TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 19

Electromagnetic Field Theory: A Problem Solving Approach Part 19. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Conduction 155 where n is the number density of charges T is the absolute temperature and k x 10-23 joule K is called Boltzmann s constant. The net pressure force on the small rectangular volume shown in Figure 3-10 is p x-bx -p x p y -p y y . f I----1------- ------Z------- Ax Ay z -p z Az . H------ ------ij I Ax Ay Az 12 Az where we see that the pressure only exerts a net force on the volume if it is different on each opposite surface. As the volume shrinks to infinitesimal size the pressure terms in 12 define partial derivatives so that the volume force density becomes hm Ax- O A - O Ax- 0 Ax Ay Az dx dy dz 13 Then using 11 13 Newton s force law for each charge carrier within the small volume is dv 1 m ---- gE m v v --------V n kT 14 dt n p z As Figure 3-10 Newton s force law applied to a small rectangular volume Ax Ay Az moving with velocity v enclosing positive charges with number density ri. The pressure is the force per unit area acting normally inward on each surface and only contributes to the net force if it is different on opposite faces. 156 Polarization and Conduction where the electric field E is due to the imposed field plus the field generated by the charges as given by Gauss s law. b Drift-Diffusion Conduction Because in many materials the collision frequencies are typically on the order of v 10ls Hz the inertia terms in 14 are often negligible. In this limit we can easily solve 14 for the velocity of each carrier as lim v iE- V n kT 15 The charge and current density for each carrier are simply given as p qn p v qn v 16 Multiplying 15 by the charge densities then gives us the constitutive law for each current as J in v p E - D p 17 where p are called the particle mobilities and are their diffusion coefficients A --- A-kg- -s-2 D - - m2-s- 18 m v m v assuming that the system is at constant temperature. We see that the ratio D lp for each carrier is the same having units of voltage thus called the thermal voltage Z kT 2 - -S volts kg-m2-A l-s 3 .

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