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# sourcesmagfields - Chapter 9 Sources of Magnetic Fields 9.1...

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Chapter 9 Sources of Magnetic Fields 9.1 Biot-Savart Law. ................................................................................................... 9-3 Interactive Simulation 9.1 : Magnetic Field of a Current Element. ...................... 9-4 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 . ................................................. 9-10 Animation 9.1 : Magnetic Field of a Moving Charge . ......................................... 9-11 Animation 9.2 : Magnetic Field of Several Charges Moving in a Circle. ............ 9-12 Interactive Simulation 9.2 : Magnetic Field of a Ring of Moving Charges . ...... 9-12 9.2 Force Between Two Parallel Wires . ................................................................... 9-13 Animation 9.3 : Forces Between Current-Carrying Parallel Wires. ..................... 9-14 9.3 Ampere’s Law. .................................................................................................... 9-14 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 . ................................................................... 9-25 Animation 9.4 : A Bar Magnet in the Earth’s Magnetic Field . ............................ 9-27 9.6 Magnetic Materials . ............................................................................................ 9-28 9.6.1 Magnetization . ............................................................................................. 9-28 9.6.2 Paramagnetism. ............................................................................................ 9-31 9.6.3 Diamagnetism . ............................................................................................. 9-32 9.6.4 Ferromagnetism . .......................................................................................... 9-32 9.7 Summary. ............................................................................................................ 9-33 9.8 Appendix 1: Magnetic Field off the Symmetry Axis of a Current Loop. ........... 9-35 9.9 Appendix 2: Helmholtz Coils . ............................................................................ 9-39 Animation 9.5 : Magnetic Field of the Helmholtz Coils . ..................................... 9-41 Animation 9.6 : Magnetic Field of Two Coils Carrying Opposite Currents . ....... 9-43 Animation 9.7 : Forces Between Coaxial Current-Carrying Wires. ..................... 9-44 9-1

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Animation 9.8 : Magnet Oscillating Between Two Coils . ................................... 9-44 Animation 9.9 : Magnet Suspended Between Two Coils. .................................... 9-45 9.10 Problem-Solving Strategies . ............................................................................. 9-46 9.10.1 Biot-Savart Law:. ....................................................................................... 9-46 9.10.2 Ampere’s law:. ........................................................................................... 9-48 9.11 Solved Problems . .............................................................................................. 9-49 9.11.1 Magnetic Field of a Straight Wire . ............................................................ 9-49 9.11.2 Current-Carrying Arc. ................................................................................ 9-51 9.11.3 Rectangular Current Loop. ......................................................................... 9-52 9.11.4 Hairpin-Shaped Current-Carrying Wire. .................................................... 9-54 9.11.5 Two Infinitely Long Wires . ....................................................................... 9-55 9.11.6 Non-Uniform Current Density. .................................................................. 9-57 9.11.7 Thin Strip of Metal. .................................................................................... 9-59 9.11.8 Two Semi-Infinite Wires . .......................................................................... 9-60 9.12 Conceptual Questions . ...................................................................................... 9-62 9.13 Additional Problems . ........................................................................................ 9-62 9.13.1 Application of Ampere's Law . ................................................................... 9-62 9.13.2 Magnetic Field of a Current Distribution from Ampere's Law. ................. 9-63 9.13.3 Cylinder with a Hole. ................................................................................. 9-64 9.13.4 The Magnetic Field Through a Solenoid . .................................................. 9-64 9.13.5 Rotating Disk . ............................................................................................ 9-65 9.13.6 Four Long Conducting Wires . ................................................................... 9-65 9.13.7 Magnetic Force on a Current Loop. ........................................................... 9-65 9.13.8 Magnetic Moment of an Orbital Electron. ................................................. 9-66 9.13.9 Ferromagnetism and Permanent Magnets. ................................................. 9-67 9.13.10 Charge in a Magnetic Field. ..................................................................... 9-67 9.13.11 Permanent Magnets. ................................................................................. 9-68 9.13.12 Magnetic Field of a Solenoid. .................................................................. 9-68 9.13.13 Effect of Paramagnetism. ......................................................................... 9-69 9-2
Sources of Magnetic Fields 9.1 Biot-Savart Law Currents which arise due to the motion of charges are the source of magnetic fields. When charges move in a conducting wire and produce a current I , the magnetic field at any point P due to the current can be calculated by adding up the magnetic field contributions, , from small segments of the wire d B G d s G , (Figure 9.1.1).

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## This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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sourcesmagfields - Chapter 9 Sources of Magnetic Fields 9.1...

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