Chapter One: Vector Analysis The use of vectors and vector analysis ...

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Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department We have ∙ ∙ ∙ ∙ ∙ ∙ If this is zero; then either is parallel to (including the case in which they point in opposite directions, or one is zero), or else ∙ ∙ 0 in which case is perpendicular to and (including the case 0). Concluding: either: 1‐ is parallel to , or 2‐ is perpendicular to and . Position Displacement: The location of a point in three dimensions can be described by listing its Cartesian coordinates , , . The vector to that point form the origin is called the position vector; Its magnitude: The unit vector pointing radially outword, is || ̂ || z , , y x The infinitesimal displacement vector, from , , to , , is: The infinitesimal surface of Cartesian Coordinate is: 8
Electromagnetic Theorem (Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department Vector Transformation: Suppose, the , , system is rotated by angle , relative to , , , about the common ′. cos sin z' z While; y' ′ cos cos cos cos sin sin cos sin sin sin sin cos cos sin sin cos In matrix notation; ′ ′ More generally, for rotation about an arbitrary axis in three dimensions: ′ ′ ′ Tenser of rank 2 In general an n th ‐rank tensor has 3 n components. y 9
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Chapter One: Vector Analysis The use of vectors and vector analysis ...

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