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CHAPTER 9 MAGNETIC FORCES, MATERIALS, AND INDUCTANCE The magnetic field quantities H , B , ± , V m , and A introduced in the last chapter were not given much physical significance. Each of these quantities is merely defined in terms of the distribution of current sources throughout space. If the current distribution is known, we should feel that H , B , and A are determined at every point in space, even though we may not be able to evaluate the defining integrals because of mathematical complexity. We are now ready to undertake the second half of the magnetic field problem, that of determining the forces and torques exerted by the magnetic field on other charges. The electric field causes a force to be exerted on a charge which may be either stationary or in motion; we shall see that the steady mag- netic field is capable of exerting a force only on a moving charge. This result appears reasonable; a magnetic field may be produced by moving charges and may exert forces on moving charges; a magnetic field cannot arise from station- ary charges and cannot exert any force on a stationary charge. This chapter initially considers the forces and torques on current-carrying conductors which may either be of a filamentary nature or possess a finite cross section with a known current density distribution. The problems associated with the motion of particles in a vacuum are largely avoided. 274
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With an understanding of the fundamental effects produced by the mag- netic field, we may then consider the varied types of magnetic materials, the analysis of elementary magnetic circuits, the forces on magnetic materials, and finally, the important electrical circuit concepts of self-inductance and mutual inductance. 9.1 FORCE ON A MOVING CHARGE In an electric field the definition of the electric field intensity shows us that the force on a charged particle is F ± Q E ² 1 ³ The force is in the same direction as the electric field intensity (for a positive charge) and is directly proportional to both E and Q . If the charge is in motion, the force at any point in its trajectory is then given by (1). A charged particle in motion in a magnetic field of flux density B is found experimentally to experience a force whose magnitude is proportional to the product of the magnitudes of the charge Q , its velocity v , and the flux density B , and to the sine of the angle between the vectors v and B . The direction of the force is perpendicular to both v and B and is given by a unit vector in the direction of v ´ B . The force may therefore be expressed as F ± Q v ´ B ² 2 ³ A fundamental difference in the effect of the electric and magnetic fields on charged particles is now apparent, for a force which is always applied in a direction at right angles to the direction in which the particle is proceeding can never change the magnitude of the particle velocity. In other words, the acceleration vector is always normal to the velocity vector. The kinetic energy
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This note was uploaded on 03/30/2010 for the course EE 2317 taught by Professor Wilton during the Spring '10 term at University of Houston.

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