§2.4 Conductors – capacitance Christopher Crawford PHY 311 2014-02-14

Outline Exam on Monday question types, review sheet Conductors vs. dielectrics Charge, field, and potential Induced charge Electrostatic presure Capactitors Field lines, equipotentials Capacitance = flux / flow Energy = flux x flow

Exam – 4 questions Calculate vector derivatives Curvilinear coordinates Integrate electric field or potential over a charge distribution Parametrize surface, path or volume Differentiate between r, r’, r_script Split integrals and factor out x, y, z Proof of relationships between five formulations of electrostatics See study sheet Essay question – prose and diagrams Relation between field, flux/flow, sources, especially applied to electrostatics Geometric interpretation of laws

Plotting field lines and equipotentials

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 Coefficients of potential, capacitance

Induced charges 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 Faraday cage – shields external flux inside a hollow conductor field lines from charge inside a hollow conductor are “communicated” outside the conductor by induction (compare: displacement field, 7.3)

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

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