A Longitudinal Electromagnetic Beam Wave with Mechanical Sextuplet Property and An Electron Substructure Derived from The Wave

Yasutsugu O

Published on: 2024-02-09

Abstract

This paper proposes a system of three electromagnetic waves constituted the traverse waves and a longitudinal wave with mechanical sextuplet properties for the longitudinal direction, derived from one-dimensional Maxwell equations based on exact differential equation in the Cartesian coordinate system under invariable permittivity ε and permeability μ in empty space. So, the longitudinal function g(L) with the unit vector k, is defined as the momentum density ρ(M) k [Ns/Cub(m)] equal to DB k cross product of electric flux density D i and magnetic flux density B j, where i, j, k, are the unit vector in the x-axis, the y-axis, the z -axis for the wave to travel along at the speed of beam wave, respectively.

Therefore, the representative wave function g(t, z) is described:   The longitudinal wave is g(L) = A(L) Exp(4πj(ft-kz))/2, where the speed of beam wave b is defined as the square-rooted reciprocal of εμ in a mobile-self-medium, A(L) is amplitude of the longitudinal wave, f is the frequency and k is the wave number.

Total differentiating the momentum ρ(M), we can get wave function equations: the momentum density wave ρ(M) = b ρ(m), the energy function ρ(E) = b ρ(M), and the mass function ρ(m) = ε Sq(D) = μ Sq(B). Next, using the dimensional analysis, ρ(M) = DB [Ns/Cub(m)] = Quad(h) [Js/Quad(m)], when integrating both their hands with volume dV(=dxdydz) dz, so, M [Ns] ∫dz = ∫ρ(M)dVdz, the Planck constant, h [Js] = ∫Quad(h) dVdz. So, an electromagnetic indeterminacy equation: h = M Δz = E Δt, the energy equation E = nfh, the momentum equation, M = nkh, and the mass equation m = εμE. Moreover, an electron mass confined the three waves, m (e) = μSq(e)/4πR(e), where R(e) is the radius, e is elementary charge, and the electron radiates as a gamma beam in annihilating.