The Dynamics of Charged Particle Navigating Through an Electromagnetic Field and Landau Levels

This text begins by applying a theoretical framework and mathematical derivation to ascertain the magnetic induction intensity generated by electrons within an electromagnetic field. Following this foundational analysis, it explores the specific scenario of electrons undergoing uniform linear motion within the electromagnetic field, calculating the corresponding magnetic induction intensity for this motion. The narrative progresses to consider the broader implications of charged particle motion in electromagnetic fields, culminating in a discussion of Landau levels. By employing calculation and derivation within the context of a symmetric gauge, it determines the magnitude of these Landau levels. The findings reveal that the electric displacement flux created by a uniformly moving charge on a circular plane displays a symmetric distribution. Additionally, it highlights a consistent relationship between the changes in displacement current and magnetic induction intensity, both of which vary according to their spatial positioning. Importantly, the results pertaining to Landau levels align with theoretical expectations, offering a coherent and insightful exploration of the physical principles at play.