§4.1–2 Polarization Christopher Crawford PHY

Outline Introduction Goal of chapter 4: (ε 0  ε)E  D Dielectric material – bound charge Geometry of chapter 4 – polarization chains Dipoles in a material Properties of a dipole – force, torque, energy Induced dipoles – polarizability α Alignment of polar molecules Polarization field (density) P(r) Field of dipole distribution – bound charge Example – dielectric sphere 2

Dielectric materials Three material properties – three electrical components – Permittivity (dielectric)D = ε E– capacitance C = ε A/d – Permeability (magnet)B = μ H– inductance L = μ A/d – Conductivity (conductor)J = σ E– conductanceG = σ A/d Free charge vs. bound charge – dielectric – Insulator (dielectric) – semiconductor – conductor – superconductor – Conduction band in a solid, Ionization in a liquid – Polarization – stretching of charge or rotation of permanent dipoles Charge screening – Polarization chains – Example: capacitor 3

Properties of dipole Dipole field – multipole expansion – Dipole chain – middle charges cancel Force on a dipole – Force on a quadrupole? Torque on a dipole in a field – Analogous to force on a point charge Dipole energy in a field – Alternate derivation of force 4

Polarizability Atomic polarizability tensor:  – Field stretches +/- charge in opposite directions: polarization – May depend on intrinsic directions of the material: birefringence Example: atomic nucleus in uniform electron cloud 5

Alignment of polar molecules 6

Polarization density Recall: field of spherical dipole distribution: dipole density – Same problem: pepper dipole all throughout sphere! Dipole density is naturally treated as a flux 7

Field due to a polarization distribution 8

Example: dielectric sphere 9