ECE320_Chapter_2 - ECE 320 Energy Conversion and Power Electronics Spring 2009 Instructor Tim Hogan Chapter 2 Magnetic Circuits and Materials

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1- 1 ECE 320 Energy Conversion and Power Electronics Spring 2009 Instructor: Tim Hogan Chapter 2: Magnetic Circuits and Materials Chapter Objectives In this chapter you will learn the following: How Maxwell’s equations can be simplified to solve simple practical magnetic problems The concepts of saturation and hysteresis of magnetic materials The characteristics of permanent magnets and how they can be used to solve simple problems How Faraday’s law can be used in simple windings and magnetic circuits Power loss mechanisms in magnetic materials How force and torque is developed in magnetic fields 2.1 Ampere’s Law and Magnetic Quantities Ampere’s experiment is illustrated in Figure 1 where there is a force on a small current element I 2 l when it is placed a distance, r , from a very long conductor carrying current I 1 and that force is quantified as: l I r I F 2 1 2 π μ = (N) (2.1) I 1 r I 2 F Conductor 1 Current Element of Length l Figure 1. Ampere’s experiment of forces between current carrying wires. The magnetic flux density, B , is defined as the first portion of equation (2.1) such that: l BI F 2 = (N) (2.2)
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1- 2 From (2.1) and (2.2) we see the magnetic flux density around conductor 1 is proportional to the current through conductor 1, I 1 , and inversely proportional to the distance from conductor 1. Looking at the units and constants handout given in class, or from (2.2) the units of, B , are seen as m A N , thus μ , called permeability, has units of 2 A N . More commonly, the relative permeability of a given material is given where 0 μ r = and × = m A N 10 400 9 0 π . Since a Newton-meter is a Joule, and a Joule is a Watt-second: = = = = 2 2 2 2 m s V m A s A V m A J m A m N m A N . This shows B is a per meter squared quantity, and the (V·s) units represents the magnetic flux and is given units of Webers (Wb). This flux can be found by integrating the normal component of B over the area of a given surface: = S ds n B ˆ φ (2.3) The magnetic field intensity is related to the magnetic flux density by the permeability of the media in which the magnetic flux exists. B H (2.4) For the system in Figure 1, r I B H 2 1 = = and have units of m A . If there were multiple conductors in place of conductor 1, for example in a coil, then the units would be ampere-turns per meter. A line integration of H over a closed circular path gives the current enclosed by that path, or for the system in Figure 1: 1 2 0 1 2 I dl r I dl H H r C = = = (2.5) again, if the system contained multiple conductors within the enclosed path, the result would give ampere-turns. Equation (2.5) is Ampere’s circuital law.
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This note was uploaded on 05/30/2009 for the course ECE ECE 320 taught by Professor Timhogan during the Spring '09 term at Michigan State University.

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ECE320_Chapter_2 - ECE 320 Energy Conversion and Power Electronics Spring 2009 Instructor Tim Hogan Chapter 2 Magnetic Circuits and Materials

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