§4.1–2 Polarization

Christopher CrawfordPHY 311

2014-03-05

Outline• Introduction

Goal of chapter 4: (ε0ε)E D

Dielectric material – bound chargeGeometry of chapter 4 – polarization chains

• Dipoles in a materialProperties of a dipole – force, torque, energyInduced dipoles – polarizability αAlignment of polar molecules

• Polarization field (density) P(r)Field of dipole distribution – bound chargeExample – dielectric sphere

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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 – conductance G = 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

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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

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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

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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

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Field due to a polarization distribution

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Example: dielectric sphere

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