Chapter 11IInductance and Magnetic EnergyMutual InductanceExample 11.1 Mutual Inductance of Two Concentric Coplanar LoSelf-InductanceExample 11.2 Self-Inductance of a SolenoidExample 11.3 Self-Inductance of a ToroidExample 11.4 Mutual Inductance of a Coil Wrapped Around a SoEnergy Stored in Magnetic FieldsExample 11.5 Energy Stored in a SolenoidAnimation 11.1: Creating and Destroying Magnetic EnergyAnimation 11.2: Magnets and Conducting RingsRL CircuitsSelf-Inductance and the Modified Kirchhoff's Loop RuleRising CurrentDecaying CurrentLC OscillationsThe RLC Series CircuitSummaryAppendix 1: General Solutions for the RLC Series CircuitQuality FactorAppendix 2: Stresses Transmitted by Magnetic FieldsAnimation 11.3: A Charged Particle in a Time-Varying MagnetiProblem-Solving StrategiesCalculating Self-InductanceCircuits containing inductorsSolved ProblemsEnergy stored in a toroidMagnetic Energy DensitySolution:Mutual InductanceRL CircuitRL CircuitLC CircuitConceptual QuestionsAdditional ProblemsSolenoidSelf-InductanceCoupled InductorsRL CircuitRL CircuitInductance of a Solenoid With and Without Iron CoreRLC CircuitSpinning CylinderSpinning LoopChapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance ..................................................................................................2 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops .....................4 11.2 Self-Inductance.......................................................................................................4 Example 11.2 Self-Inductance of a Solenoid..............................................................5 Example 11.3 Self-Inductance of a Toroid.................................................................6 Example 11.4 Mutual Inductance of a Coil Wrapped Around a Solenoid .................7 11.3 Energy Stored in Magnetic Fields ..........................................................................9 Example 11.5 Energy Stored in a Solenoid..............................................................10 Animation 11.1: Creating and Destroying Magnetic Energy..................................11 Animation 11.2: Magnets and Conducting Rings ...................................................12 11.4 RL Circuits............................................................................................................14 11.4.1 Self-Inductance and the Modified Kirchhoff's Loop Rule.............................14 11.4.2 Rising Current................................................................................................17 11.4.3 Decaying Current...........................................................................................19 11.5 LC Oscillations .....................................................................................................20 11.6 The RLC Series Circuit.........................................................................................25 11.7 Summary...............................................................................................................27 11.8 Appendix 1: General Solutions for the RLC Series Circuit..................................29 11.8.1 Quality Factor ................................................................................................31 11.9 Appendix 2: Stresses Transmitted by Magnetic Fields ........................................32 Animation 11.3: A Charged Particle in a Time-Varying Magnetic Field...............36 11.10 Problem-Solving Strategies ................................................................................37 11.10.1 Calculating Self-Inductance.........................................................................37 11.10.2 Circuits containing inductors.......................................................................38 11.11 Solved Problems .................................................................................................38 11.11.1 Energy stored in a toroid..............................................................................38 11.11.2 Magnetic Energy Density ............................................................................39 11.11.3 Mutual Inductance .......................................................................................40 11.11.4 RL Circuit.....................................................................................................41 11.11.5 RL Circuit.....................................................................................................43 11.11.6 LC Circuit.....................................................................................................44 11.12 Conceptual Questions .........................................................................................46 011.13 Additional Problems ...........................................................................................47 11.13.1 Solenoid .......................................................................................................47 11.13.2 Self-Inductance ............................................................................................47 11.13.3 Coupled Inductors........................................................................................47 11.13.4 RL Circuit.....................................................................................................48 11.13.5 RL Circuit.....................................................................................................49 11.13.6 Inductance of a Solenoid With and Without Iron Core ...............................49 11.13.7 RLC Circuit..................................................................................................50 11.13.8 Spinning Cylinder........................................................................................51 11.13.9 Spinning Loop..............................................................................................51 1Inductance and Magnetic Energy 11.1 Mutual Inductance Suppose two coils are placed near each other, as shown in Figure 11.1.1 Figure 11.1.1 Changing current in coil 1 produces changing magnetic flux in coil 2. The first coil has N1 turns and carries a current I1 which gives rise to a magnetic field 1BG. Since the two coils are close to each other, some of the magnetic field lines through coil 1 will also pass through coil 2. Let 21Φdenote the magnetic flux through one turn of coil 2 due to I1. Now, by
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