Quiz on Electromagnetic Theory: Gauss' Law, Electric Field, and Potential - Prof. James J., Quizzes of Physics

Download Quiz on Electromagnetic Theory: Gauss' Law, Electric Field, and Potential - Prof. James J. and more Quizzes Physics in PDF only on Docsity! Name: PHYS4210 Electromagnetic Theory Quiz #2 7 Feb 2011 This is a closed book quiz! You have thirty minutes to complete it. This quiz has multiple steps; be sure to work all of them. First, show that Gauss’ Law (in differential form for electric field E(x)) implies that ∮ S E·dS = 4πQ for a closed surface S that contains total charge Q. Use this result to find the electric field E(r) at a (perpendicular) distance r from the center of a long, cylindrical charge distribution with radius R and constant charge density ρ0. (Divide your answer in to the regions r < R and r > R.) Next, integrate the electric field to find the electric potential Φ(r), fixing Φ(0) = 0. Finally, prove that Φ satisfies Poisson’s equation for r < R and Laplaces’ equation for r > R.