(a) Compute the electric potential inside and outside the sphere.
Given constants:
Computing electric fields
Electrostatics relies on multiple methods for computing electric fields and potentials. In this problem, we will explore two of them, Gauss's Law and Legendre polynomials.
Uniform charge distributions
Let us consider a hollow conducting sphere of radius R charged with the electric charge Q, uniformly distributed on its surface. In order to calculate its potential, we can use Gauss's Law, which states that the flux of the electric field dF=E⋅dA across a closed surface is proportional to the charge enclosed by that surface: F=Q/ε0. We have denoted dA=dAn the elementary oriented (towards the exterior) surface element.