3: Polarization and Conduction
- Page ID
- 48125
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
The presence of matter modifies the electric field because even though the material is usually charge neutral, the field within the material can cause charge motion, called conduction, or small charge displacements, called polarization. Because of the large number of atoms, 6.02 x 1023 per gram molecular weight (Avogadro's number), slight imbalances in the distribution have large effects on the fields inside and outside the materials. We must then self-consistently solve for the electric field with its effect on charge motion and redistribution in materials, with the charges, resultant effect back as another source of electric field.
- 3.1: Polarization
- In many electrically insulating materials, called dielectrics, electrons are tightly bound to the nucleus. They are not mobile, but if an electric field is applied, the negative cloud of electrons can be slightly displaced from the positive nucleus, as illustrated in Figure 3-1a.
- 3.2: Conduction
- In contrast to dielectrics, most metals have their outermost band of electrons only weakly bound to the nucleus and are free to move in an applied electric field.
- 3.3: Field Boundary Conditions
- In many problems there is a surface of discontinuity separating dissimilar materials, such as between a conductor and a dielectric, or between different dielectrics. We must determine how the fields change as we cross the interface where the material properties change abruptly
- 3.4: Resistance
- Two conductors maintained at a potential difference V within a conducting medium will each pass a total current I, as shown in Figure 3-15.
- 3.5: Capacitance
- Parallel plate electrodes of finite size constrained to potential difference v enclose a dielectric medium with permittivity \(\varepsilon\). The surface charge density does not distribute itself uniformly, as illustrated by the fringing field lines for infinitely thin parallel plate electrodes in Figure 3-17a.
- 3.6: Lossy Media
- Many materials are described by both a constant permittivity \(\varepsilon\) and constant Ohmic conductivity \(\sigma\). When such a material is placed between electrodes do we have a capacitor or a resistor? We write the governing equations of charge conservation and Gauss's law with linear constitutive laws:
- 3.7: Field-dependent Space-Charge Distributions
- A stationary Ohmic conductor with constant conductivity was shown in Section 3-6-1 to not support a steady-state volume charge distribution.
- 3.8: Energy Stored in a Dielectric Medium
- The work needed to assemble a charge distribution is stored as potential energy in the electric field because if the charges are allowed to move this work can be regained as kinetic energy or mechanical work.
- 3.9: Fields and their Forces
- A confusion arises in applying Coulomb's law to find the perpendicular force on a sheet of surface charge as the normal electric field is different on each side of the sheet.
- 3.10: Electrostatic Generators
- In the 1930s, reliable means of generating high voltages were necessary to accelerate charged particles in atomic studies.