Abstract
In this work we study the electric field of a dipole immersed in a medium with permittivity controlled by a real scalar field which is non-minimally coupled to the Maxwell field. We model the system with an interesting function, which allows the presence of exact solutions, describing the possibility of the permittivity to encapsulate the charges at very high values, giving rise to an effect that is not present in the standard situation. The results are of direct interest to applications for emission and absorption of radiation, and may motivate new studies concerning binary stars and black holes in gravity scenarios of current interest.
Highlights
We study the electric field of a dipole immersed in a medium with permittivity controlled by a real scalar field which is nonminimally coupled to the Maxwell field
160 years ago, Maxwell considered results described by Ampere, Coulomb, Faraday and Gauss to write down a set of four equations that changed the physics in some important ways
Its Lagrange density is very well known in physics, but in the present work we consider a much less known system, described by the addition of a real scalar field φ which is nonminimally coupled to the gauge field in the form in the presence of the external current jμ
Summary
We start varying the action associated to the above Lagrange density to get the following equations of motion:. The charge density of the dipole has the following form, j0 1⁄4 2πeðδðx − aÞδðyÞ − δðx þ aÞδðyÞÞ, and the electric field is obtained from Eq (3b), which leads us to the expression. We suppose the potential engenders two neighbor minima, say φ Æ such that Vðφ ÆÞ 1⁄4 0, which may be connected asymptotically by the field configuration φðξÞ. In this situation, since the potential and the permittivity are related by Eq (10), one can see that the permittivity diverges at the two zeros of the potential, and this feature may be used to compensate the divergence caused by the cosh ξ in the electric field, as we have commented below Eq (7). We dive further into the construction of stable structures attaining a topological feature; we follow the Bogomol’nyi procedure [31] and introduce another function, W 1⁄4 WðφÞ, such that dW
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