A novel method to calculate the electric field using solid angles

TL;DR

This paper introduces a new approach to calculating electric fields inside spherical shells with surface charge using solid angles, simplifying the integral calculation without special functions.

Contribution

The paper presents a novel method leveraging solid angles to compute electric fields, avoiding complex special functions used in classical solutions.

Findings

Electric field inside a spherical shell is proportional to the solid angle.

The method simplifies calculations for flat charged surfaces.

Integral calculations are more straightforward without special functions.

Abstract

A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical problem. For a flat surface of uniform charge density, the electric field normal to the surface is shown to be proportional to the solid angle subtended by the surface only.