TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 44

Electromagnetic Field Theory: A Problem Solving Approach Part 44. 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 Circuits 405 6-2 MAGNETIC CIRCUITS Various alloys of iron having very high values of relative permeability are typically used in relays and machines to constrain the magnetic flux to mostly lie within the permeable material. 6-2-1 Self-Inductance The simple magnetic circuit in Figure 6-8 has an N turn coil wrapped around a core with very high relative permeability idealized to be infinite. There is a small air gap of length s in the core. In the core the magnetic flux density B is proportional to the magnetic field intensity H by an infinite permeability The B field must remain finite to keep the flux and coil voltage finite so that the H field in the core must be zero ÍH 0 lim B jtiH p. CO B finite Contour of integration of turn coil in the direction of the current Closed surface S has zero net flux through it Figure 6-8 The magnetic field is zero within an infinitely permeable magnetic core and is constant in the air gap if we neglect fringing. The flux through the air gap is constant at every cross section of the magnetic circuit and links the N turn coil N times. 1 406 Electromagnetic Induction The H field can then only be nonzero in the air gap. This field emanates perpendicularly from the pole faces as no surface currents are present so that the tangential component of H is continuous and thus zero. If we neglect fringing field effects assuming the gap s to be much smaller than the width d or depth D the H field is uniform throughout the gap. Using Ampere s circuital law with the contour shown the only nonzero contribution is in the air gap H dl Hs Itota enclosed Aff 2 where we realize that the coil current crosses perpendicularly through our contour N times. The total flux in the air gap is then 3 s Because the total flux through any closed surface is zero B-dS 0 4 all the flux leaving S in Figure 6-8 on the air gap side enters the surface through the iron core as we neglect leakage flux in the fringing field. The flux at any cross section in the .

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