Analitical computation of the electrostatic potential within a uniformly charged triangle

undergraduate thesis

• Title: Analitički izračun elektrostatskog potencijala unutar jednoliko nabijenog trokuta
• Author: Antonio Stipanović
• Mentor: Saša Ilijić (mentor)
• Committee member: Dubravko Horvat (predsjednik povjerenstva)
• Committee member: Zoran Narančić (član povjerenstva)
• Committee member: Saša Ilijić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu izveden je analitički izraz za izračun elektrostatskog potencijala u točki P koja se nalazi unutar jednoliko nabijenog trokuta △A1A2A3. Pri izvodu izraza, polazni trokut rastavljen je na sljedeće segmente, △PA1A2, △PA1A3, △PA2A3, te je korišten princip superpozicije električnog polja i elektrostatskog potencijala. Također su korištene metode dvodimenzionalne integracije u ne-ortogonalnom koordinatnom sustavu. Predložena je i numerička metoda za izračun elektrostatskog potencijala, te na temelju nekoliko primjera uspoređeni su rezultati s analitičkom metodom, time pokazujući superiornost analitičke metode nad numeričkom. Dobiveni analitički izraz može se koristiti za brzo pronalaženje maksimuma potencijala numeričkim putem, za čime postoji stanoviti interes, a što potvrđuje nedavno raspisani natječaj tvrtke Artes Calculi.

Abstract (english)

Within this paper lies the presentation of the analytic expression for calculating electrostatic potential at a point P which is found inside a uniformly charged triangle △A1A2A3. During the presentation of the expression, the starting triangle is split into the following segments, △PA1A2, △PA1A3, △PA2A3, and the principle of superposition of the electric field and electrostatic potential is used. Also used is a method of two-dimensional integration inside a non-ortogonal coordinate system. A numerical method for calculating the electrostatic potential is also shown, and based on a couple of examples, the results are compared with that of the analytic method, thus showing the superiority of the analytic method over the numerical. The given analytic expression can be used for fast calculation of the potential maximum through a numeric route, for which there is substantial interest, which confirms the recently published competition by the company Artes Calculi.

• Keywords: Elektrostatski potencijal; dvodimenzionalna integracija; ne-ortogonalni koordinatni sustav; superpozicija; Artes Calculi
• Keywords (english): Electrostatic potential; twodimensional integration; non-ortogonal coordinate system; superposition; Artes Calculi
• Language: croatian
• URN:NBN: urn:nbn:hr:168:203566
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2018-02-06 07:23:46