§4.4.3-4 Dielectric capacitors: energy and force Christopher Crawford PHY 416 2014-12-10

Outline Review of geometry: flux Q=ΦD and flow V=ΦE Different “personalities” of same electric field Capacitance: C = Q / V = flux / flow Example calculation in COMSOL Energy: W = Q × V = flux × flow Field energy Review: force on a dipole Fringe field Relation between partial derivatives Force on a dielectric

Review of geometry of electric fields Flux of D-field Flow of E-field Boundary conditions

Capacitance Flux of D-field Flow of E-field

Example: COMSOL Parallel disk capacitor in a 1 m sphere: capacitor.mph Plate radius: 45 cm, separation: 60 cm, dielectric constant K=25 Analytic capacitance: C = ε A / d = 235 pF From simulations: = 235 pF

Energy Flux of D-field Flow of E-field

Field energy in a dielectric Integration by parts: transfer derivative

Dipole in a fringe field Review of force on a dipole – fringe fields Example – dipole passing through a capacitor Curl – constraint on partial derivatives

Force on a dielectric slab Gradient of the system energy