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EEE340Lecture 181 Let us assume From 1).
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EEE340Lecture 182 Boundary conditions: 0 b a x y Vo
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EEE340Lecture 183 Boundary conditions: Hence, or
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EEE340Lecture 184 Boundary conditions: Hence, or 0 b a x Vo
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EEE340Lecture 185 2. Find unknown constant C n. 1.) Superposition (Linear Space) Let 2.) Boundary condition (to find C n ) (1)
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EEE340Lecture 186 3.) Orthogonality of the Fourier Series Fourier invented his series and his transform from his work of the PDE for heat transfer. Multiplying (1) by
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EEE340Lecture 187 i.e.,
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EEE340Lecture 188 Hence, Substituting Cn into (1), we obtain (4-113) (4-114)
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EEE340Lecture 189
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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)
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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)
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EEE340Lecture 1812 Therefore On the other hand, from Poisson’s Equation, where Therefore (5.14) (5.12) (5.13)
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EEE340Lecture 1813 Solving (5.14), one obtains Or Child-Langmuir law. The I-V curve can be plotted (non-linear) (5.17)
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