Capacitance and Dielectrics

5.1 Introduction...5-3
5.2 Calculation of Capacitance...................................................................................5-4
Example 5.1: Parallel-Plate Capacitor....................................................................5-4
Interactive Simulation 5.1: Parallel-Plate Capacitor...........................................5-6
Example 5.2: Cylindrical Capacitor........................................................................5-6
Example 5.3: Spherical Capacitor...........................................................................5-8
5.3 Capacitors in Electric Circuits..............................................................................5-9
5.3.1 Parallel Connection......................................................................................5-10
5.3.2 Series Connection........................................................................................5-11
Example 5.4: Equivalent Capacitance..................................................................5-12
5.4 Storing Energy in a Capacitor.............................................................................5-13
5.4.1 Energy Density of the Electric Field............................................................5-14
Interactive Simulation 5.2: Charge Placed between Capacitor Plates..............5-14
Example 5.5: Electric Energy Density of Dry Air................................................5-15
Example 5.6: Energy Stored in a Spherical Shell.................................................5-15
5.5 Dielectrics...5-16
5.5.1 Polarization..................................................................................................5-18
5.5.2 Dielectrics without Battery..........................................................................5-21
5.5.3 Dielectrics with Battery...............................................................................5-22
5.5.4 Gauss's Law for Dielectrics.........................................................................5-23
Example 5.7: Capacitance with Dielectrics..........................................................5-25
5.6 Creating Electric Fields......................................................................................5-26
Animation 5.1: Creating an Electric Dipole........................................................5-26
Animation 5.2: Creating and Destroying Electric Energy...................................5-28
5.7 Summary...5-29
5.8 Appendix: Electric Fields Hold Atoms Together...............................................5-30
5.8.1 Ionic and van der Waals Forces...................................................................5-31
Interactive Simulation 5.3: Collection of Charges in Two Dimensions............5-32
Interactive Simulation 5.4: Collection of Charges in Three Dimensions..........5-34
Interactive Simulation 5.5: Collection of Dipoles in Two Dimensions............5-34
Interactive Simulation 5.6: Charged Particle Trap............................................5-35
Interactive Simulation 5.6: Lattice 3D..............................................................5-36
Interactive Simulation 5.7: 2D Electrostatic Suspension Bridge......................5-36
Interactive Simulation 5.8: 3D Electrostatic Suspension Bridge......................5-37

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