Impact of the Evolution of a Curved Charge Distribution on Electric Field

Abstract

Theoretically, it is plausible to assume for a chosen charge distribution the electric field can be calculated. However, in practice depending on the geometry of the distribution one faces mathematical challenges. In this research- oriented project, we select a set of related familiar 2D geometric curves addressing the mathematical issues. Specifically, we consider a family of curves that evolved via step-by-step “evolution” . The evolution begins from a segment of a circular arc to a complete circle. The electric fields are formulated, evaluated, and graphed. Accomplishing these objectives relied heavily on utilizing a Computer Algebra System (CAS), specifically Mathematica [1] . The CPU’s expensive runtimes are circumvented by introducing mathematical procedures.