Comparation of Magnetic Flux Cases Solution in Around Electrified Wire between Analytical and Computational Methods

Abstract

Have analyzed comparative analytical and numerical computation solutions in the case of magnetic flux to the circular loop of radius R as far apart as H around the current I in the wire. The aim is to know how the methods used have an accurate solutions calculated based on relative error value. The analytical method use taking concept of polar coordinates and the computational method using the function of analytic equations modified based on Simpson and Monte Carlo method. Both methods are aprroaches in numerical integration.After test with variation of combination of R=0.1 and 0.2 and H=0.1 and 0.2, the Simpson and Monte Carlo indicate the integration value corresponding to the exact or analytical solution value, the relative error value of the Simpson method range from 0,004% - 0,017% and the relatif error value for Monte Carlo method range from 0.056% - 3.4296%.

Keywords: magnetic flux, analytical, simpson, monte carlo, relative error