EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
7th Edition
ISBN: 8220100663659
Author: ULABY
Publisher: PEARSON
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Question
Chapter 3.1, Problem 3E
To determine
The angle between
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B. Once we divide a vector by its
magnitude, we will get
Direction of a scalar
Direction of a vector
Direction of a unit vector
Direction of a field
Find the unit vector n perpendicular in the right-hand sense to the two vectors A and B. What is the angle between A and B? A=-i+j+k, B=i-j+k
Objective:
Use properties of right triangles to add electrical vectors. Draw a force triangle
from given vectors. Convert vectors between Polar to Rectangular forms.
Formulas: Given (R Z0) x=R cos 0
y = R sin 0
Given (x, y)
R= x? + y?
y
-1-
0 = tan
Add the following sets of vectors. Draw a vector diagram. Draw a force triangle
diagram. Convert the vectors to Rectangular form to add. Express the answer
in Polar form.
Chapter 3 Solutions
EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Objective: Use properties of right triangles to add electrical vectors. Draw a force triangle from given vectors. Convert vectors between Polar to Rectangular forms. Formulas: Given (R Z0) x=R cos 0 y = R sin 0 Given (x, y) R= x? + y? y -1- 0 = tan Add the following sets of vectors. Draw a vector diagram. Draw a force triangle diagram. Convert the vectors to Rectangular form to add. Express the answer in Polar form, Z = 3.1 KOL65° Z2 = 6.1 kaL-15° 1. Zr = Reose Rsino Σχ Ey = Zz = 4.3 KN230° Z2 = 5.2 k0Z-60° 2. ZT = Rcos0 Rsine Ex = Ey = Zz = 12 kOL26° Zz = 15 kQL-56° 3. Z = Rcose Rsine Z1 Z2 Ex = Ey =arrow_forwardP1. 17. Given the components of vector Q, Qx-2 :Qy--3:Qz- 1, which of the following is perpendicular to vector Q? Select one: O a. 2i - 9j -31k Ob. 2i + 2j + k Oc. 4i-j Od.-i- 2j -3karrow_forwardThe relation between flux density and vector potential is O B = Curl(A) O A = Curl(B) O B = Div(A) O A = Div(B) O none of the abovearrow_forward
- 7. Find the curl of the vector a = x²y?z?i+y²z?j+ x²z²k. %3Darrow_forwardThe operator 'B' which should cause 120° rotation in anticlockwise direction when multiplied by each vector, then the equivalent value of the 'B3' in rectangular form isarrow_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
- find the absolute value of the vector P= 2i - 6j +9k and express its direction as a unit vector.arrow_forward2. Bring out the importance of Curl of a vector with an application.arrow_forwardIf A=2xz², what is the curl of this vector, V XA, in Cartesian coordinates? A B 222 xz² -xz² D -ýz²arrow_forward
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