1. §4.4.3-4 Dielectric capacitors: energy and force
Christopher Crawford
PHY 416

2. 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

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

4. Capacitance
Flux of D-field
Flow of E-field

5. 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

6. Energy
Flux of D-field
Flow of E-field

7. Field energy in a dielectric
Integration by parts: transfer derivative

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

9. Force on a dielectric slab
Gradient of the system energy