Need help for electromagnetic theory question:   E(r) [electric field] inside a spherical shell of radius R that carries uniform surface charge density is zero. Make an arguement based on pairing off elements of the charge distribution that confirms this result for r (vector) = 0 (the center of shell). PLEASE do include a sketch of the arguement showing that every arrow representing electric field on the shell is an equal-length arrow and how these pairs cancel each other out when added, resulting in a net electric field of zero

Problem An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E =