Electric Field Inside of a Homogeneous Charged Spherical Surface
DOI:
https://doi.org/10.37891/kpej.v8i1.917Abstract
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.
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