9-0 99-1 Chapter 9 Sources of Magnetic Fields !9.1! Biot-Savart Law .................................................................................................. 9-3!Example 9.1: Magnetic Field due to a Finite Straight Wire ................................... 9-4!Example 9.2: Magnetic Field due to a Circular Current Loop ............................... 9-7!9.1.1! Magnetic Field of a Moving Point Charge .................................................. 9-9!9.1.2! Magnetic Field of a Moving Charge Movie .............................................. 9-10!9.1.3! Magnetic Field of Four Charges Moving in a Circle Movie ..................... 9-11!9.2! Force Between Two Parallel Wires .................................................................. 9-11!9.2.1! Forces between Current-Carrying Parallel Wires—The Experiment ........ 9-11!9.2.2! Forces between Parallel Wires—The Standard Argument ........................ 9-12!9.2.3! Forces between Parallel Wires Movie—Faraday’s Argument .................. 9-13!9.3! Ampere’s Law (see also Ampere’s Law Simulation in Section 9.14) .............. 9-13!Example 9.3: Field Inside and Outside a Current-Carrying Wire ........................ 9-17!Example 9.4: Magnetic Field Due to an Infinite Current Sheet ........................... 9-18!9.4! Solenoid ............................................................................................................ 9-20!Examaple 9.5: Toroid ............................................................................................. 9-23!9.5! Magnetic Field of a Dipole ............................................................................... 9-24!9.5.1! Earth’s Magnetic Field at MIT .................................................................. 9-26!9.6! Magnetic Materials ........................................................................................... 9-28!9.6.1! Magnetization ............................................................................................ 9-29!9.6.2! Paramagnetism ........................................................................................... 9-31!9.6.3! Diamagnetism ............................................................................................ 9-32!9.6.4! Ferromagnetism ......................................................................................... 9-32!9.7! Summary ........................................................................................................... 9-34!9.8! Appendix 1: Magnetic Field off the Symmetry Axis of a Current Loop .......... 9-35!9.9! Appendix 2: Helmholtz Coils ........................................................................... 9-40!9-2 9.9.1! Magnetic Field of the Helmholtz Coils Movie .......................................... 9-42!9.9.2! Magnetic Field of Two Coils Carrying Opposite Currents Movie ............ 9-44!9.9.3! Forces Between Coaxial Current-Carrying Wires Movie .......................... 9-45!9.9.4! Magnet Oscillating Between Two Coils Movie ......................................... 9-46!9.9.5! Magnet Suspended Between Two Coils Movie ......................................... 9-46!9.10! Problem-Solving Strategies .............................................................................. 9-47!9.10.1! Biot-Savart Law: ........................................................................................ 9-47!9.10.2! Ampere’s law: ............................................................................................ 9-49!9.11! Solved Problems ............................................................................................... 9-51!9.11.1! Magnetic Field of a Straight Wire .............................................................. 9-51!9.11.2! Current-Carrying Arc ................................................................................. 9-53!9.11.3! Rectangular Current Loop .......................................................................... 9-54!9.11.4! Hairpin-Shaped Current-Carrying Wire ..................................................... 9-56!9.11.5! Two Infinitely Long Wires ......................................................................... 9-57!9.11.6! Non-Uniform Current Density ................................................................... 9-59!9.11.7! Thin Strip of Metal ..................................................................................... 9-61!9.11.8! Two Semi-Infinite Wires ............................................................................ 9-62!9.12! Conceptual Questions ....................................................................................... 9-64!9.13! Additional Problems ......................................................................................... 9-64!9.13.1! Application of Ampere's Law ..................................................................... 9-64!9.13.2! Magnetic Field of a Current Distribution from Ampere's Law .................. 9-65!9.13.3! Cylinder with a Hole .................................................................................. 9-66!9.13.4! The Magnetic Field Through a Solenoid .................................................... 9-67!9.13.5! Rotating Disk .............................................................................................. 9-67!9.13.6! Four Long Conducting Wires ..................................................................... 9-67!9.13.7! Magnetic Force on a Current Loop ............................................................ 9-68!9.13.8! Magnetic Moment of an Orbital Electron .................................................. 9-68!9.13.9! Ferromagnetism and Permanent Magnets .................................................. 9-69!9.13.10! Charge in a Magnetic Field .................................................................... 9-70!9.13.11! Permanent Magnets ................................................................................ 9-70!9.13.12! Magnetic Field of a Solenoid ................................................................. 9-70!9.13.13! Effect of Paramagnetism ........................................................................ 9-71!9.14! Ampere’s Law Simulation ................................................................................ 9-71!9-3 Sources of Magnetic Fields In Chapter 8, we defined what we mean by a magnetic field and discussed at length the effect the magnetic
View Full Document
Unlocking...