inductance - Chapter 11 Inductance and Magnetic Energy 11.1...

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Chapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance . ........................................................................................... 11-3 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops . .............. 11-5 11.2 Self-Inductance. ................................................................................................ 11-5 Example 11.2 Self-Inductance of a Solenoid. ....................................................... 11-6 Example 11.3 Self-Inductance of a Toroid. .......................................................... 11-7 Example 11.4 Mutual Inductance of a Coil Wrapped Around a Solenoid . .......... 11-8 11.3 Energy Stored in Magnetic Fields . ................................................................. 11-10 Example 11.5 Energy Stored in a Solenoid . ....................................................... 11-11 Animation 11.1 : Creating and Destroying Magnetic Energy. ........................... 11-12 Animation 11.2: Magnets and Conducting Rings . ............................................ 11-13 11.4 RL Circuits. ..................................................................................................... 11-15 11.4.1 Self-Inductance and the Modified Kirchhoff's Loop Rule. ...................... 11-15 11.4.2 Rising Current. ......................................................................................... 11-18 11.4.3 Decaying Current. .................................................................................... 11-20 11.5 LC Oscillations . .............................................................................................. 11-21 11.6 The RLC Series Circuit. .................................................................................. 11-26 11.7 Summary. ........................................................................................................ 11-28 11.8 Appendix 1: General Solutions for the RLC Series Circuit. ........................... 11-30 11.8.1 Quality Factor . ......................................................................................... 11-32 11.9 Appendix 2: Stresses Transmitted by Magnetic Fields . ................................. 11-33 Animation 11.3 : A Charged Particle in a Time-Varying Magnetic Field. ........ 11-37 11.10 Problem-Solving Strategies . ......................................................................... 11-38 11.10.1 Calculating Self-Inductance. .................................................................. 11-38 11.10.2 Circuits containing inductors. ................................................................ 11-39 11.11 Solved Problems . .......................................................................................... 11-39 11.11.1 Energy stored in a toroid. ....................................................................... 11-39 11.11.2 Magnetic Energy Density . ..................................................................... 11-40 11.11.3 Mutual Inductance . ................................................................................ 11-41 11.11.4 RL Circuit. .............................................................................................. 11-42 11.11.5 RL Circuit. .............................................................................................. 11-44 11.11.6 LC Circuit. .............................................................................................. 11-45 11.12 Conceptual Questions . .................................................................................. 11-47 11-1
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11.13 Additional Problems . .................................................................................... 11-48 11.13.1 Solenoid . ................................................................................................ 11-48 11.13.2 Self-Inductance . ..................................................................................... 11-48 11.13.3 Coupled Inductors. ................................................................................. 11-48 11.13.4 RL Circuit. .............................................................................................. 11-49 11.13.5 RL Circuit. .............................................................................................. 11-50 11.13.6 Inductance of a Solenoid With and Without Iron Core . ........................ 11-50 11.13.7 RLC Circuit. ........................................................................................... 11-51 11.13.8 Spinning Cylinder. ................................................................................. 11-52 11.13.9 Spinning Loop. ....................................................................................... 11-52 11-2
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Inductance 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 N 1 turns and carries a current I 1 which gives rise to a magnetic field 1 B G . 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 21 ) denote the magnetic flux through one turn of coil 2 due to I 1 . Now, by varying I 1 with time, there will be an induced emf associated with the changing magnetic flux in the second coil: 21 21 2 1 2 coil 2 d d N dt dt H d ) ± ± ² ³³ B A G G ( 1 1 . 1 . 1 ) The time rate of change of magnetic flux 21 ) in coil 2 is proportional to the time rate of change of the current in coil 1: 21 1 2 2 d N M dt dt 1 dI ) (11.1.2) where the proportionality constant 21 M is called the mutual inductance. It can also be written as 2 21 21 1 N M I ) (11.1.3) The SI unit for inductance is the henry (H): 11-3
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( 1 1 . 1 . 4 ) 2 1 henry 1 H 1 T m /A ± We shall see that the mutual inductance 21 M depends only on the geometrical properties of the two coils such as the number of turns and the radii of the two coils. In a similar manner, suppose instead there is a current I 2 in the second coil and it is varying with time (Figure 11.1.2). Then the induced emf in coil 1 becomes 12 12 1 2 1 coil 1 d d N dt dt H d ) ² ² ± ³³ B A G G ( 1 1 . 1 . 5 ) and a current is induced in coil 1.
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inductance - Chapter 11 Inductance and Magnetic Energy 11.1...

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