Electromagnetic Field Theory: A Problem Solving Approach Part 50. 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. | Problems 465 11 can be rewritten as Fx M Z ox The total force is then fi-fio n2i2d 2 s 15 where the fields at x oo are zero and the field at x x0 is given by 12 . High permeability material is attracted to regions of stronger magnetic Held. It is this force that causes iron materials to be attracted towards a magnet. Diamagnetic materials p no will be repelled. This same result can more easily be obtained using 6 where the flux through the gap is 0 HD fi0 a - x i P Po x ano 16 so that the inductance is jV N2D L -------- 4- 40 oAto 17 I s Then the force obtained using 6 agrees with 15 f _ir2 dL x 4-2 dT p-po N2l2D 18 PROBLEMS Section 6-1 1. A circular loop of radius a with Ohmic conductivity tr and cross-sectional area A has its center a small distance D away from an infinitely long time varying current. 466 Electromagnetic Induction v Cross-sectional area A a Find the mutual inductance M and resistance R of the loop. Hint f dx 2_i rVa2 i2 tan x 2 1 I a a tan I I J a b cos x -Ja2 b2 L a b -I b This loop is stationary and has a self-inductance L. What is the time dependence of the induced short circuit current when the line current is instantaneously stepped on to a de level I at t 0 c Repeat b when the line current has been on a long time and is suddenly turned off at t T. d If the loop has no resistance and is moving with radial velocity vT dr dt what is the short circuit current and open circuit voltage for a de line current e What is the force on the loop when it carries a current i Hint cos d d b D a cos d 1 -1 r JL1 sm cos p D . . ia D cos d a Di-a1 Sm f a cos d 2. A rectangular loop at the far left travels with constant velocity I7ix towards and through a de surface current sheet Xoi at x 0. The right-hand edge of the loop first reaches the current sheet at t 0. a What is the loop s open circuit voltage as a function of time b What is the short circuit current if the loop has selfinductance L and resistance R c Find the open circuit voltage if the surface
