§ 1. 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).....................................73a,b

 

 

Maxwell's curl equations (equ 73a,b) are expanded to form,

 

 

dE_z/dy - dE_y/dz = - dB_x/dt...........................................................................74

 

dE_x/dz - dE_z/dx = - dB_y/dt...........................................................................75

 

dE_y/dx - dE_x/dy = - dB_z/dt...........................................................................76

 

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

 

dB_z/dy - dB_y/dz = 1/c (dE_x/dt)....................................................................77

 

dB_x/dz - dB_z/dx = 1/c (dE_y/dt)....................................................................78

 

dB_y/dx - dB_x/dy = 1/c (dE_z/dt)..................................................... ..............79

 

The z-direction electric transverse wave equations is derived using equations 74 and 78 by eliminating dE_y/dz and dB_z/dx  to form (Jenkins, p. 410),

 

 

 

dE_y/dz = 1/c (dB_x/dt)..............................dB_x/dz = 1/c (dE_y/dt)...................80a,b

 

 

Differentiating equation 80a, with the respect to d/dz, and equation 80b with respect to d/dt produces (Condon, p, 1-108),

 

 

d²E_y/d²z = 1/c (d²B_x/dtdz)......................d²B_x/dtdz = 1/c (d²E_y/d²t)...........81a,b

 

 

Equating equations 81a,b,

 

 

d²E_y/d²z = 1/c² (d²E_y/d²t)...........................................................................82

 

 

Differentiating equation 82a, with the respect to d/dt, and equation 82b with respect to d/dz produces ,

 

 

d²E_y/dtdz = 1/c (d²B_x/d²t)......................d²B_x/d²z = 1/c (d²E_y/dtdz)...........83a,b

 

 

Equating equations 83a,b forms,

 

 

d²B_x/d²z = 1/c² (d²B_x/d²t)..........................................................................84

 

 

Equations 82 and 84 are used to derive the z direction electromagnetic transverse wave equations of light (fig 17),

 

 

E_y = E_o cos(kz - wt) ĵ ..............................................................................85

 

B_x = B_o cos(kz -wt) î ................................................................................86

 

 

In the derivation of equations 80a,b, 14 of the 18 differential components that constitute Maxwell's equations are eliminated since an electromagnetic field within a volume forms a horizontal wave.

 

 

What do you think of the mathematic that is being depicted?

43 minutes ago, reerer said:

What do you think of the mathematic that is being depicted?

Why do you start with equation 73? 

Who did you copy this from? And why? What is the point? 

1 hour ago, reerer said:

What do you think of the mathematic that is being depicted?

 

Well I think that that the equations found at the end of your post, labelled 85 and 86 tell something important about the phase relationship between the magnetic component and the electric component of an electromagnetic wave.

Do you think either of those components could exist on their own?