By Yeon Ho Lee (auth.)
This textual content presents scholars with the lacking hyperlink which may aid them grasp the fundamental ideas of electromagnetics. the concept that of vector fields is brought via beginning with transparent definitions of place, distance, and base vectors. The symmetries of usual configurations are mentioned intimately, together with cylindrical, round, translational, and two-fold rotational symmetries. to prevent critical confusion among symbols with indices, the textual content adopts a brand new notation: a letter with subscript 1-2 for the paintings performed in relocating a unit cost from element 2 to indicate 1, within which the subscript 1-2 mimics the variation in potentials, whereas the hyphen implies a feeling of backward course, from 2 to one. this article contains three hundred figures within which actual information are attracted to scale. Many figures supply a 3-dimensional view. every one subsection incorporates a variety of examples which are solved through analyzing rigorous techniques in steps. every one subsection ends with user-friendly routines and solutions by which scholars can cost in the event that they accurately understood the ideas. a complete 350 of examples and routines are supplied. on the finish of every part, evaluation questions are inserted to show key techniques and kinfolk mentioned within the part. they're given with tricks relating the comparable equations and figures. The booklet features a overall of 280 end-of-chapter problems.
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Extra resources for Introduction to Engineering Electromagnetics
Example text
A) a vector in a vector field, (b) r, (c) R , (d) dl, and (f) ds. Ans. (a) Initial, (b) Terminal, (c) Terminal, (d) Initial, (f) Initial point of the vector. 16 What are (a) the similarity and (b) the dissimilarity between the position vector r = x ax + y ay + z az and a vector field A = x ax + y ay + z az . Ans. (a) Magnitude and direction, (b) Location. 2 27 Cylindrical Coordinate System Cylindrical coordinate system specifies a point p1: ( ρ1, φ1, z1 ) by the intersection of three surfaces; that is, a cylindrical surface of radius ρ1 centered on the z-axis, a half-plane rotated about the z-axis by an angle φ1 , and the z = z1 plane.
Since dl is infinitesimally small, the differential volume may be considered to be a rectangular parallelepiped of sides dρ, ρ1d φ , and dz, having a volume of ρ1 d ρ d φ dz . The differential volume in cylindrical coordinates is in general defined as d v = ρ d ρ d φ dz [m3 ] (1-56) Although dv may vary with position, the differential volume is always defined as Eq. (1-56) in cylindrical coordinates. The differential volume is useful for subdividing a volume in cylindrical coordinates into many differential elements of volume, and vice versa.
For instance, an infinitely long filament lying along the z-axis has the cylindrical, translational, and 2-fold rotational symmetries. The translational symmetry assures that the resultant field is independent of z as well, namely, G (r ) = G (ρ) and H(r ) = H ρ (ρ) aρ + H φ (ρ) aφ + H z (ρ) az . Moreover, the 2-fold rotational symmetry guarantees that the resulting vector field has neither the φcomponent nor the z-component. This is because the vector components H φ (ρ) aφ and H z (ρ) az do not have the 2-fold rotational symmetry: they reverse the sign when turned upside down(see Fig.