magnetic field - Chapter 8 Introduction to Magnetic Fields...

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Chapter 8 Introduction to Magnetic Fields 8.1 Introduction. .......................................................................................................... 8-2 8.2 The Definition of a Magnetic Field . ..................................................................... 8-3 8.3 Magnetic Force on a Current-Carrying Wire. ....................................................... 8-4 Example 8.1: Magnetic Force on a Semi-Circular Loop. ....................................... 8-6 8.4 Torque on a Current Loop . ................................................................................... 8-8 8.4.1 Magnetic force on a dipole . ......................................................................... 8-11 Animation 8.1: Torques on a Dipole in a Constant Magnetic Field. ................... 8-12 8.5 Charged Particles in a Uniform Magnetic Field. ................................................ 8-13 Animation 8.2: Charged Particle Moving in a Uniform Magnetic Field. ............ 8-15 8.6 Applications. ....................................................................................................... 8-15 8.6.1 Velocity Selector. ......................................................................................... 8-16 8.6.2 Mass Spectrometer. ...................................................................................... 8-17 8.7 Summary. ............................................................................................................ 8-18 8.8 Problem-Solving Tips. ........................................................................................ 8-19 8.9 Solved Problems . ................................................................................................ 8-20 8.9.1 Rolling Rod. ................................................................................................. 8-20 8.9.2 Suspended Conducting Rod. ........................................................................ 8-21 8.9.3 Charged Particles in Magnetic Field. ........................................................... 8-22 8.9.4 Bar Magnet in Non-Uniform Magnetic Field. ............................................. 8-23 8.10 Conceptual Questions . ...................................................................................... 8-24 8.11 Additional Problems . ........................................................................................ 8-24 8.11.1 Force Exerted by a Magnetic Field. ........................................................... 8-24 8.11.2 Magnetic Force on a Current Carrying Wire. ............................................ 8-24 8.11.3 Sliding Bar . ................................................................................................ 8-25 8.11.4 Particle Trajectory. ..................................................................................... 8-26 8.11.5 Particle Orbits in a Magnetic Field. ........................................................... 8-26 8.11.6 Force and Torque on a Current Loop. ........................................................ 8-27 8.11.7 Force on a Wire. ......................................................................................... 8-27 8.11.8 Levitating Wire. ......................................................................................... 8-28 8-1
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Introduction to Magnetic Fields 8.1 Introduction We have seen that a charged object produces an electric field E G at all points in space. In a similar manner, a bar magnet is a source of a magnetic field B G . This can be readily demonstrated by moving a compass near the magnet. The compass needle will line up along the direction of the magnetic field produced by the magnet, as depicted in Figure 8.1.1. Figure 8.1.1 Magnetic field produced by a bar magnet Notice that the bar magnet consists of two poles, which are designated as the north (N) and the south (S). Magnetic fields are strongest at the poles. The magnetic field lines leave from the north pole and enter the south pole. When holding two bar magnets close to each other, the like poles will repel each other while the opposite poles attract (Figure 8.1.2). Figure 8.1.2 Magnets attracting and repelling Unlike electric charges which can be isolated, the two magnetic poles always come in a pair. When you break the bar magnet, two new bar magnets are obtained, each with a north pole and a south pole (Figure 8.1.3). In other words, magnetic ±monopoles² do not exist in isolation, although they are of theoretical interest. Figure 8.1.3 Magnetic monopoles do not exist in isolation 8-2
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How do we define the magnetic field B G ? In the case of an electric field E , we have already seen that the field is defined as the force per unit charge: G e q F E G G (8.1.1) However, due to the absence of magnetic monopoles, B G must be defined in a different way. 8.2 The Definition of a Magnetic Field To define the magnetic field at a point, consider a particle of charge q and moving at a velocity . Experimentally we have the following observations: v G (1) The magnitude of the magnetic force B F G exerted on the charged particle is proportional to both v and q .
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This note was uploaded on 01/20/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas.

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magnetic field - Chapter 8 Introduction to Magnetic Fields...

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