TAILIEUCHUNG - Electromagnetic Field Theory: A Problem Solving Approach Part 57

Electromagnetic Field Theory: A Problem Solving Approach Part 57. 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. | Oblique Incidence onto a Perfect Conductor 535 There are no transmitted Helds within the perfect conductor but there is a reflected field with power flow at angle 0r from the interface normal. The reflected electric field is also in the y direction so the magnetic field which must be perpendicular to both E and S ExH is in the direction shown in Figure 7-17a Er Re ri - -x k I i T _ -I 3 Hr Re cos 04 sin e L-i J where the reflected wavenumbers are k k sin 0r 4 kir k cos Or At this point we do not know the angle of reflection 0T or the reflected amplitude Er. They will be determined from the boundary conditions at z 0 of continuity of tangential E and normal B. Because there are no fields within the perfect conductor these boundary conditions at z 0 are i r ilI re x O 5 - sin Oi e r sin 6U 0 These conditions must be true for every value of x along z 0 so that the phase factors given in 2 and 4 must be equal kx k O. 0r O 6 giving the well-known rule that the angle of incidence equals the angle of reflection. The reflected field amplitude is then r - i 7 with the boundary conditions in 5 being redundant as they both yield 7 . The total fields are then Ey Re i e v - e v 2 sin ktz sin cot kjc H Re f 4cos 0 e 1 sin 0 e c 1 i i8 2 ----- cos 0 cos Axz cos oot kjc ix V sin 0 sin kzz sin cot k x izj where without loss of generality we take to be real. 536 Electrodynamics Fields and Waves We drop the i and r subscripts on the wavenumbers and angles because they are equal. The fields travel in the x direction parallel to the interface but are stationary in the z direction. Note that another perfectly conducting plane can be placed at distances d to the left of the interface at ktd nir 9 where the electric field is already zero without disturbing the solutions of 8 . The boundary conditions at the second conductor are automatically satisfied. Such a structure is called a waveguide and is discussed in Section 8-6. Because the tangential component of H is discontinuous at z 0 a .

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