tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 55

Electromagnetic Field Theory: A Problem Solving Approach Part 55. 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. | Sinusoidal Time Variations 515 while the second has its electric field polarized in the y direction. Each solution alone is said to be linearly polarized because the electric field always points in the same direction for all time. If both Held solutions are present the direction of net electric field varies with time. In particular let us say that the x and y components of electric field at any value of z differ in phase by angle 4 E Re e e E cos wtix cos cot i 31 We can eliminate time as a parameter realizing from 31 that cos tot EJE . 32 . cos tot cos 6 EJE EJE - cos Ey EK sm tot ------ -------- -------- ---------- sin p sm p and using the identity that sin8 tot cos8 tot 1 _ i V i o 2 cos2 o 2 - ZEJSJEtgE cos tf eJ sin8 6 33 to give us the equation of an ellipse relating Ex to E I Ex 2 I E. 2EXEX t U xcos sin 34 as plotted in Figure 7-1 la. As time increases the electric field vector traces out an ellipse each period so this general case of the superposition of two linear polarizations with arbitrary phase 0 is known as elliptical polarization. There are two important special cases a Linear Polarization If Ex and are in phase so that J 0 34 reduces to 35 The electric field at all times is at a constant angle 0 to the x axis. The electric field amplitude oscillates with time along this line as in Figure 7-116. Because its direction is always along the same line the electric field is linearly polarized. b Circular Polarization If both components have equal amplitudes but are 90 out of phase o o. 6 w 2 36 516 Electrodynamics Fields and Waves _És_ 2 -5 2- 2 -V Exo Evo E Evo cos0 sin20 Elliptical polarization Figure 7-11 a Two perpendicular field components with phase difference have the tip of the net electric field vector tracing out an ellipse each period b If both field components are in phase the ellipse reduces to a straight line c If the field components have the same magnitude but are 90 out of phase the ellipse becomes a circle. The polarization is left .