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# guide05 - Chapter 5 Capacitance and Dielectrics 5.1...

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Chapter 5 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 5-1

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5.9 Problem-Solving Strategy: Calculating Capacitance. ......................................... 5-37 5.10 Solved Problems . .............................................................................................. 5-39 5.10.1 Equivalent Capacitance. ............................................................................. 5-39 5.10.2 Capacitor Filled with Two Different Dielectrics. ....................................... 5-40 5.10.3 Capacitor with Dielectrics. ......................................................................... 5-40 5.10.4 Capacitor Connected to a Spring. ............................................................... 5-42 5.11 Conceptual Questions . ...................................................................................... 5-42 5.12 Additional Problems . ........................................................................................ 5-43 5.12.1 Capacitors in Series and in Parallel . .......................................................... 5-43 5.12.2 Capacitors and Dielectrics . ........................................................................ 5-43 5.12.3 Gauss’s Law in the Presence of a Dielectric. ............................................. 5-44 5.12.4 Gauss’s Law and Dielectrics. ..................................................................... 5-44 5.12.5 A Capacitor with a Dielectric . ................................................................... 5-45 5.12.6 Force on the Plates of a Capacitor . ............................................................ 5-45 5.12.7 Energy Density in a Capacitor with a Dielectric . ...................................... 5-46 5-2
Capacitance and Dielectrics 5.1 Introduction A capacitor is a device which stores electric charge. Capacitors vary in shape and size, but the basic configuration is two conductors carrying equal but opposite charges (Figure 5.1.1). Capacitors have many important applications in electronics. Some examples include storing electric potential energy, delaying voltage changes when coupled with resistors, filtering out unwanted frequency signals, forming resonant circuits and making frequency-dependent and independent voltage dividers when combined with resistors. Some of these applications will be discussed in latter chapters.

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## This note was uploaded on 05/07/2010 for the course DMO electro23 taught by Professor Taflove during the Spring '10 term at Unicamp.

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guide05 - Chapter 5 Capacitance and Dielectrics 5.1...

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