Chapter 5 Capacitance and Dielectrics 5.1 Introduction..… 2 5.2 Calculation of Capacitance................... 3 Example 5.1:Parallel-Plate Capacitor.... 3 Interactive Simulation 5.1:Parallel-Plate Capacitor Example 5.2:Cylindrical Capacitor 5 Example 5.3:Spherical Capacitor.... .7 5.3 Capacitors in Electric Circuits......... .8 5.3.1 Parallel Connection............... .9 5.3.2 Series Connection.... 10 Example 5.4:Equivalent Capacitance.... 11 5.4 Storing Energy in a Capacitor............... 12 5.4.1 Energy Density of the Electric Field....... 13 Interactive Simulation 5.2:Charge Placed between Capacitor Plates 13 Example 5.5:Electric Energy Density of Dry Air..................................... 14 Example 5.6:Energy Stored in a Spherical Shell...... 14 5.5 Dielectrics. 15 5.5.1 Polarization............ 17 5.5.2 Dielectrics without Battery.............. 20 5.5.3 Dielectrics with Battery........... 21 5.5.4 Gauss's Law for Dielectrics.............. 22 Example 5.7:Capacitance with Dielectrics 24 5.6 Creating Electric Fields 25 Animation 5.1:Creating an Electric Dipole..... 25 Animation 5.2:Creating and Destroying Electric Energy 27 5.7 Summary.… 28 5.8 Appendix:Electric Fields Hold Atoms Together............... 29 5.8.1 Ionic and van der Waals Forces.................... 30 Interactive Simulation 5.3:Collection of Charges in Two Dimensions ..31 Interactive Simulation 5.4:Collection of Charges in Three Dimensions 33 Interactive Simulation 5.5: Collection of Dipoles in Two Dimensions.............33 Interactive Simulation 5.6: Charged Particle Trap. 4 Interactive Simulation 5.6:Lattice 3D ........................... 35 Interactive Simulation 5.7:2D Electrostatic Suspension Bridge 35 Interactive Simulation 5.8:3D Electrostatic Suspension Bridge 36 5.9 Problem-Solving Strategy:Calculating Capacitance. 36 0Chapter 5 Capacitance and Dielectrics 5.1 Introduction.............................................................................................................. 2 5.2 Calculation of Capacitance ...................................................................................... 3 Example 5.1: Parallel-Plate Capacitor....................................................................... 3 Interactive Simulation 5.1: Parallel-Plate Capacitor .............................................. 5 Example 5.2: Cylindrical Capacitor........................................................................... 5 Example 5.3: Spherical Capacitor.............................................................................. 7 5.3 Capacitors in Electric Circuits................................................................................. 8 5.3.1 Parallel Connection........................................................................................... 9 5.3.2 Series Connection ........................................................................................... 10 Example 5.4: Equivalent Capacitance ..................................................................... 11 5.4 Storing Energy in a Capacitor................................................................................ 12 5.4.1 Energy Density of the Electric Field............................................................... 13 Interactive Simulation 5.2: Charge Placed between Capacitor Plates................. 13 Example 5.5: Electric Energy Density of Dry Air................................................... 14 Example 5.6: Energy Stored in a Spherical Shell.................................................... 14 5.5 Dielectrics.............................................................................................................. 15 5.5.1 Polarization ..................................................................................................... 17 5.5.2 Dielectrics without Battery ............................................................................. 20 5.5.3 Dielectrics with Battery .................................................................................. 21 5.5.4 Gauss’s Law for Dielectrics............................................................................ 22 Example 5.7: Capacitance with Dielectrics............................................................. 24 5.6 Creating Electric Fields ......................................................................................... 25 Animation 5.1: Creating an Electric Dipole ........................................................... 25 Animation 5.2: Creating and Destroying Electric Energy...................................... 27 5.7 Summary................................................................................................................ 28 5.8 Appendix: Electric Fields Hold Atoms Together .................................................. 29 5.8.1 Ionic and van der Waals Forces...................................................................... 30 Interactive Simulation 5.3: Collection of Charges in Two Dimensions............... 31 Interactive Simulation 5.4: Collection of Charges in Three Dimensions............. 33 Interactive Simulation 5.5: Collection of Dipoles in Two Dimensions ............... 33 Interactive Simulation 5.6: Charged Particle Trap ............................................... 34 Interactive Simulation 5.6: Lattice 3D ................................................................. 35 Interactive Simulation 5.7: 2D Electrostatic Suspension Bridge ......................... 35 Interactive Simulation 5.8: 3D Electrostatic Suspension Bridge ......................... 36 5.9 Problem-Solving Strategy: Calculating Capacitance............................................. 36 0