Related papers: Notes on the Dipole Coordinate System
In this work, we characterize self-adjoint operators that commute with magnetic translations. We use this characterization to derive effective kinetic energy functionals for homogeneous electron gases and three-dimensional electronic…
The Euler-Heisenberg effective Lagrangian is used to obtain general expressions for electric and magnetic fields induced by non-linearity, to leading order in the non-linear expansion parameter, and for quasistatic situations. These…
We derive a closed-form expression of the magnetic field of a finite-size current sheet and use it to calculate the field of permanent magnets, which are modeled through their surface current densities. We illustrate the method by…
The Earth's magnetic field can be decomposed into spherical harmonics, and the exact coefficients of the decomposition can be determined through a few measurements of its value at different locations. Using measurements from a magnetometer…
In order to satisfy the symmetry between electric and magnetic fields in the source free Maxwell's equations, electric charges might have magnetic counterparts: magnetic monopoles. Many methods and techniques are proposed to search for the…
With the development of condensed-matter physics and nanotechnology, attention has turned to the fields near and on surfaces that result from interactions between electric dipole radiation and mesoscale structures. It is hoped that studying…
In this letter we study the classical motion of an electric dipole in the presence of a uniform magnetic field in the approximation of small oscillations. The normal modes of oscillations are obtained and propose a criterion of…
Magnetostatic fields in accelerators are conventionally described in terms of multipoles. We show that in two dimensions, multipole fields do provide solutions of Maxwell's equations, and we consider the distributions of electric currents…
Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic…
In this review, I will first introduce possible methods to probe the large-scale magnetic fields in our Galaxy and discuss their limitations. The magnetic fields in the Galactic halo, mainly revealed by the sky distribution of rotation…
Homogeneous magnetic fields can be generated through the strategic arrangement of permanent magnets. The Halbach array serves as a prominent example of an effective design following this principle. However, it is a two-dimensional approach…
We give a derivation for the indirect interaction between two magnetic dipoles induced by the quantized electromagnetic field. It turns out that the interaction between permanent dipoles directly returns to the classical form; the…
The existence of magnetic monopoles is predicted by many theories of particle physics beyond the Standard Model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic…
Anisotropic magnetic colloids with permanent dipole moments exhibit rich field-responsive behavior arising from the interplay between particle geometry, dipolar interactions, and external driving. Modeling these systems remains challenging…
Aggregates immersed in a plasma or radiative environment will have charge distributed over their extended surface. Previous studies have modeled the aggregate charge using the monopole and dipole terms of a multipole expansion, with results…
We demonstrate that a non-vanishing interaction force exists between pairs of induced dipoles in random, statistically stationary electromagnetic field. This new type of optical binding force leads to long-range interaction between dipolar…
The Laplace's equations for the scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates with translational invariance along azimuthal coordinate are considered. The series of special functions which,…
It is proposed that Magnetic Monopoles (MMs) could originate from a new $\mbox{U(1)}_{M}$ symmetry. Such an abelian symmetry is then assumed to be related to the conservation of a magnetic number $M$. This magnetic number is associated with…
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
The current density of a moving electric dipole is expressed as the sum of polarization and magnetization currents. The magnetic field due to the latter current is that of a magnetic dipole moment that is consistent with the relativistic…