chapter 08 - Chapter 8 MAGNETIC FORCES, MATERIALS, AND...

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Chapter 8 MAGNETIC FORCES, MATERIALS, AND DEVICES Do all the good you can, By all the means you can, In all the ways you can, In all the places you can, At all the times you can, To all the people you can, As long as ever you can. —JOHN WESLEY 8.1 INTRODUCTION Having considered the basic laws and techniques commonly used in calculating magnetic field B due to current-carrying elements, we are prepared to study the force a magnetic field exerts on charged particles, current elements, and loops. Such a study is important to problems on electrical devices such as ammeters, voltmeters, galvanometers, cyclotrons, plasmas, motors, and magnetohydrodynamic generators. The precise definition of the mag- netic field, deliberately sidestepped in the previous chapter, will be given here. The con- cepts of magnetic moments and dipole will also be considered. Furthermore, we will consider magnetic fields in material media, as opposed to the magnetic fields in vacuum or free space examined in the previous chapter. The results of the preceding chapter need only some modification to account for the presence of materi- als in a magnetic field. Further discussions will cover inductors, inductances, magnetic energy, and magnetic circuits. 8.2 FORCES DUE TO MAGNETIC FIELDS There are at least three ways in which force due to magnetic fields can be experienced. The force can be (a) due to a moving charged particle in a B field, (b) on a current element in an external B field, or (c) between two current elements. 304
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8.2 FORCES DUE TO MAGNETIC FIELDS 305 A. Force on a Charged Particle According to our discussion in Chapter 4, the electric force F e on a stationary or moving electric charge Q in an electric field is given by Coulomb's experimental law and is related to the electric field intensity E as F e = QE (8.1) This shows that if Q is positive, F e and E have the same direction. A magnetic field can exert force only on a moving charge. From experiments, it is found that the magnetic force F m experienced by a charge Q moving with a velocity u in a magnetic field B is F m = Qn X B (8.2) This clearly shows that F m is perpendicular to both u and B. From eqs. (8.1) and (8.2), a comparison between the electric force ¥ e and the magnetic force F m can be made. F e is independent of the velocity of the charge and can perform work on the charge and change its kinetic energy. Unlike F e , F m depends on the charge ve- locity and is normal to it. F m cannot perform work because it is at right angles to the direc- tion of motion of the charge (F m d\ = 0); it does not cause an increase in kinetic energy of the charge. The magnitude of F m is generally small compared to F e except at high ve- locities. For a moving charge Q in the presence of both electric and magnetic fields, the total force on the charge is given by F = F + F or F = g(E + u X B) (8.3) This is known as the Lorentz force equation.
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This note was uploaded on 12/20/2010 for the course E E 330_315 taught by Professor Dinavahiandiyer during the Fall '10 term at University of Alberta.

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chapter 08 - Chapter 8 MAGNETIC FORCES, MATERIALS, AND...

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