Polarization of Dielectric Sphere ..... - Maple Application Center
Application Center Applications Polarization of Dielectric Sphere .....

Polarization of Dielectric Sphere .....

Authors
: Prof. EL MAHDI ASSAID
Engineering software solutions from Maplesoft
This Application runs in Maple. Don't have Maple? No problem!
 Try Maple free for 15 days!
In this worksheet, we investigate the polarization of a dielectric sphere (dot) with a relative permittivitty "epsilon[Dot]" embedded in a dielectric matrix with a relative permittivitty "epsilon[Matrix]" and submitted to an uniform electrostatic field F oriented in z-axis direction. It's a fondamental and popular problem present in most of electromagnetism textbooks. First of all, we express Poisson equation in appropriate coordinates system: "Delta V(r,theta,phi) = 0". We proceed to a full separation of variables and derive general expression of scalar electrostatic potential V(r,theta,phi). Then we particularize to a dielectric sphere surrounded by a dielectric matrix and give expressions of electrostatic potential V(r,theta) in the meridian plane (x0z) inside and outside the sphere by taking into account: i) invariance property of the system under rotation around z-axis, ii) choice of the plane z=0 as a reference of scalar electrostatic potential, iii) regularity of V(r,theta) at the origine and very far from the sphere, iv) continuity condition of scalar electrostatic potential V(r,theta) at the sphere surface, v) continuity condition of normal components of electric displacement field D at the sphere surface. The obtained expressions of V(r,theta) inside and outside the sphere allows as to derive expressions of electrostatic field F, electric displacement field D and polarization field P inside and outside dielectric dot in spherical coordinates as well as in cartesian rectangular coordinates. The paper is a proof of Maple algebraic and graphical capabilities in tackling the resolution of Poisson equation as a second order partial differential equation and also in displaying scalar electrostatic potential contourplot, electrostatic field lines as well as fieldplots of F, D and P inside and outside dielectric sphere.

Application Details

Publish Date: September 18, 2017
Created In: Maple 15
Language: English

More Like This

Arc Flash Calculation (IEEE 1584-2018)
Effect of Source Inductance on MOSFET Rise and Fall Times
Cable Ampacity using the Nehers-McGrath Method
Cross Conduction in Modern Power MOSFETs
Load Flow Analysis of a Five-Bus Power System
アナログフィルターのワーストケース解析
Arc Flash Calculation (IEEE 1584-2018)
Classroom Tips and Techniques: Electric Field from Distributed Charge