Related papers: The Fields of a Charged Particle in Hyperbolic Mot…
We find the electric field of a point charge in `truncated hyperbolic motion', in which the charge moves at a constant velocity followed by motion with a constant acceleration in its instantaneous rest frame. The same Lienard-Wiechert…
Calculating the electromagnetic field of a uniformly accelerated charged particle is a surprisingly subtle problem that has been long discussed in the literature. While the correct field has been obtained many times and through various…
The problem of the motion of a charged particle in an electric dipole field is used to illustrate that the Hamilton-Jacobi method does not necessarily give all solutions to the equations of motion of a mechanical system. The mathematical…
Electromagnetic waves propagate with the speed of light. The reason is that electrostatic fields as well as magnetic fields propagate with this speed. Both types of objects, waves as well as static fields contain and transport energy.…
The change of the electromagnetic field in a particular place due to the event of a change in the motion of a charged particle can occur only after the light signal from the event can reach this place. Naive calculations of the…
A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of…
The electric field of a uniformly accelerated charge shows a plane of discontinuity, where the field extending only on one side of the plane, terminates abruptly on the plane with a finite value. This indicates a non-zero divergence of the…
As a simple application of special conformal transformations, we derive the electromagnetic field produced by an electric charge in hyperbolic motion. Unlike other purely algebraic derivations, here we develop a more intuitive geometrical…
We give a rigorous derivation of a theorem showing that charged particles in an arbitrary electromagnetic field with at least one ignorable spatial coordinate remain forever tied to a given magnetic-field line. Such a situation contrasts…
The paradox of a free falling radiating charged particle in a gravitational field, is a well-known fascinating conceptual challenge that involves classical electrodynamics and general relativity. We discuss this paradox considering the…
We systematically examine all possible Gauss laws obeying spatial rotation symmetry, characterising the corresponding conserved charges. In the case of conserved higher moments, this gives rise to fractonic behaviour. We show that many…
It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never…
The Inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. Obtained formulae allow calculation of the position and dynamics of the dipole which…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
The energy-impulse flow of electromagnetic field, produced by the arbitrary moving charged particle, through the sphere of large radius is calculated. The result formulae are used in problem of radiation produced by hyperbolically moving…
The determination of the electromagnetic field generated by a charge in hyperbolic motion is a classical problem for which the majority view is that the Li\'enard-Wiechert solution which implies that the charge radiates) is the correct one.…
It is commonly observed that objects in a gravitational field experience a rate of acceleration that is independent of their mass and that, as a result, all massive objects with the same initial conditions follow the same trajectory. It is…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these…
We present a few charge distributions for which the application of Gauss' law in its integral form, as typically outlined in standard textbooks, results in a contradiction. We identify the root cause of such contradictions and put forward a…