tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 48

Electromagnetic Field Theory: A Problem Solving Approach Part 48. 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. | Magnetic Diffusion into an Ohmic Conductor 445 W Figure 6-28 a A conducting material moving through a magnetic field tends to pull the magnetic field and current density with it. b The magnetic field and current density are greatly disturbed by the flow when the magnetic Reynolds number is large Rm aftUl 1. when substituted back into 41 yield two allowed values of p 2 P nov0p 0 p Q p zav0 43 Since 41 is linear the most general solution is just the sum of the two allowed solutions Hz x AieR x A2 44 446 Electromagnetic Induction where the magnetic Reynold s number is defined as mu. 2 Rm ff ivol 45 l vo and represents the ratio of a representative magnetic diffusion time given by 28 to a fluid transport time Hv0 . The boundary conditions are Hz x 0 Ko Hz x l Q 46 so that the solution is Hz x - eR xl -eR 47 1 e m The associated current distribution is then j VxH iy dx y -A-v 1 e m l The field and current distributions plotted in Figure 6-284 for various Rm show that the magnetic field and current are pulled along in the direction of flow. For small the magnetic field is hardly disturbed from the zero flow solution of a linear field and constant current distribution. For very large Rm 1 the magnetic field approaches a uniform distribution while the current density approaches a surface current at x I. The force on the moving fluid is independent of the flow velocity f i jXgoHsDdx Jo 1 e I Jq _ K oSD R leR g I- - 2 2 lox oK osDix 49 6-4-6 A Linear Induction Machine The induced currents in a conductor due to a time varying magnetic field give rise to a force that can cause the conductor to move. This describes a motor. The inverse effect is when we cause a conductor to move through a time varying Magnetic Diffusion into an Ohmic Conductor 447 magnetic field generating a current which describes a generator. The linear induction machine shown in Figure 6-29o assumes a conductor moves to the right at constant velocity 7iz. Directly below the conductor with no gap is a surface