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2017-11-07 21:21:05 UTC

§ 26. Maxwell's Equations

With the method developed in the derivation of the equations of the atomic orbitals allows for the derivation of Maxwell's equations and Maxwell's structure of light. Maxwell's electric curl equation is derived using Faraday's wire loop induction effect represented with the magnetic flux (fig 15),

emf = - ʃʃ (dB/dt)· dA...........................................89

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.......................................................90

Equating equations 89 and 90,

ʃ E · dl = - ʃʃ (dB/dt)· dA.......................................91

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

ʃ E · dl = - ʃʃ (∇ x E)· dA......................................92

Equating equations 91 and 92,

- ʃʃ(dB/dt)· dA = ʃʃ (∇ x E)· dA.............................93

Maxwell electric curl equation is derived using equation 93,

∇ x E = - dB/dt...................................................94

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 which violates Faraday's induction mechanism. Furthermore, Faraday's induction effect is not luminous yet Maxwell's equations are used to represent the structure of light. In addition, the magnetic flux of Faraday's induction effect is pointing in the direction of the propagation which represents a longitudinal magnetic wave yet Maxwell's electric curl equation is being used to derive the electromagnetic transverse wave equations of light.

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With the method developed in the derivation of the equations of the atomic orbitals allows for the derivation of Maxwell's equations and Maxwell's structure of light. Maxwell's electric curl equation is derived using Faraday's wire loop induction effect represented with the magnetic flux (fig 15),

emf = - ʃʃ (dB/dt)· dA...........................................89

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.......................................................90

Equating equations 89 and 90,

ʃ E · dl = - ʃʃ (dB/dt)· dA.......................................91

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

ʃ E · dl = - ʃʃ (∇ x E)· dA......................................92

Equating equations 91 and 92,

- ʃʃ(dB/dt)· dA = ʃʃ (∇ x E)· dA.............................93

Maxwell electric curl equation is derived using equation 93,

∇ x E = - dB/dt...................................................94

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 which violates Faraday's induction mechanism. Furthermore, Faraday's induction effect is not luminous yet Maxwell's equations are used to represent the structure of light. In addition, the magnetic flux of Faraday's induction effect is pointing in the direction of the propagation which represents a longitudinal magnetic wave yet Maxwell's electric curl equation is being used to derive the electromagnetic transverse wave equations of light.

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