The McGraw-Hill Companies. Engineering Electromagnetics. Sixth Edition. William H. Hayt, Jr.. John A. Buck. Textbook Table of Contents. The Textbook Table. Library of Congress Cataloging-in-Publication Data Hayt, William Hart, – Engineering electromagnetics / William H. Hayt, Jr., John A. Buck. — 8th ed. p. cm. Engineering electromagnetics / William H. Hayt, Jr., John A. Buck. industry, Professor Hayt joined the faculty of Purdue University, where he served as.
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In addition, quizzes are provided to aid in further study. The theme of the text is the same as it has been since the first edition of An inductive approach is used that is consistent with the historical development. After the first chapter on vector analysis, additional math- ematical tools are introduced in the text on an as-needed basis.
Throughout every edition, as well as this one, the primary goal has been to enable students to learn independently. Numerous examples, drill problems usually having multiple parts , end-of-chapter problems, and material on the web site, are provided to facilitate this.
Engineering Electromagnetics 8th Edition William H. Hayt Original
Answers to the drill problems are given below each problem. Answers to odd- numbered end-of-chapter problems are found in Appendix F. A solutions manual and a set of PowerPoint slides, containing pertinent figures and equations, are avail- able to instructors.
These, along with all other material mentioned previously, can be accessed on the website:.
Engineering Electromagnetics 8th Edition William H. Hayt Original
I would like to acknowledge the valuable input of several people who helped to make this a better edition. Special thanks go to Glenn S.
Smith Georgia Tech , who reviewed the antennas chapter and provided many valuable comments and sug- gestions. Other reviewers provided detailed com- ments and suggestions at the start of the project; many of the suggestions affected the outcome. They include:. Jackson — University of Houston Karim Y.
I also acknowledge the feedback and many comments from students, too numerous to name, including several who have contacted me from afar.
I continue to be open and grateful for this feedback and can be reached at john. Many suggestions were made that I considered constructive and actionable. I regret that not all could be incorporated because of time restrictions. Creating this book was a team effort, involving several outstanding people at McGraw-Hill.
These include my publisher, Raghu Srinivasan, and sponsoring editor, Peter Massar, whose vision and encouragement were invaluable, Robin Reed, who deftly coordinated the production phase with excellent ideas and enthusiasm, and Darlene Schueller, who was my guide and conscience from the beginning, providing valuable insights, and jarring me into action when necessary. Diana Fouts Georgia Tech applied her vast artistic skill to designing the cover, as she has done for the previous two editions.
Finally, I am, as usual in these projects, grateful to a patient and supportive family, and particularly to my daughter, Amanda, who assisted in preparing the manuscript. On the cover: Radiated intensity patterns for a dipole antenna, showing the cases for which the wavelength is equal to the overall antenna length red , two-thirds the antenna length green , and one-half the antenna length blue.
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Be sure to ask your local McGraw-Hill representative for details. V ector analysis is a mathematical subject that is better taught by mathematiciansthan by engineers. Most junior and senior engineering students have not hadthe time or the inclination to take a course in vector analysis, although it is likely that vector concepts and operations were introduced in the calculus sequence.
These are covered in this chapter, and the time devoted to them now should depend on past exposure. The viewpoint here is that of the engineer or physicist and not that of the mathe- matician. Proofs are indicated rather than rigorously expounded, and physical inter- pretation is stressed. It is easier for engineers to take a more rigorous course in the mathematics department after they have been presented with a few physical pictures and applications.
Vector analysis is a mathematical shorthand. It has some new symbols and some new rules, and it demands concentration and practice.
The drill problems, first found at the end of Section 1. They should not prove to be difficult if the material in the accompanying section of the text has been thoroughly understood. The x, y , and z we use in basic algebra are scalars, and the quantities they represent are scalars. If we speak of a body falling a distance L in a time t , or the temperature T at any point in a bowl of soup whose coordinates are x, y , and z , then L , t, T, x, y , and z are all scalars.
Other scalar quantities are mass, density, pressure but not force , volume, volume resistivity, and voltage.
A vector quantity has both a magnitude1 and a direction in space. We are con- cerned with two- and three-dimensional spaces only, but vectors may be defined in. Force, velocity, acceleration, and a straight line from the positive to the negative terminal of a storage battery are examples of vectors. Each quantity is characterized by both a magnitude and a direction.
Our work will mainly concern scalar and vector fields. A field scalar or vector may be defined mathematically as some function that connects an arbitrary origin to a general point in space. Note that the field concept invariably is related to a region. Some quantity is defined at every point in a region. Both scalar fields and vector fields exist. The temperature throughout the bowl of soup and the density at any point in the earth are examples of scalar fields.
The gravitational and magnetic fields of the earth, the voltage gradient in a cable, and the temperature gradient in a soldering-iron tip are examples of vector fields. The value of a field varies in general with both position and time. In this book, as in most others using vector notation, vectors will be indicated by boldface type, for example, A. Scalars are printed in italic type, for example, A. When writing longhand, it is customary to draw a line or an arrow over a vector quantity to show its vector character.
This is the first pitfall. Sloppy notation, such as the omission of the line or arrow symbol for a vector, is the major cause of errors in vector analysis. Some of the rules will be similar to those of scalar algebra, some will differ slightly, and some will be entirely new.
To begin, the addition of vectors follows the parallelogram law. Figure 1. Vector addition also obeys the associative law,. Coplanar vectors are vectors lying in a common plane, such as those shown. Vectors in three dimensions may likewise be added by expressing the vectors in terms of three components and adding the corresponding components.
Examples of this process of addition will be given after vector components are discussed in Section 1. Vectors may be multiplied by scalars. The magnitude of the vector changes, but its direction does not when the scalar is positive, although it reverses direction when multiplied by a negative scalar. The projection is:. The angle is found through the dot product of the associated unit vectors, or:. The four vertices of a regular tetrahedron are located at O 0 , 0 , 0 , A 0 , 1 , 0 , B 0.
To express this in cartesian, we use. Express in cartesian components: Convert to cylindrical: Taking A and B as vectors directed from the origin, the requested length is. Each does, as shown above. This will be. First transform the points to cartesian: Express the unit vector a x in spherical components at the point: First, transform the point to spherical coordinates.
Again, convert the point to spherical coordinates. First convert A and B to cartesian: The requested arc length is then. A fifth 10nC positive charge is located at a point 8cm distant from the other charges. Arrange the charges in the xy plane at locations 4,4 , 4,-4 , -4,4 , and -4, By symmetry, the force on the fifth charge will be z -directed, and will be four times the z component of force produced by each of the four other charges.
To solve this problem, the z coordinate of the third charge is immaterial, so we can place it in the xy plane at coordinates x, y, 0.
We take its magnitude to be Q 3. The force on the third charge is now. Find the total force on the charge at A.
This force will be. This force in general will be:. Note, however, that all three charges must lie in a straight line, and the location of Q 3 will be along the vector R 12 extended past Q 2. Therefore, we look for P 3 at coordinates x, 2.
With this restriction, the force becomes:. The coordinates of P 3 are thus P 3 This field will be. This expression simplifies to the following quadratic:. The field will take the general form:. The total field at P will be:.
The x component of the field will be. At point P , the condition of part a becomes. Determine E at P 0 , y, 0: The field will be. This field will be:. Now, since the charge is at the origin, we expect to obtain only a radial component of E M. This will be:.
Calculate the total charge present: A uniform volume charge density of 0. If the integral over r in part a is taken to r 1, we would obtain[. With the limits thus changed, the integral for the charge becomes:. This is only a preview.
Load more. Search in the document preview. Plots are shown below. So the projection will be: The projection is: The angle is found through the dot product of the associated unit vectors, or: Describe the surfaces defined by the equations: This is the equation of a cylinder, centered on the x axis, and of radius 2.
Express in cylindrical components: Sketch F: The force will be: This force in general will be: With this restriction, the force becomes: Now the x component of E at the new P 3 will be: This expression simplifies to the following quadratic: The field will take the general form: The total field at P will be: At point P , the condition of part a becomes 3.
This field will be: This will be: With the limits thus changed, the integral for the charge becomes: This field will in general be: Therefore, at point P: Since all line charges are infinitely-long, we can write: We use the superposition integral: The integral becomes: Performing the z integration first on the x component, we obtain using tables: The superposition integral for the z component of E will be: The sum of the fields at the origin from each charge in order is: Taking the sum of the fields at the origin from the surface and line charges, respectively, we find: Access your Docsity account.
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You already have an account?What force per unit length does each line charge exert on the other? This is only a preview. Do not have an account? Buck Georgia Institute of Technology. Proofs are indicated rather than rigorously expounded, and physical inter- pretation is stressed.
I agree to the Terms and Conditions of this Service and I authorize the treatment of my personal data. We perform a line integral of Eq. All coins were insulated during the entire procedure, so they will retain their original charges: A uniform volume charge density of 0.
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