scholarly journals The Dubious Authority of Maxwell’s Equations in Free Space

2021 ◽  
Author(s):  
Charles MacCluer
Keyword(s):  
Plane Wave ◽  
Free Space ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Uniform Plane

Because of the differential homogeneity of Maxwell's equations in free space, each solution can be additively perturbed in infinitely many ways into a physically unreasonable solution. Thus to be a solution holds no cachet. In particular, the traditional first example --- the uniform plane wave --- must be considered as only a metaphor.

scholarly journals The Dubious Authority of Maxwell’s Equations in Free Space

2021 ◽  
Author(s):  
Charles MacCluer
Keyword(s):  
Plane Wave ◽  
Free Space ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Uniform Plane

Because of the differential homogeneity of Maxwell's equations in free space, each solution can be additively perturbed in infinitely many ways into a physically unreasonable solution. Thus to be a solution holds no cachet. In particular, the traditional first example --- the uniform plane wave --- must be considered as only a metaphor.

Plane wave ℋ (curl; Ω) conforming finite elements for Maxwell's equations

2003 ◽  
Vol 31 (3) ◽  
pp. 272-283 ◽  
Author(s):  
P. D. Ledger ◽  
K. Morgan ◽  
O. Hassan ◽  
N. P. Weatherill
Keyword(s):  
Finite Elements ◽  
Plane Wave ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell fields satisfying Huygens's principle

1968 ◽  
Vol 64 (3) ◽  
pp. 779-785 ◽  
Author(s):  
H. P. Künzle
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Maxwell Fields ◽  
Wave Space

AbstractIt is shown that Huygens's principle holds for the solutions of Maxwell's equations for p-forms of all degrees in a gravitational plane wave space, while the solutions of the wave equation for 1, 2, and 3-forms, however, may have tails.

On Maxwell's equations in non-stationary media

2008 ◽  
Vol 366 (1871) ◽  
pp. 1781-1788 ◽  
Author(s):  
I Vorgul
Keyword(s):  
Analytical Solution ◽  
Plane Wave ◽  
Integral Equations ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Exact Analytical Solution ◽  
Charge Injection ◽  
Incident Field ◽  
Volterra Integral Equations ◽  
Numerical Investigations

Maxwell's equations formulated for media with gradually changing conductivity are reduced to Volterra integral equations. Analytical and numerical investigations of the equations are presented for the case of gradual splash-like change in conductivity. Splash-like change in medium parameters can model any discharge phenomena, growing plasma, charge injection, etc. Exact analytical solution for the resolvent is presented and different field behaviours are analysed for the incident field as a plane wave and as an impulse.

On the integration of Maxwell’s equations, and charge and dipole fields

1964 ◽  
Vol 279 (1379) ◽  
pp. 562-571 ◽  
Keyword(s):  
Electromagnetic Fields ◽  
Free Space ◽  
Integral Identity ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Direct Integration ◽  
Magnetic Dipoles ◽  
Dimensional Integral

It is shown how the direct integration of Maxwell’s equations for free space may be accomplished by using a four-dimensional integral identity constructed for this purpose. The method is applied to the calculation of the electromagnetic fields of moving electric charges, and electric and magnetic dipoles.

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