electric curl equation (equ 94) is used to represent an electric field of an electromagnetic light wave that exists in the space outside the conduction wire. Faraday's induction effect is not luminous yet Maxwell's equations are used to represent the structure of light, and, the magnetic flux of Faraday's induction effect is pointing in the direction of the propagating magnetic field which represents a longitudinal magnetic wave yet Maxwell's electric curl equation is used to derive equations that depict electromagnetic transverse waves.


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    Maxwell's magnetic curl equation is derived using Ampere's law (Hecht, p. 42),





    ʃ B dl = ui................................................ ..........99

    ..



    Maxwell electric current (dE/dt), that forms in the space between a varying capacitor (fig 25), is added to Ampere's law,





    ʃ B dl = ʃʃ (J + ε dE/dt) dA ..............................100





    Using Stokes' theorem, on the left side of equation 96 forms (Hecht, p. 649),





    ʃ B dl = ʃʃ (∇ x B) dA........................................101





    Equating equations 96 and 97 then using J = 0,





    ʃʃ (ε dE/dt) dA = ʃʃ (∇ x B) dA............................102





    Maxwell's magnetic curl equation is derived using equation 98,





    ∇ x B = 1/c (dE/dt)..............................................1 03





    Hecht's electric current (dE/dt) forms in the open space between the plates of a varying capacitor which conflicts with Faraday's induction effect that electric current only forms within the current wire. In Maxwell's derivation of Maxwell's equations, Maxwell only uses Faraday's induction effect to derive Maxwell's equations (Maxwell, Part III) yet Hecht's derivation of the magnetic curl equation is using a varying capacitor. Hecht is using Stokes' theorem to derive equations 92 and 97 that depict the equating of a line integral with a surface integral which is physically and mathematically invalid.




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    27. Maxwell's Structure of Light





    The electromagnetic transverse wave equations of light are derived using Maxwell's equations,





    ∇ x E = - dB/dt........................∇ x B = 1/c (dE/dt).....................................104a,b





    Maxwell's curl equations (equ 100a,b) are expanded to form,





    dEz/dy - dEy/dz = - dBx/dt................................................ ...........................105




    dEx/dz - dEz/dx = - dBy/dt................................................ ..........................106




    dEy/dx - dEx/dy = - dBz/dt................................................ ...........................107



    .................................................. .........




    dBz/dy - dBy/dz = 1/c (dEx/dt)............................................... .....................108




    dBx/dz - dBz/dx = 1/c (dEy/dt)............................................... ....................109




    dBy/dx - dBx/dy = 1/c (dEz/dt)............................................... ...... ..............110




    The z-direction electric transverse wave equations is derived using equations 101 and 105 by eliminating dEy/dz and dBz/dx to form (Jenkins, p. 410),




    dEy/dz = 1/c (dBx/dt)..............................dBx/dz = 1/c (dEy/dt)...................111a,b





    Differentiating equation 107a, with the respect to d/dz, and equation 107b with respect to d/dt produces (Condon, p, 1-108),





    d2Ey/d2z = 1/c (d2Bx/dtdz)......................d2Bx/dtdz = 1/c (d2Ey/d2t)...........112a,b





    Equating equations 108a,b,




    d2Ey/d2z = 1/c2 (d2Ey/d2t).............................................. ............................113




    Differentiating equation 107a, with the respect to d/dt, and equation 107b with respect to d/dz produces ,




    d2Ey/dtdz = 1/c (d2Bx/d2t)......................d2Bx/d2z = 1/c (d2Ey/dtdz)...........114a,b





    Equating equations 110a,b forms,



    d2Bx/d2z = 1/c2 (d2Bx/d2t).............................................. ............................115



    Equations 109 and 111 are used to derive the z direction electromagnetic transverse wave equations of light (fig 17),





    Ey = Eo cos(kz - wt) ĵ .................................................. ............................116



    Bx = Bo cos(kz -wt) .................................................. ..............................117



    To test the derivation, the z-directional electric and magnetic transverse wave equations of light (equ 112 & 113) are used in equation 107a,





    d/dz[Eo cos(kz - wt)] ĵ = - (1/c) d/dt[Bo cos(kz - wt)] .........................118





    Equation 114 forms,





    Eo ĵ = Bo .................................................. ..........................................119





    Equation 107a that is used to derive the electromagnetic transverse wave equations of light produces a unite vector catastrophe since equation 115 depicts the equating of the and ĵ unit vectors which is produced since Maxwell's equations represents electromagnetic longitudinal waves. Can anyone explain what is going on?



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  2. #2  
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    Quote Originally Posted by discovered799 View Post





    Equation 107a that is used to derive the electromagnetic transverse wave equations of light produces a unite vector catastrophe since equation 115 depicts the equating of the and ĵ unit vectors which is produced since Maxwell's equations represents electromagnetic longitudinal waves. Can anyone explain what is going on?
    You is what is going wrong, you are incapable of getting the math right. I'll give you a hint: your "equations" 116,117 are total rubbish. Can you figure out why? BTW, i thought you were gone, why did you come back? Yo post more crackpot stuff?
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    The math come out of book by Jenkins that has a PHD in physics! Do you have a PHD in physics? So, I humbly believe that Jenkins' math is correct. If it is not please by all means indicate where the mathematic is in error and I will try and contact the man if he is still alive and we can include him in your conservation. In addition, your statement that equations are incorrect is just maybe your own misunderstanding since those equations are the sinusiodinal electromagnetic wave equations of light that are found in any college physics text book. Also, the main part of what I have post can be found in any advance physics text book regarding Maxwell's equations but the derivation of Maxwell's structure of light which is extremely unique is limited to Jenkins and a few other books. Does anyone know why? Eagerly waiting for your response or lack of thereof.
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    Quote Originally Posted by discovered799 View Post
    The math come out of book by Jenkins that has a PHD in physics!
    But "equations" 116,117 are your "contribution". Complete garbage, to be only topped by the gross error in eq 118.



    are the sinusiodinal electromagnetic wave equations of light that are found in any college physics text book.
    But they "benefit" from your OWN errors. You don't see them, do you? Why don't you go troll one of the crank forums? This one is for mainstream science.
    Last edited by AndrewC; 04-08-2018 at 01:27 AM.
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    Equations 116 and 117 can be found in Jenkins and Condon's books. Maybe you could develop your argument so that I can analyse it more thoroughly, my good friend. Example, give more details but no links please. Use your own words and also try an be neutral since your aggressive tone is completely unnecessary and scaring my 7th grade class since we a jolly English from the great country of England. You are giving my girls nightmares and making them wet their beds!
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  6. #6  
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    Also, I could derive the electromagnetic wave equations that represents the electromagnetic transverse waves of light propagating in the y and x directions, if you would like to see it but since you are so so so smart or pretend to be why don't you do it so that I can see where you are at, baby. So, start deriving. Hikikomi gaeshi
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  7. #7  
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    Quote Originally Posted by discovered799 View Post
    Equations 116 and 117 can be found in Jenkins and Condon's books.
    ....NOT in the grossly ignorant form you posted them.


    Maybe you could develop your argument so that I can analyse it more thoroughly, my good friend. Example, give more details
    The errors stare you in the face. You copy stuff from books, you ADD your OWN errors amd you end up claiming that mainstream. basic science is wrong. Classic crackpot strategy.


    but no links please. Use your own words and also try an be neutral since your aggressive tone is completely unnecessary and scaring my 7th grade class since we a jolly English from the great country of England. You are giving my girls nightmares and making them wet their beds!
    Then , this forum is not for you. This is a mainstream science forum, not a place for cranks to push their rubbish.
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