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All Journal Kasuari: Physics Education Journal (KPEJ)
del Vigo, Ángel
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Education Physics

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Electric Field of a Homogeneous Charged Volumetric Hemisphere Over Its Symmetry Axes Marón, Pablo; del Vigo, Ángel
Kasuari: Physics Education Journal (KPEJ) Vol. 7 No. 2 (2024): December 2024
Publisher : Universitas Papua, Jurusan Pendidikan Fisika FKIP Unipa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37891/kpej.v7i2.668

Abstract

Analytical study of homogeneous charged volumetric hemisphere electric field along its symmetry axes is presented in this article. Solution was obtained by two different ways; on one hand, superposition of finite thickness disks with increasing radius, and, on the other hand, straightforward integration of finite volume elements in cylindrical coordinates. The same result is obtained in both cases. Additionally, a numerical solution based on the electric field created by a random distribution of discrete charges inside the hemisphere was calculated to check the analytical solution. Concordance between the analytical and numerical solutions was found. The interest of this theoretical result at electronics investigation field resides on its utility to determine the capacity of two opposite hemispheres capacitor system.
Electric Field Inside of a Homogeneous Charged Spherical Surface Raguani, Soufiane; Garrido, Alberto; Chitu, Andrei; Mutke, Jokin; del Vigo, Ángel
Kasuari: Physics Education Journal (KPEJ) Vol. 8 No. 1 (2025): June 2025
Publisher : Universitas Papua, Jurusan Pendidikan Fisika FKIP Unipa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37891/kpej.v8i1.917

Abstract

It is widely known that the electric field inside an uniformly charged close surface is null at any point inside the body with independence of its geometry. This result, which is considered as a Physics theorem, is typically justified by applying symmetry arguments based on Gauss law inside the surface. However, a formal proof is not frequently given due to its mathematical complexity. In the present article a formal study of the electric field inside a uniformly charged spherical surface is given. The solution is presented through three different approaches: derivation of the electric potential inside the body, superposition of the electric field contributions from infinitesimal ring-elements, and finally, direct integration of the electric field Coulomb’s law for all the surface elements of the sphere. In all cases, the same result is achieved, confirming a null electric field inside the sphere. This formal solution that is not given in the most classical books of General Physics and Electromagnetism, might be interesting in an academic context, for undergraduate students and professors of science and engineering curricula.
Co-Authors Chitu, Andrei Garrido, Alberto Marón, Pablo Mutke, Jokin Raguani, Soufiane