Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356816
Author: Fawwaz T. Ulaby, Umberto Ravaioli
Publisher: PEARSON
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Chapter 3, Problem 47P
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determine the divergence of the vector field
Express the uniform vector field F = 5a, in cylindrical components.
Select the correct response:
F = - 5sinpa, + 5cospa,
F= p(zcoso + psino coso - zsino)
F= 5cosya, - 5sinpa,
O F= p(zcosp - psino coso + zsiny)
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Chapter 3 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 3.1 - When are two vectors equal and when are they...Ch. 3.1 - Prob. 2CQCh. 3.1 - If AB = 0, what is AB?Ch. 3.1 - If AB = 0, what is AB?Ch. 3.1 - Is A(BC) a vector triple product?Ch. 3.1 - If AB = AC, does it follow that B = C?Ch. 3.1 - Find the distance vector between P1 = (1, 2, 3)...Ch. 3.1 - Find the angle AB between vectors A and B of...Ch. 3.1 - Prob. 3ECh. 3.1 - Vectors A and B lie in the y-z plane and both have...
Ch. 3.1 - If AB=AC, does it follow that B = C?Ch. 3.2 - A circular cylinder of radius r = 5 cm is...Ch. 3.3 - Why do we use more than one coordinate system?Ch. 3.3 - Prob. 8CQCh. 3.3 - Prob. 9CQCh. 3.3 - How is the position vector of a point in...Ch. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Find the directional derivative of V=rz2cos2 along...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.5 - Given A=e2y(xsin2x+ycos2x), find A.Ch. 3.5 - Given A=rrcos+rsin+z3z , find A at (2,0, 3).Ch. 3.5 - If E=RAR in spherical coordinates, calculate the...Ch. 3.5 - Verify the divergence theorem by calculating the...Ch. 3.5 - Prob. 17ECh. 3.6 - Find A at (2, 0, 3) in cylindrical coordinates for...Ch. 3.6 - Find A at (3, /6, 0) in spherical coordinates for...Ch. 3.7 - What do the magnitude and direction of the...Ch. 3.7 - Prob. 12CQCh. 3.7 - Prob. 13CQCh. 3.7 - Prob. 14CQCh. 3.7 - What is the meaning of the transformation provided...Ch. 3.7 - Prob. 16CQCh. 3.7 - Prob. 17CQCh. 3.7 - When is a vector field conservative?Ch. 3 - Prob. 1PCh. 3 - Given vectors A=x2y3+z, B=x2y+z3, and C=x4+y2+z2,...Ch. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Given vectors A=x+y2z3, B=x2y4, and C=y2z4, find...Ch. 3 - Given vectors A=x2y+z3 and B=x3z2, find a vector C...Ch. 3 - Given A=x(x+2y)y(y+3z)+z(3xy), determine a unit...Ch. 3 - By expansion in Cartesian coordinates, prove: (a)...Ch. 3 - Find an expression for the unit vector directed...Ch. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - A given line is described by x+2y=4. Vector A...Ch. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Given B=x(z3y)+y(2x3z)z(x+y), find a unit vector...Ch. 3 - Find a vector G whose magnitude is 4 and whose...Ch. 3 - A given line is described by the equation: y=x1....Ch. 3 - Vector field E is given by E=R5Rcos12Rsincos+3sin....Ch. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Use the appropriate expression for the...Ch. 3 - Prob. 26PCh. 3 - A section of a sphere is described by 0 R 2, 0 ...Ch. 3 - A vector field is given in cylindrical coordinates...Ch. 3 - At a given point in space, vectors A and B are...Ch. 3 - Given vectors...Ch. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Transform the vector A=Rsin2cos+cos2sin into...Ch. 3 - Transform the following vectors into cylindrical...Ch. 3 - Transform the following vectors into spherical...Ch. 3 - Find the gradient of the following scalar...Ch. 3 - For each of the following scalar fields, obtain an...Ch. 3 - The gradient of a scalar function T is given by...Ch. 3 - Prob. 39PCh. 3 - For the scalar function V = xy2 z2, determine its...Ch. 3 - Evaluate the line integral of E=xxyy along the...Ch. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Each of the following vector fields is displayed...Ch. 3 - Prob. 45PCh. 3 - For the vector field E=xxzyyz2zxy, verify the...Ch. 3 - For the vector field E=r10erz3z, verify the...Ch. 3 - A vector field D=rr3 exists in the region between...Ch. 3 - For the vector field D=R3R2, evaluate both sides...Ch. 3 - For the vector field E=xxyy(x2+2y2), calculate (a)...Ch. 3 - Repeat Problem 3.50 for the contour shown in Fig....Ch. 3 - Verify Stokess theorem for the vector field...Ch. 3 - Prob. 53PCh. 3 - Prob. 54PCh. 3 - Verify Stokess theorem for the vector field B = (r...Ch. 3 - Prob. 56PCh. 3 - Prob. 57PCh. 3 - Find the Laplacian of the following scalar...
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- Transform the vector field H= (5/p) ao, from cylindrical coordinates to spherical coordinates.arrow_forwardPROBLEM # 3 EXPRESS THE VECTOR FIELD D= (x²+y²)"(xaxtyay) IN CULINDRICAL COMPONENTS AND CYLINDRICAL VARIABLES.arrow_forwardExpress the field D = (x2 + y2) – 1 (6ax + 8ay) in cylindrical components and cylindrical variables.arrow_forward
- Given the vector field H = xy²zax + x²yzay + xyz²a, express it in cylindrical system at point (3,-4, 5). type your answer... a type your answer... az = type your answer...arrow_forwardCalculate the divergence theorem for the vector function in the circular cylindrical region surrounded by r = 5, z = 0 and z = 4.arrow_forwardQ4. Find the angle that the vector A = 3î – 4î makes with the positive x-axis Q5. Show that the vectors à = 3î + ĵ – 3k and B = 4î + 2ĵ + 7k are orthogonal?arrow_forward
- Determine the curl for vector M = 4xsecy i - 2y2z j + (ztany)/2 k at point (π/5 , π/9, π/7).arrow_forwardA vector field is given by A = 3xyî - y ĵ. Find ſ. Á .dí . where 'c' is the curve y = 2x? in the x-y plane from (0,0) to (1,2) a) -9/2 b) 7/6 c) -7/6 d) 2/3arrow_forwardThe angle between vector A (2i+3j+k) and ? vector B (i-2j+2k) is 1100 1000 100 2100arrow_forward
- Q4) Consider an arbitrary vector A = Agâr + Agâg+Agâg in spherical coordinates and express in Cartesian coordinatesarrow_forwardTransform vector 5ax-2ay -4a-, at A(x = 4, y = 6, z = 5) to cylindrical coordinates at the point specified.arrow_forwardGiven vector A = [5,–8,5] and C = [1,4,–3]. Which is the angle between these vector, if we take the dot product F = A•C? if not in the choices, choose the closestif not in the choices, choose the closestarrow_forward
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The Divergence Theorem; Author: Professor Dave Explains;https://www.youtube.com/watch?v=vZGvgru4TwE;License: Standard Youtube License