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Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electrom

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

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Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electrom

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  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. 5.3Poisson’s and Laplace’s Equations

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

  4. If eis 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 efirst 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

  11. area of plates For nonuniform e, For

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

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