Second Gradient Electromagnetostatics: Electric Point Charge, Electrostatic and Magnetostatic Dipoles

  title={Second Gradient Electromagnetostatics: Electric Point Charge, Electrostatic and Magnetostatic Dipoles},
  author={Markus Lazar and Jakob Leck},
In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical Maxwell electrodynamics whose Lagrangian is both Lorentz and U ( 1 ) -gauge invariant. Second gradient electromagnetostatics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian. Moreover, it… 
4 Citations

Figures and Tables from this paper

Dissipative extension of Electrodynamics

In nonequilibrium thermodynamics, electrodynamic interaction and electrodynamic forces appear as non-dissipative, external phenomena. Irreversibility is due to Ohm's law and polarisation. However,

Gradient modification of Newtonian gravity

A second gradient generalization of Newtonian gravity is presented within the framework of gradient field theory. Weak nonlocality is introduced via first and second gradients of the gravitational

Effects of CPT -odd terms of dimensions three and five on electromagnetic propagation in continuous matter

In this work we study how CPT -odd Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics as well as a dimension-5 extension of it affect the optical activity of continuous media. The starting point is



On gradient field theories: gradient magnetostatics and gradient elasticity

In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For

Introduction to Electrodynamics

1. Vector Analysis. Vector Algebra. Differential Calculus. Integral Calculus. Curvilinear Coordinates. The Dirac Delta Function. The Theory of Vector Fields. 2. Electrostatics. The Electrostatic

On the self-force in Bopp–Podolsky electrodynamics

In the classical vacuum Maxwell–Lorentz theory the self-force of a charged point particle is infinite. This makes classical mass renormalization necessary and, in the special relativistic domain,

Finite Self —Energies in Radiation Theory. Part II

The “cutting-off method” proposed in Part I is equivalent to a field theory basedon Maxwell’s equations supplemented by Yukawa’s equations, both fields having the samepoint charges as sources. The

Multipole expansion in generalized electrodynamics

In this paper, we study some classical aspects of Podolsky electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic

Green functions and propagation in the Bopp–Podolsky electrodynamics

A non-singular continuum theory of point defects using gradient elasticity of bi-Helmholtz type

  • M. Lazar
  • Mathematics
    Philosophical Magazine
  • 2019
ABSTRACT In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a