Per unit length capacitance

1

• Per unit length capacitance

2

• 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 -gt electric energy)
• Inductance (current -gt magnetic energy)
• Resistance (conductor ohmic loss)
• Conductance (dielectric leakage loss)

3

• 3-11 Electrostatic Energy and Forces
• To bring a charge Q2 from to the field
  produced by Q1, the work
• which is independent of the path
• If we bring in another charge Q3

(3.159)
(3.161)
(3.162)
4

• A better way to recognize physics from the
  following chart
• i.e.,

5

• In general
• where
• For distributed charges
• For distributed charges with a given density

(3.165)
(3.166)
(3.170)
6

• Example 3-22 Energy stored in a uniform sphere
  of charge with radius b and charge density rv
• Solution 1
• From Gausss law
• Where
• The differential charge in the layer of dr is
• The differential work to bring up dQr is

7

• 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)
8

• 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)
9

• Hence
• We conclude from (3.175) that
• The electrostatic energy density

(3.176)
(3.178)
10

• The energy formulas are analogous of the
  Newtonian counterparts

Particle kinetic energy
Rigid body rotation energy
Potential energy of a spring
11

• Example 3-24 Energy stored in a parallel plate
  capacitor
• Solution

Q
-Q