PHY 712: Solving Poisson Equation for 1D Charge Distribution - Prof. Natalie Holzwarth, Assignments of Electromagnetism and Electromagnetic Fields Theory

Download PHY 712: Solving Poisson Equation for 1D Charge Distribution - Prof. Natalie Holzwarth and more Assignments Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity! January 18, 2007 PHY 712 – Problem Set #2 1. Consider a one-dimensional charge distribution of the form: ρ(x) =    0 for x ≤ −a/2 ρ0x/a for −a/2 ≤ x ≤ a/2 0 for x ≥ a/2, where ρ0 and a are constants. (a) Solve the Poisson equation for the electrostatic potential Φ(x) with the boundary conditions Φ(−a/2) = 0 and dΦ(−a/2)/dx = 0. (b) Find the corresponding electrostatic field E(x). (c) Plot Φ(x) and E(x). (d) Discuss your results in terms of elementary Gauss’s Law arguments.