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 ...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.展开更多
文摘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.
