Capacitance and Dielectrics

5.1Introduction ... 5-3
5.2Calculation of Capacitance ................................................................................. 5-4
Example 5.1: Parallel-Plate Capacitor ..................................................................... 5-4
Example 5.2: Cylindrical Capacitor ......................................................................... 5-6
Example 5.3: Spherical Capacitor ............................................................................ 5-7
5.3Storing Energy in a Capacitor ............................................................................. 5-8
5.3.1Energy Density of the Electric Field .......................................................... 5-10
Example 5.4: Electric Energy Density of Dry Air ................................................. 5-11
Example 5.5: Energy Stored in a Spherical Shell .................................................. 5-11
5.4Dielectrics ... 5-12
5.4.1Polarization ................................................................................................ 5-14
5.4.2Dielectrics without Battery ........................................................................ 5-17
5.4.3Dielectrics with Battery ............................................................................. 5-18
5.4.4Gauss's Law for Dielectrics ....................................................................... 5-19
Example 5.6: Capacitance with Dielectrics ........................................................... 5-21
5.5Creating Electric Fields .................................................................................... 5-22
5.5.1Creating an Electric Dipole Movie ............................................................ 5-22
5.5.2Creating and Destroying Electric Energy Movie ....................................... 5-24
5.6Summary ... 5-25
5.7Appendix: Electric Fields Hold Atoms Together ............................................. 5-27
5.7.1Ionic and van der Waals Forces ................................................................. 5-27
5.8Problem-Solving Strategy: Calculating Capacitance ........................................ 5-29
5.9Solved Problems ............................................................................................... 5-31
5.9.1Capacitor Filled with Two Different Dielectrics ....................................... 5-31
5.9.2Capacitor with Dielectrics .......................................................................... 5-32
5.9.3Capacitor Connected to a Spring ............................................................... 5-33
5.10Conceptual Questions ....................................................................................... 5-34
5.11Additional Problems ......................................................................................... 5-35
5.11.1Capacitors and Dielectrics .......................................................................... 5-35
5.11.2Gauss's Law in the Presence of a Dielectric .............................................. 5-35
5.11.3Gauss's Law and Dielectrics ...................................................................... 5-36
5.11.4A Capacitor with a Dielectric ..................................................................... 5-36
5.11.5Force on the Plates of a Capacitor .............................................................. 5-37
5.11.6Energy Density in a Capacitor with a Dielectric ........................................ 5-38

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