EEE340Lecture 151 Per unit length capacitance

EEE340Lecture 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)

EEE340Lecture : 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)

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

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

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

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)

EEE340Lecture 158 Finally Solution 3. To Use (3.176) : 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)

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

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

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