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## Chapter 4 Electrostatic Fields in Matter

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**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**Induced dipole 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**aijdepend on the orientation of the axis you chose. It’s possible to select axes such that aij = 0 for Usually the most general linear relation ( is polarizability tensor) or in (x,y,z)**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**and**represent perfectly genuine accumulations of charge. 4.2.2 Physical Interpretation of Bound 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**s**4.2.2 (4) Ex.3 as Ex.2 for points outside,**4.2.3**uniform Ex.3 (averaged field) 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**need to know > Ex.4 R r inside 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: ?**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)**for b > r > a for r > b dielectric Ex.5 ? for r < a for r > a**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**?**4.4.2 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: 0 , for linear dielectric,**4.4.4 Forces on dielectrics**with Q constant**4.4.4 (2)**with Vconstant, 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 αandXe ? non-self-consistent field 2. 3. 4. 5. 5 equations, 5 variables**4.4.5 (3)**Clausius-Mossott formula Lorentz-Lorenz equation in its application to optics