4 1 2 Polarization Christopher Crawford PHY 416

§ 4. 1– 2 Polarization Christopher Crawford PHY 416 2014 -11 -21

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) – Permeability (magnet) – Conductivity (conductor) D = ε E – capacitance B = μ H – inductance J = σ E – conductance C = ε A/d L = μ A/d G = σ A/d • Free charge vs. bound charge – dielectric – Insulator (dielectric) – semiconductor – 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

Pure spherical dipole 4

Pure spherical dipole 5

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 6

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 7

Alignment of polar molecules 8