Loose Leaf For Engineering Electromagnetics
9th Edition
ISBN: 9781260472370
Author: John A. Buck, William H. Hayt
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 1, Problem 1.6P
Find the acute angle between the two
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Express the unit vector ax in spherical components at the point:a) r = 2, θ = 1 rad, φ = 0.8 rad;b) x = 3, y = 2, z = −1;c) ρ = 2.5, φ = 0.7 rad, z = 1.5.
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Using the coordinate system named, give the vector al point A(2,-1,-3) that extends to B(1,3,4): (a) cartesian; (b) cylindrical; (e) spherical.
Calculate the divergence theorem for the vector function in the circular cylindrical region surrounded by r = 5, z = 0 and z = 4.
Chapter 1 Solutions
Loose Leaf For Engineering Electromagnetics
Ch. 1 - If A represents a vector two units in length...Ch. 1 - Vector A extends from the origin to (1, 2, 3), and...Ch. 1 - 1.3 The vector from the origin to point A is given...Ch. 1 - A circle, centered at the origin with a radius of...Ch. 1 - An equilateral triangle lies in the xy plane with...Ch. 1 - Find the acute angle between the two vector...Ch. 1 - Given the field F=xax+yay. If F. G =2xy and FĂ— G...Ch. 1 - Prob. 1.8PCh. 1 - A field is given as G=[25/(x2+y2)](xax+yay). Find...Ch. 1 - Prob. 1.10P
Ch. 1 - Given the points M(0.1, -0.2, -0.1), N(-02, 0.1,...Ch. 1 - 1.21 Write an expression recrangu1ar components...Ch. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Three vectors extending from the origin are given...Ch. 1 - Prob. 1.16PCh. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Exercise in cylinder components ;(a) the vector...Ch. 1 - Prob. 1.22PCh. 1 - The surfaces p=3,p=5,=130o,z=3andz=4.5 define a...Ch. 1 - Two unit vectors, a1 and a2, lie in the xy plane...Ch. 1 - Prob. 1.25PCh. 1 - Prob. 1.26PCh. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - A vector field is expressed as F = Az az where A...Ch. 1 - Consider a problem analogous to the varying wind...
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- Express the vector field B = (x^2- y^2)ay + xzaz in cylindrical coordinates at ( 6, 60o, -4arrow_forwardSpherical Coordinate System ( show your solution) Transform the following vectors to spherical coordinates at thepoints given:(a) 10ax at P(x = −3, y = 2, z = 4);(b) 10ay at Q(ρ = 5, φ = 30◦, z = 4);(c) 10az at M(r = 4, θ = 110◦, φ = 120◦)arrow_forwardA vector field S is expressed in rectangular coordinates as S = {125/ [(x − 1)2+(y – 2)2 +(z + 1)}}{(x — 1)ax +(y — 2)ay +(2+1)a;}. (a) Evaluate S at P(2, 4, 3). (b) Determine a unit vector that gives the direction of S at P. (c) Specify the surface f(x, y, z) on which |S| = 1.arrow_forward
- Using the coordinate system named, give the vector at point A (5, -4, 6) that extends to B (-1, 5, 3) a. Cartesian b. Cylindrical c. Sphericalarrow_forward1. Determine the initial point of the vector <2, 4, -1> whose terminal point is (3, -2, 2) 2. Find the magnitude and angle of the resultant vector if the given vectors are V1=-7i+7J and V2=6i-9j 3. for what values of "a" and "b" are the vectors <a-b, 2> and <4, a+b> equal?arrow_forwardConsider the vector field G = yx ax + 2.5x ay – 2y2 az and the point Q(6, 5, -2). Find: (a) G at Q; (b) the scalar component of G at Q in the direction of aN = 1/3 (2ax + ay − 2az ); (c) the scalar and vector component of G at Q in the direction of aN ; (d) the angle θGa between GQ and aN .arrow_forward
- If a scalar field φ(x,y,z)=3x2y-y3z2, calculate the gradient ∇φ at point M(1,-2,1).arrow_forwardThe point M and N are located at (-7,-7,-7) and (0,9,5) a. calculate the position vector at M and N b. calculate the distance vectors from M and N c. calculate the distance between M and Narrow_forwardWhich is the divergence for the vector field (M) at (1,1,1)arrow_forward
- Given points A(x = 2, y = 3, z = −1) and B(ρ = 4, ∅ = −50°, z = 2),Find the distance from:(a) A to origin;(b)B to the origin;(c)A to B.arrow_forwardThe ff vector fields are given: A = -10ax + 20x(y-1) ay B = 2x²y ax - 4ay + zaz For the given point P (2, -3, 4) find the Unit vector from B to Aarrow_forwardThe ff vector fields are given: A = -10ax + 20x(y-1) ay B = 2x²y ax - 4ay + zaz For the given point P (2, -3, 4) find: a. Magnitude of Vector A b. Magnitude of Vector B c. Unit vector in the direction of (A+B) d. Unit vector from B to Aarrow_forward
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