ReviewofVectorAnalysis

ReviewofVectorAnalysis - EEL 3472 EEL 3472 Review of Vector...

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Unformatted text preview: EEL 3472 EEL 3472 Review of Vector Review of Vector Analysis Analysis EEL 3472 EEL 3472 2 Review of Vector Analysis Vector analysis is a mathematical tool with which electromagnetic (EM) concepts are most conveniently expressed and best comprehended. A quantity is called a scalar if it has only magnitude (e.g., mass, temperature, electric potential, population). A quantity is called a vector if it has both magnitude and direction (e.g., velocity, force, electric field intensity). The magnitude of a vector is a scalar written as A or A A A Review of Vector Analysis Review of Vector Analysis EEL 3472 EEL 3472 3 A unit vector along is defined as a vector whose magnitude is unity (that is,1) and its direction is along A A A A A A e A = = ) e ( A 1 = Thus A e which completely specifies in terms of A and its direction A e A A e A A = Review of Vector Analysis Review of Vector Analysis EEL 3472 EEL 3472 4 A vector in Cartesian (or rectangular) coordinates may be represented as or where A X , A y , and A Z are called the components of in the x, y, and z directions, respectively; , , and are unit vectors in the x, y and z directions, respectively. z z y y x x e A e A e A + + ) A , A , A ( z y x A A Review of Vector Analysis Review of Vector Analysis x e z e y e EEL 3472 EEL 3472 5 Suppose a certain vector is given by The magnitude or absolute value of the vector is (from the Pythagorean theorem) z y x e 4 e 3 e 2 V + + = V 385 . 5 4 3 2 V 2 2 2 = + + = V Review of Vector Analysis Review of Vector Analysis EEL 3472 EEL 3472 6 The Radius Vector A point P in Cartesian coordinates may be represented by specifying (x, y, z). The radius vector (or position vector ) of point P is defined as the directed distance from the origin O to P; that is, The unit vector in the direction of r is z y x e z e y e x r + + = r r z y x e z e y e x e z y x r = + + + + = 2 2 2 Review of Vector Analysis Review of Vector Analysis EEL 3472 EEL 3472 7 Vector Algebra Two vectors and can be added together to give another vector ; that is , Vectors are added by adding their individual components....
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ReviewofVectorAnalysis - EEL 3472 EEL 3472 Review of Vector...

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