Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois, USA Amrita Viswa Vidya Peetham, Coimbatore July 10 – August 11, 2006
5.3 Poisson’s and Laplace’s Equations
5.3-2 Poisson’s Equation For static electric field, Then from If is uniform, Poisson’s equation
5.3-3 If is nonuniform, then using Thus Assuming uniform , we have For the one-dimensional case of V(x),
5.3-4 Anode, x = d V = V 0 Cathode, x = 0 V = 0 Vacuum Diode D5.7 (a)
5.3-5 (b)
5.3-6 (c)
5.3-7 Laplace’s Equation Let us consider uniform first Parallel-plate capacitor If Poisson’s equation becomes x = d, V= V 0 x = 0, V = 0
5.3-8 Neglecting fringing of field at edges, General solution
5.3-9 Boundary conditions Particular solution
5.3-10
area of plates For nonuniform For
Example x = d, V = V 0 x = 0, V = 0
5.3-13
5.3-14