In electromagnetism, a free moving particle charged particle has its electric and magnetic fields perpendicular to each other, and to the particle velocity. Is this true even if the photon is considered massive and that the Lorenz gauge condition is not satisfied?
I have found in a recent publication the orthogonality relations depend whether the electron is considered massive or mass-less. Visit the link below to read the full article.
http://www.jpier.org/PIERM/pierm34/18.13111603.pdf
I think you may be confused with electromagnetic waves, where the electric and magnetic field vectors are orthogonal to each other and to the ray direction.
For a moving charge, which can be considered a current , the magnetic field wraps
around the direction of motion, according to the fingers of the right hand rule.
The electirc field lines are a deformation of that of a stationary charge, with field lines coming out radially in all directions.
The photon has no rest mass, in the relativistic sense.
Dear Arbab,
You understood correctly.
Here is how de Broglie's double particle photon hypothesis allows representing localized photons, with their electric and magnetic aspects perpendicular to each other and to the direction of motion in space. See first paper below.
The very same is true by structure for the electromagnetic carrying energy of all elementary massive electromagnetic particles, which can be demonstrated with the Lorentz force equation when both fields are of equal density v=E/B. See second article.
https://www.omicsonline.com/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.pdf
Article Field Equations for Localized Photons and Relativistic Field...
Dear Juan,
The magnetic field of a moving charge with velocity v is given by the Biot-Savart law B=vxE/c^2 which is perpendicular to v and B using vector properties. May be you mean accelerating charge but not freely moving one.
B and v are perpendicular , but not in the same spatial position (esentially Ampere law)
A Lorenz transformation of a static charge to a uniformly moving frame leavs the electric field lines more perpendicular to the line of motion,so the net electric field is also perpendicular to v and B
so I guess we all essentially agree
You can find geometriies where the magnetic and electrical fields are imposed
from the outside (not the fields of the moving charge) where there are crossed
electric and magnetic fields, where the Lorenz forcé exactly compensates the electric forcé and the geometry is as you described. Important in the Hall effect.
Arbab
I would be careful about explaining electromagnetism in terms of 'perpendicularity'.
Although this is a common description, it is in fact merely a mathematical construct describing a phase relationship.
If you take the case of an AC sinusoidal current moving in a wire, both the electric and the magnetic fields can be measured at any point around that wire, regardless of spatial position. However the absolute values on whatever scales you are using are 'out of phase' by what is assumed, mathematically to be 90 degrees in the sinusoidal frame of reference.
The perpendicular aspect you see in the text books is just a graphical representation of the mathematical explanation of this.
Similarly the construct around an atom or a photon is phase-space not 'spatial-space'
Ian
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