Chapter 4 Electrostatic Fields in Matter 4.1 Polarization 4.2 The Field of a Polarized Object 4.3 The Electric Displacement 4.4 Self-Consistance of Electric Field and Polarization; Linear Dielectrics

4.1 Polarization 4.1.1 Dielectrics 4.1.2 Induced Dipoles and Polarizability 4.1.3 Alignment of polar molecules 4.1.4 Polarization and Susceptubility

4.1.1 Dielectrics According to their response to electrostatic field, most everyday objects belong to one of two large classes: conductors and insulators (or dielectrics): all charges are attached to specific atoms or molecules. Stretching and rotating are the two principle mechanisms by which electric fields can distort the charge distribution of a dielectric atom or molecule.

4.1.2 Induced Dipoles and Polarizability applied A neutral atom Polarized atom Atomic polarizability A simple estimate: The field at a distance d from the center of a uniform charge sphere At equilibrium, (v is the volume of the atom)

4.1.2 Usually the most general linear relation ( is polarizability tensor) or in (x,y,z) aij depend on the orientation of the axis you chose. It’s possible to select axes such that aij = 0 for

4.1.3 Alignment of Polar Molecules Polar molecules have built-in, permanent dipole moments s applied electric field (uniform) Torque

4.1.3 If the applied electric field is nonuniform, the total force is not zero. for short dipole,

4.1.4 Polarization and Susceptibility The polarization of a polarized dielectric dipole moment per unit volume is electric susceptibility tensor for linear dielectric is electric susceptibility

4.2 The Field of a Polarized Object 4.2.1 Bound charges 4.2.2 Physical Interpretation of Bound Charge 4.2.3 The Field Inside a Dielectric

4.2.1 Bound charges bound charges: surface charge volume charge

4.2.2 Physical Interpretation of Bound Charge and represent perfectly genuine accumulations of charge. for uniformly distributed dipoles for a uniform polarization and perpendicular cut s

4.2.2 (2) for a uniform polarization and oblique cut for the polarization is nonuniform ,

4.2.2 (3) Ex.2 Ex.9 of chapter 3 potential of a dipole moment

4.2.3 The Field Inside a Dielectric V averaged microscopic microscopic field is defined as the averaged field over region large enough. dielectric microscopic field at P or out

4.2.2 (4) Ex.3 as Ex.2 s for points outside,

4.2.3 Ex.3 (averaged field) uniform or

4.3 The Electric Displacement 4.3.1 Gauss’s Law in The Presence of Dielectrics 4.3.2 A Deceptive Parallel

4.3.1 Gauss’s Law in The Presence of Dielectrics bound free Gauss’s Law Gauss’s Law electric displacement

4.3.1 Ex.4 R r inside need to know outside >

4.3.2 A Deceptive Parallel or one equation need 2 more equations [ i.e., ] to get unique solution one unknown V, one equation. ? One equation: ?

Polarization; Linear Dielectrics 4.4 Self-Consistence of Electric Field and Polarization; Linear Dielectrics 4.4.1 Permittivity, Dielectric Constant 4.4.2 Special Problems Involving Linear Dielectrics 4.4.3 Energy in Dielectric System 4.4.4 Forces on Dielectrics 4.4.5 Polarizability and Susceptibility

4.4.1 Permittivity, Dielectric Constant self- consistence for linear dielectrics permittivity permittivity of free space dielectric constant

4.4.1 (2) Ex.5 ? for r < a for r > a for b > r > a dielectric ? for r < a for r > a for b > r > a for r > b

4.4.1 (3) for b > r > a at r = b at r = a

4.4.1 (4) ? even in linear dielectric may or may not ? If the surface or the loop is entirely in a uniform linear dielectric, But for vacuum Dielectric

4.4.1 (5) Q

4.4.2 Special problems Involving Linear Dielectrics Ex.7 ? Method 1.

4.4.2 (2) dielectric constant Method 2.

4.4.2 (3) Ex.8

4.4.2 (4) Total bound charge Method 1.

4.4.2 (5) Method 2. method of image

4.4.2 (6) Satisfy Poission’s eq The potential shown at above is the correct solution.

4.4.3 Energy in Dielectric System Suggestion: to charge a capacitor up with linear dielectric (constant K) energy stored in any electrostatic system (vacuum) with linear dielectric

4.4.3 (2) derivation: , for linear dielectric,

4.4.4 Forces on dielectrics with Q constant

4.4.4 (2) with V constant, such as with a battery that does work,

4.4.5 Polarizability and Susceptibility 1. polarization for linear dielectric susceptibility induced dipole moment of each atom or molecular atom polarizability What is the constant between α and Xe ? non-self-consistent field 2. 3. 4. 5. 5 equations, 5 variables

4.4.5 (2)

4.4.5 (3) Clausius-Mossott formula Lorentz-Lorenz equation in its application to optics