Analysis of electric field in asymmetrically arranged dielectric media using simple mathematical methods

Calculations of electric field strength in various structures are essential in the design of most electrical and electronic equipment and devices, because electric field tendencies vary greatly with respect to a given voltage, dielectric constants of insulating media, and the geometry of the structure. Electric field simulation is very convenient to calculate and predict electric field tendencies, but it is time-consuming, expensive, and difficult to understand the physical meaning with. To address this problem in a simpler way than time-consuming and costly electric field simulations, we derive analytical equation-based solutions for pre-designing electrical and electronic devices. In this paper, we consider a simple mathematical model based on Laplace equation, particularly with respect to asymmetrically arranged dielectric structures. In these structures, we analyze electric field tendencies using axis rotation and Legendre polynomials associated with each fitted axis, especially in asymmetrically arranged models.