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EEE340Lecture 151 Per unit length capacitance

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EEE340Lecture 152 3-10.2 Multi-conductor Systems This section is very useful in high speed electronics interconnects and packaging. The following parameters are in matrix forms: Capacitance (charge -> electric energy) Inductance (current -> magnetic energy) Resistance (conductor ohmic loss) Conductance (dielectric leakage loss)

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EEE340Lecture 153 3-11: Electrostatic Energy and Forces To bring a charge Q 2 from to the field produced by Q 1, the work which is independent of the path If we bring in another charge Q 3 (3.159) (3.161) (3.162)

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EEE340Lecture 154 A better way to recognize physics from the following chart: i.e.,

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EEE340Lecture 155 In general where For distributed charges For distributed charges with a given density (3.165) (3.166) (3.170)

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EEE340Lecture 156 Example 3-22: Energy stored in a uniform sphere of charge with radius b and charge density v Solution 1: From Gauss’s law Where The differential charge in the layer of dr is The differential work to bring up dQ r is b r dr

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EEE340Lecture 157 Hence the total work (or energy) required to assemble a uniform charge sphere is Solution 2: Apply formula (3.170) Where the voltage V( r) (3.168)

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EEE340Lecture 158 Finally Solution 3. To Use (3.176) 3.11.1: Electrostatic energy Substituting the divergence equation Into (3.170), we obtain the electrostatic energy Where we have used The first term in (3.175) is zero. In fact, As (3.175)

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EEE340Lecture 159 Hence We conclude from (3.175) that The electrostatic energy density (3.176) (3.178)

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EEE340Lecture 1510 The energy formulas are analogous of the Newtonian counterparts: Rigid body rotation energy Potential energy of a spring Particle kinetic energy

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EEE340Lecture 1511 Example 3-24: Energy stored in a parallel plate capacitor Solution: +Q -Q

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