Abbas Asgharian - Academia.edu (original) (raw)
Drafts by Abbas Asgharian
An analytical expression for displacement current density has been derived for both a line curren... more An analytical expression for displacement current density has been derived for both a line current and a current element or a point charge particle in motion. We have shown that the divergence of the inverse square field is zero, in contrast to the accepted notion that it is a delta function. As a result, Maxwell's equations are source-free and the displacement current density is free of divergence;furthermore, both the displacement current and magnetic field are produced simultaneously by a current.
In the past I have shown that Maxwell’s equations are source free Asgharian [1]. Unfortunately, m... more In the past I have shown that Maxwell’s equations are source free Asgharian [1]. Unfortunately, my
proof has not attracted notice. Here again I prove the same thing using a more elegant approach. This
method is very simple and I believe that the readers will find it interesting if they study it seriously.
It is shown that the solutions of the source-free Maxwell's equations are the same as those obtai... more It is shown that the solutions of the source-free Maxwell's equations are the same as those obtained from Maxwell's equations which contain the source, and that the choice of the Lorentz gauge is compulsory rather arbitrary.
We shall point out the source of error, which leads one to define a delta function. We show that ... more We shall point out the source of error, which leads one to define a delta function. We show that a similar argument applies to Stokes' theorem. Also using Stokes' theorem, once more we demonstrate that Maxwell's Equations are source-free. The divergence theorem is given by the following equation, τ (·F)dτ = s F·ds, (1) where τ is the volume bounded by the closed surface s. To simplify the argument, we choose a central field, i.e. F(r) = F (r)ˆ r, (2) wherê r is a unit vector in the direction of r. Substituting (2) in the right-hand side of (1) yields s F·ds = 4πr 2 F (r). (3) Note that the variable r is indefinite, i.e., 0 ≤ r < ∞. Substituting (2) in the left-hand side of (1), and writing the divergence operator in spherical coordinates, yields τ (·F)dτ = r Ω 1 r 2 ∂ ∂r [r 2 F (r)]r 2 drdΩ = r ∂ ∂r [4πr 2 F (r)]dr = 4πr 2 F (r). (4) Note again that the integral with respect to r is indefinite. Comparing (4) to (3) we observe the validity of the divergence theorem for any vector function F(r). We now elaborate on the case of the inverse square field vector, which has zero divergence and it is the subject of confusion. For example, the electric field of a point charge q is, E(r) = qˆr 4πr 2 , (5) which has zero divergence, ·E = 0. (6)
An analytical expression for displacement current density has been derived for both a line curren... more An analytical expression for displacement current density has been derived for both a line current and a current element or a point charge particle in motion. We have shown that the divergence of the inverse square field is zero, in contrast to the accepted notion that it is a delta function. As a result, Maxwell's equations are source-free and the displacement current density is free of divergence; furthermore, both the displacement current and magnetic field are produced simultaneously by a current. Résumé : Une expression analytique pour le courant densité de déplacement a ´ eté tirée pour un courant de ligne et un courantélément ou une particule point-chargée en marche. Nous avons demontré que le divergence de l'inverse square field est zéro, en contraste au notion accepteé que c'est une fonction delta. Conséquemment, leséquations de Maxwell sont source-free et le courant densité de déplacement n'a aucun divergence ; de plus les deux, le courant de déplacement et le champ magnétique sont produit simultanément par un courant.
Papers by Abbas Asgharian
![Research paper thumbnail of Comments on ‘‘Superposition and energy conservation for small amplitude mechanical waves’’ [Am. J. Phys. 54, 233 (1986)]](https://a.academia-assets.com/images/blank-paper.jpg)
](American Journal of Physics, 1988
An analytical expression for displacement current density has been derived for both a line curren... more An analytical expression for displacement current density has been derived for both a line current and a current element or a point charge particle in motion. We have shown that the divergence of the inverse square field is zero, in contrast to the accepted notion that it is a delta function. As a result, Maxwell's equations are source-free and the displacement current density is free of divergence;furthermore, both the displacement current and magnetic field are produced simultaneously by a current.
In the past I have shown that Maxwell’s equations are source free Asgharian [1]. Unfortunately, m... more In the past I have shown that Maxwell’s equations are source free Asgharian [1]. Unfortunately, my
proof has not attracted notice. Here again I prove the same thing using a more elegant approach. This
method is very simple and I believe that the readers will find it interesting if they study it seriously.
It is shown that the solutions of the source-free Maxwell's equations are the same as those obtai... more It is shown that the solutions of the source-free Maxwell's equations are the same as those obtained from Maxwell's equations which contain the source, and that the choice of the Lorentz gauge is compulsory rather arbitrary.
We shall point out the source of error, which leads one to define a delta function. We show that ... more We shall point out the source of error, which leads one to define a delta function. We show that a similar argument applies to Stokes' theorem. Also using Stokes' theorem, once more we demonstrate that Maxwell's Equations are source-free. The divergence theorem is given by the following equation, τ (·F)dτ = s F·ds, (1) where τ is the volume bounded by the closed surface s. To simplify the argument, we choose a central field, i.e. F(r) = F (r)ˆ r, (2) wherê r is a unit vector in the direction of r. Substituting (2) in the right-hand side of (1) yields s F·ds = 4πr 2 F (r). (3) Note that the variable r is indefinite, i.e., 0 ≤ r < ∞. Substituting (2) in the left-hand side of (1), and writing the divergence operator in spherical coordinates, yields τ (·F)dτ = r Ω 1 r 2 ∂ ∂r [r 2 F (r)]r 2 drdΩ = r ∂ ∂r [4πr 2 F (r)]dr = 4πr 2 F (r). (4) Note again that the integral with respect to r is indefinite. Comparing (4) to (3) we observe the validity of the divergence theorem for any vector function F(r). We now elaborate on the case of the inverse square field vector, which has zero divergence and it is the subject of confusion. For example, the electric field of a point charge q is, E(r) = qˆr 4πr 2 , (5) which has zero divergence, ·E = 0. (6)
An analytical expression for displacement current density has been derived for both a line curren... more An analytical expression for displacement current density has been derived for both a line current and a current element or a point charge particle in motion. We have shown that the divergence of the inverse square field is zero, in contrast to the accepted notion that it is a delta function. As a result, Maxwell's equations are source-free and the displacement current density is free of divergence; furthermore, both the displacement current and magnetic field are produced simultaneously by a current. Résumé : Une expression analytique pour le courant densité de déplacement a ´ eté tirée pour un courant de ligne et un courantélément ou une particule point-chargée en marche. Nous avons demontré que le divergence de l'inverse square field est zéro, en contraste au notion accepteé que c'est une fonction delta. Conséquemment, leséquations de Maxwell sont source-free et le courant densité de déplacement n'a aucun divergence ; de plus les deux, le courant de déplacement et le champ magnétique sont produit simultanément par un courant.