1. Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by
Nannapaneni Narayana Rao
Edward C. Jordan Professor of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
Distinguished Amrita Professor of Engineering
Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

2. 5.3 Poisson’s and Laplace’s Equations

3. Poisson’s Equation For static electric field, Then from
If e is uniform,
Poisson’s
equation

4. If e is nonuniform, then using
Thus
Assuming uniform e, we have
For the one-dimensional case of V(x),

5. D5.7
Anode, x = d
V = V0
Vacuum Diode
Cathode, x = 0
V = 0
(a)

6. (b)

7. (c)

8. Laplace’s Equation If r = 0, Poisson’s equation becomes
Let us consider uniform e first
Parallel-plate capacitor
x = d, V= V0
x = 0, V = 0

9. Neglecting fringing of field at edges,
General solution

10. Boundary conditions
Particular solution

12. area of plates
For nonuniform e,
For

13. Example
x = d, V = V0
x = 0, V = 0