TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 47

Electromagnetic Field Theory: A Problem Solving Approach Part 47. 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 435 If the flux itself depends on the number of turns as in Figure 6-246 there may be a contribution to the voltage even if the exciting current is de. This is true for the turns being wound onto the cylinder in Figure 6-246. For the tap changing configuration in Figure 6-24c with uniformly wound turns the ratio of turns to effective length is constant so that a de current will still not generate a voltage. 6-4 MAGNETIC DIFFUSION INTO AN OHMIC CONDUCTOR If the current distribution is known the magnetic field can be directly found from the Biot-Savart or Ampere s laws. However when the magnetic field varies with time the generated electric field within an Ohmic conductor induces further currents that also contribute to the magnetic field. 6-4-1 Resistor-Inductor Model A thin conducting shell of radius Rit thickness A and depth I is placed within a larger conducting cylinder as shown in Figure 6-25. A step current Io is applied at t 0 to the larger cylinder generating a surface current K loll . If the length I is much greater than the outer radius Ro the magnetic field is zero outside the cylinder and uniform inside for Ri r R0. Then from the boundary condition on the discontinuity of tangential H given in Section 5-6-1 we have Ho Ri r R0 1 i The magnetic field is different inside the conducting shell because of the induced current which from Lenz s law flows in the opposite direction to the applied current. Because the shell is assumed to be very thin A R this induced current can be considered a surface current related to the volume current and electric field in the conductor as K J A orA E 2 The product o-A is called the surface conductivity. Then the magnetic fields on either side of the thin shell are also related by the boundary condition of Section 5-6-1 Hi Ho K t arà E f 3 Much of the treatment of this section is similar to that of H. H. Woodson and J. R. Melcher Electromechanical Dynamics Part II Wiley . 1968 Ch.

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