1. §2.4 Conductors – capacitance
Christopher Crawford
PHY 416

2. Exam 2 – Friday Oct 24
Integrate E(r) or V(r) over a charge distribution
Parametrize source points r’(u,…) on surface, path or volume
Calculate field point r and displacement vector, r=r-r’
Reduce integrals to parameters and constants, including unit vectors
Capacitance calculation
Application of Gauss’ law
Rectangular, cylindrical, or spherical symmetry
Proofs between five formulations of electrostatics
See study sheet
Essay question – prose and diagrams
Relations between field, flux/flow, sources; applied to electrostatics
Geometric interpretation of laws

3. Outline
Conductors vs. dielectrics Charge, field, and potential Induced charge; shielding Electrostatic pressure
Capacitors Field lines, equipotentials Capacitance = flux / flow Capacitance matrix

4. Conductors vs. dielectrics
Free vs. bound charge
metal: conduction band electrons, ~ 1 / atom
electrolyte: positive & negative ions
Electrical properties of conductors
Field, potential, charge distribution

5. Induced charge Induction in a conductor – displacement of charge
Charge shifts until electric field is normal to surface
Surface charge terminates electric flux lines inside the conductor
Total charge remains constant unless there is an escape path
1764 Johan Carl Wilcke invented electrophorus (induction generator)

6. Induction
field lines from charge inside a hollow conductor are communicated outside the conductor by induction
compare: displacement field, Griffiths sections 4.3, 7.3

7. Faraday cage External flux shielded inside a hollow conductor
Consequence of 1/r2 force law

8. Electrostatic pressure
Force due to electric field on induced charge in conductor
Force per unit area: f = P (or electrostatic pressure)

9. Capacitor Pair of conductors held at different potential
Electric flux:
Electric flow:
Capacitance: Q = C ΔV
Parallels later in the course:
resistance, reluctance, inductance
Stored energy: E = ½ Q ΔV

10. Example: spherical shells
Two shells of radii a < b

11. Coefficients of capacitance
Linearity of electric potential represented by matrices
Coefficients of potential
Coefficients of capacitance
Two-conductor system