EEE340Lecture 181 Let us assume From 1).

EEE340Lecture 182 Boundary conditions: 0 b a x y Vo

EEE340Lecture 183 Boundary conditions: Hence, or

EEE340Lecture 184 Boundary conditions: Hence, or 0 b a x Vo

EEE340Lecture Find unknown constant C n. 1.) Superposition (Linear Space) Let 2.) Boundary condition (to find C n ) (1)

EEE340Lecture ) Orthogonality of the Fourier Series Fourier invented his series and his transform from his work of the PDE for heat transfer. Multiplying (1) by

EEE340Lecture 187 i.e.,

EEE340Lecture 188 Hence, Substituting Cn into (1), we obtain (4-113) (4-114)

EEE340Lecture 189

EEE340Lecture 1810 Chapter 5: Steady Electric Currents Charges in motion constitute current flow. Electric current consists of three types: Conduction current: current in a wire Ohm’s law Convection Current: Displacement Current: 5-2: Current Density and Ohm’s Law Total current flowing through an arbitrary surface S usually, we choose a cross-section Vacuum tube Capacitor (5.5)

EEE340Lecture 1811 Example 5-1: Vacuum-tube diode Electron cloud where  (y) is negative. The velocity is Newton’s law Hence where (5.9) (5.11) (5.8) y Cathode Anode J E 0 (5.10)

EEE340Lecture 1812 Therefore On the other hand, from Poisson’s Equation, where Therefore (5.14) (5.12) (5.13)

EEE340Lecture 1813 Solving (5.14), one obtains Or Child-Langmuir law. The I-V curve can be plotted (non-linear) (5.17)