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Jerrold Franklin

Publications and source records attributed to Jerrold Franklin.

At least 19 recordsLinked to original sources
arXiv2026

Discrete classical electromagnetism

The electric charges that make up charge distributions and currents in classical electromagnetism (EM) are point charge electrons with a fixed finite charge. This means that a truly continuous charge distribution or current cannot be formed because that would require infinitesimal charges. If the number of electrons in any distribution is very large, the distributions can be approximately continuous, and can be used in many applications, but the discrete character of the distributions has a major effect on other physical effects. We consider two of those effects in this paper. Does a point charge have infinite self-energy, and does a moving current loop have an electric dipole moment?

physics.gen-ph↗
arXiv2025

Infinite self energy?

The notion of an infinite electromagnetic self energy of point charges (presumably electrons) is accepted by many electromagnetic textbooks. See, for instance,\cite{jdj,dg,rf}. However, each of these sources acknowledge that they don't understand that result. In this paper, we show that electrons must be point particles with no electromagnetic self energy.

physics.class-ph↗
arXiv2025

Comment on "Magnetic moments in the Poynting theorem, Maxwell equations, Dirac equation, and QED"

The paper ``Magnetic moments in the Poynting theorem, Maxwell equations, Dirac equation, and QED", arXiv:2501.02022, by Peter J. Mohr, purports to show that Maxwell's equation, $\mathbf{\nabla}\cdot{\bf B}=0$, and Poynting's theorem require significant modications for the $\bf B$ field of a magnetic dipole. We show here that, because of critical errors in the paper, these claims are false, and that Maxwell's equation and the Poynting theorem are the same for a magnetic moment as for any other charge-current distribution.

physics.class-ph↗
arXiv2025

The nature of electromagnetic energy

We study the nature and location of electromagetic energy for two cases. The energy density for electromagnetic radiation is shown to be $\frac{1}{8π}(E^2+B^2)$, with the energy contained in the electromagnet fields. For a static charge distribution, the electromagnet energy is contained in the charge, with an energy density, $\frac{1}{2}ρϕ$, There is no energy outside the charge distribution. The electromagnetic fields do not contain the energy, and $\frac{1}{8π}(E^2+B^2)$ cannot be considered an energy density in this case. There is no ambiguity in either case as to where the energy is located.

physics.gen-ph↗
arXiv2024

Radiation reaction on an accelerating point charge

A point charge accelerating under the influence of an external force emits electromagnetic radiation that reduces the increase in its mechanical energy. This causes a reduction in the particle's acceleration. We derive the decrease in acceleration due to radiation reaction for a particle accelerating parallel to its velocity, and show that it has a negligible effect.

physics.class-ph↗
arXiv2024

What is the force on a magnetic dipole?

We show that attempts to modify the force on a magnetic dipole by introducing either hidden momentum or internal forces are not correct. The standard textbook result ${\bf F=\nabla(\bmu\cdot B)}$ is correct even in the presence of time dependent electromagnetic fields. Using this expression for the force, overall momentum (the sum of mechanical and electromagnetic momentum) is conserved in changing electromagnetic fields.

physics.class-ph↗
arXiv2022

Electromagnetic Power Emitted by an Accelerating Point Charge

We derive the rate of emission of electromagnetic energy by an accelerating point charge, with the acceleration and velocity in the result being taken at the present time in the motion of the accelerating charge. This contrasts with the usual textbook derivation, which calculates the energy radiated through the surface of a large sphere, and gives the rate of radiated energy in terms of the acceleration and velocity at an arbitrary retarded time.

physics.class-ph↗
arXiv2020

Complete Lorentz transformation of a charge-current density

It is generally assumed in the literature that a Lorentz transformation on a neutral current loop results in a moving current loop with a nonvanishing charge distribution and an electric dipole moment. We show in this paper that this is not, in fact, correct. The derivation that leads to the charge distribution was based on an incomplete Lorentz transformation, which transforms the charge-current four-vector $j^μ=[ρ({\bf r},t),{\bf j(r},t)]$, but not the space-time four-vector $x^μ=(t,{\bf r})$. We show that completing the Lorentz transformation by using the variable $t'$ in the moving frame, rather than keeping the rest frame time variable $t$, results in there being no induced charge density and no resulting electric dipole moment.

physics.gen-ph↗
arXiv2020

Quark model relations for b-baryon decay

Properties of b-baryon decay matrix elements (amplitudes) have been derived in a nonsymmetric quark model without any use of SU(6), SU(3), or SU(2) (isotopic spin) groups. Equalities between pairs of amplitudes are derived, and $Λ-Σ$ mixing is used to calculate the branching ratio for the transition $Λ_b\rightarrow Σ^0$.

hep-ph↗
arXiv2014

Electric field of a point charge in truncated hyperbolic motion

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 formula holds for the acceleration phase and the constant velocity phase of the charge's motion. The only modification is that the formula giving the retarded time is different for the two motions, and the acceleration is zero for the constant velocity motion. The electric field lines are continuous as the retarded time increases through the transition time between constant velocity and accelerated motion. As the transition time approaches negative infinity the electric field develops a delta function contribution that has been introduced by others as necessary to preserve Gauss's law for the electric field.

physics.class-ph↗
arXiv2014

The 'Sears paradox'

We resolve a paradox in special relativity proposed by F. W. Sears for the action of forces on a rigid body. In the paradox, a moving rigid rod is struck at different times by impulsive forces, but continues to move with unchanged velocity, with the forces having no effect. Our conclusion is that the usual laws of mechanics can be applied to a rigid body only in its rest system

physics.gen-ph↗
arXiv2013

The electromagnetic momentum of static charge-current distributions

The origin of electromagnetic momentum for general static charge-current distributions is examined. The electromagnetic momentum for static electromagnetic fields is derived by implementing conservation of momentum for the sum of mechanical momentum and electromagnetic momentum. The external force required to keep matter at rest during the production of the final static configuration produces the electromagnetic momentum. Examples of the electromagnetic momentum in static electric and magnetic fields are given. The `center of energy' theorem is shown to be violated by electromagnetic momentum. `Hidden momentum' is shown to be generally absent, and not to cancel electromagnetic momentum.

physics.gen-ph↗
arXiv2012

Green's functions for Neumann boundary conditions

Green's functions for Neumann boundary conditions have been considered in Math Physics and Electromagnetism textbooks, but special constraints and other properties required for Neumann boundary conditions have generally not been noticed or treated correctly. In this paper, we derive an appropriate Neumann Green's function with these constraints and properties incorporated.

physics.class-ph↗
arXiv2012

Rigid body motion in special relativity

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term `rigid body' in relativistic straight line motion. We show that the definition of `rigid body' in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe: 1. The motion of a rigid body undergoing constant acceleration to a given velocity. 2. The acceleration of a rigid body due to an applied impulse. 3. Collisions between rigid bodies.

physics.gen-ph↗
arXiv2011

Superluminal neutrinos

The superluminal propagation of neutrinos observed by the OPERA collaboration can be explained by an energy dependent potential for the neutrino beam in passage through the Earth.

physics.gen-ph↗
arXiv2011

Comment on 'Frozen time in hyperbolic spacetime motion'

We show that the conclusion in version 3 of the paper 'Frozen time in hyperbolic spacetime motion' that time does not move in a spaceship undergoing hyperbolic motion is wrong because of a trivial error in interpreting the distance and time variables used in the paper, and because it now incorrectly states that "Hyperbolic motion does not imply constant acceleration."

physics.gen-ph↗
arXiv2011

Comment on [arXiv:1009.5250] "Electromagnetic mass differences of SU(3) baryons within a chiral soliton model"

In a recent letter, several electromagnetic mass difference formulae for baryons were presented. However, because the derivation did not include important colormagnetic terms, the mass relations do not correctly give isospin mass splittings for the baryons. Correct mass formulae were published some time ago in a model independent approach that was more general and correct than the approach in this letter. In this Comment, the errors in the letter are pointed out and some correct formulae presented.

hep-ph↗