scholarly journals Coulomb law in the nonuniform Euler–Heisenberg theory

2020 ◽  
Vol 35 (33) ◽  
pp. 2050211
Author(s):  
A. D. Bermúdez Manjarres ◽  
M. Nowakowski ◽  
D. Batic
Keyword(s):  
Order Differential Equation ◽  
Classical Field Theory ◽  
Weak Field ◽  
Higher Order ◽  
Classical Field ◽  
Nonlinear Electrodynamics ◽  
Electric And Magnetic Fields ◽  
Coulomb Law ◽  
Derivatives Of ◽  
The Magnetic Field

We consider the nonlinear classical field theory which results from adding to the Maxwell’s Lagrangian the contributions from the weak-field Euler–Heisenberg Lagrangian and a nonuniform part which involves derivatives of the electric and magnetic fields. We focus on the electrostatic case where the magnetic field is set to zero, and we derive the modified Gauss law, resulting in a higher-order differential equation. This equation gives the electric field produced by stationary charges in the higher-order nonlinear electrodynamics. Specializing for the case of a point charge, we investigate the solutions of the modified Gauss law and calculate the correction to the Coulomb law.

scholarly journals Fractional formulation of Podolsky Lagrangian density

2022 ◽  
Vol 9 (2) ◽  
pp. 136-141
Author(s):  
Amer D. Al-Oqali ◽  
Keyword(s):  
Field Theory ◽  
Stress Tensor ◽  
Fractional Derivatives ◽  
Lagrangian Density ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Classical Field Theory ◽  
Higher Order ◽  
Classical Field ◽  
Energy Stress

Lagrangians which depend on higher-order derivatives appear frequently in many areas of physics. In this paper, we reformulate Podolsky's Lagrangian in fractional form using left-right Riemann-Liouville fractional derivatives. The equations of motion are obtained using the fractional Euler Lagrange equation. In addition, the energy stress tensor and the Hamiltonian are obtained in fractional form from the Lagrangian density. The resulting equations are very similar to those found in classical field theory.

Vakonomic Constraints in Higher-Order Classical Field Theory

2010 ◽  
Author(s):  
Cédric M. Campos ◽  
Manuel Asorey ◽  
Jesús Clemente-Gallardo ◽  
Eduardo Martínez ◽  
José F. Cariñena
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Higher Order ◽  
Classical Field

On the geometric structure of classical field theory in Lagrangian formulation

1970 ◽  
Vol 68 (2) ◽  
pp. 475-484 ◽  
Author(s):  
Jędrzej Śniatycki
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Geometric Structure ◽  
Classical Field Theory ◽  
Higher Order ◽  
Classical Field ◽  
Lagrangian Formulation ◽  
Symmetry Transformations

AbstractGeometric structure of classical field theory in Lagrangian formulation is investigated. Symmetry transformations with generators depending on higher-order derivatives are considered and the corresponding conservation laws are obtained.

scholarly journals Newton &-vs Lorentz

2018 ◽  
Vol 14 (3) ◽  
pp. 5869-5872
Author(s):  
Armando Tomas Canero
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
The Body ◽  
Circular Path ◽  
Third Law ◽  
A Minor ◽  
The Magnetic Field

Is there a point of divergence between Classical Mechanics and Electromagnetism? This discrepancy is raised by many authors and arises between Newton's third law and the equation of Lorentz forces. Due to the transcendence of these expressions, their wide application in different situations is not a minor issue and should be given a consistent interpretation with both theories. The discrepancy mentioned is based in that: according to the calculations of classical field theory, a particle with an electric charge moving immersed in a magnetic field suffers an action that diverts its trajectory, making it describe a circular path, which can not be compensated through a contrary force in the body that generated the magnetic field. The force on this second body is predicted, by this theory, at ninety degrees from the first, thus contradicting the principle of action and reaction. This study shows why the Lorentz law does not contradict Newton's third law and gives a consistent explanation of how the equations of classical field theory should be applied so that the result is correct.

Transmission line sanitary protective zones. Electromagnetic safety problems

2020 ◽  
pp. 736-736
Author(s):  
N. B. Rubtsova ◽  
A. Y. Tokarskiy
Keyword(s):  
Magnetic Field ◽  
Risk Factor ◽  
Transmission Lines ◽  
General Public ◽  
Field Component ◽  
Regulatory Requirements ◽  
Protection Zones ◽  
Electric And Magnetic Fields ◽  
Health Risk Factor ◽  
The Magnetic Field

The main problems of overhead and cable transmission lines with voltage >=110 kV electric and magnetic fields general public protection are presented. It is shown that it is necessary to develop regulatory requirements for these lines’ sanitary protection zones organization, taking into account the magnetic field component, because its possible health risk factor, up to carcinogenic.

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