Electric Field of a Homogeneous Charged Volumetric Hemisphere Over Its Symmetry Axes

Authors

  • Pablo Marón Universidad Antonio de Nebrija
  • Ángel del Vigo Universidad Politécnica de Madrid

DOI:

https://doi.org/10.37891/kpej.v7i2.668

Keywords:

Coulomb’s law, Electrostatics, Hemi-spherical capacitor

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.

References

Burbano de Ercilla, S., Burbano, E. & García, C. (2004). Problemas de Física General (27º ed.). Tebar.

del Vigo, Á. & Renedo, J. S. (2016). Campo eléctrico de una superficie semiesférica uniformemente cargada. Revista 100cias-UNED. 9, 185-190.

del Vigo, Á. & Villarino, J. (2020). Electricidad y Magnetismo. Problemas resueltos. García Maroto Editores.

Eisberg, R. M. & Lerner, L.S. (1988). Física. Fundamentos y Aplicaciones. Mc Graw-Hill.

Faiz, J., & Ojaghi, M. (2002). Instructive Review of Computation of Electric Fields using Different Numerical Techniques. Int. J. Engng Ed., 18(3), 344-356.

Feynman, R. P., Leighton, R. & Sands, M. (1972). Física (Vol.2): Electromagnetismo y Materia. Addison-Wesley Iberoamericana.

Griffiths, D. J. (2017). Introduction to Electrodynamics (4º ed.). Cambridge University Press.

Jackson, J. D. (1998). Classical Electrodynamics (3º ed.). John Wiley & Sons.

Lee, H & Koh, I. (2018). Consideration of diffraction effect in iterative physical optics combining physical theory of diffraction for conducting body. 12th European Conference on Antennas and Propagation (EuCAP 2018), London, UK, 2018, 1-5, https://doi.org/10.1049/cp.2018.1186.

Mathews, J. H. & Fink, K. D. (1999). Métodos Numéricos con MATLAB (3º ed.). Prentice Hall

Notaros, B. M. (2014). MATLAB-Based Electromagnetics. Pearson.

Pauly, J. (1909). Notions Elémentaires du Calcul Différentiel et du Calcul Intégral. Librairie Polytechnique Ch. Béranger.

Purcell, E. M. (1988). Electricidad y Magnetismo (2º ed.). Reverte.

Rodríguez, V. L. (2002). Electromagnetismo. UNED.

Romero-Mendez R, Berjano E. (2023). Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution. Mathematics, 11(21), 4447. https://doi.org/10.3390/math11214447.

Serway, R. A. & Vuille. C. (2018). College Physics (11º ed). Cengage.

Spivak, M. (1996). Calculus (2º ed.). Reverte.

Tipler, P.A. & Mosca, G. (2010). Física para la ciencia y tecnología (6º ed.). Reverte.

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Published

13-11-2024

How to Cite

Marón, P., & del Vigo, Ángel. (2024). Electric Field of a Homogeneous Charged Volumetric Hemisphere Over Its Symmetry Axes. Kasuari: Physics Education Journal (KPEJ), 7(2), 300–310. https://doi.org/10.37891/kpej.v7i2.668

Issue

Vol. 7 No. 2 (2024): December 2024

Section

Articles

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