Fundamentals of Electromagnetics with Engineering Applications
Fundamentals of Electromagnetics with Engineering Applications
1st Edition
ISBN: 9780470105757
Author: Stuart M. Wentworth
Publisher: Wiley, John & Sons, Incorporated
bartleby

Videos

Textbook Question
Book Icon
Chapter 3, Problem 3.1P

Find A × B for the following:

  1. A = 2 a x 3 a y + 4 a z , B = 5 a y 1 a z
  2. A = a ρ + 2 a ϕ + 4 a z , B = 2 a ρ + 6 a z
  3. A = 2 a r + 5 a θ + 1 a ϕ , B = a r + 3 a ϕ

(a)

Expert Solution
Check Mark
To determine

The cross product of the two fields.

Answer to Problem 3.1P

The cross product of the two vectors is 17ax+2ay+10az .

Explanation of Solution

Given:

The field A is 2ax3ay+4az .

The field B is 5ay1az .

Concept used:

Write the expression for the cross-product of the two fields.

  A×B=| a x a y a z A x A y A z B x B y B z|.........(1)

Here, Ax,Ay,Az are the components of the field A in x,y,z directions and Bx,By,Bz are the components of the field B in x,y,z directions.

Calculation:

Substitute 2 for Ax , 3 for Ay , 4 for Az , 0 for Bx , 5 for By and 1 for Bz in equation (1).

  A×B=| a x a y a z 2 3 4 0 5 1|=ax(320)ay(20)+az(100)=17ax+2ay+10az

Conclusion:

Thus, the cross product of the two vectors is 17ax+2ay+10az .

(b)

Expert Solution
Check Mark
To determine

The cross product of the two fields.

Answer to Problem 3.1P

The cross product of the two vectors is 12aρ+2aϕ4az .

Explanation of Solution

Given:

The field A is aρ+2aϕ+4az .

The field B is 2aρ+6az .

Concept used:

Write the expression for the cross-product of the two fields.

  A×B=| a ρ a ϕ a z A ρ A ϕ A z B ρ B ϕ B z| ........(2)

Here, Aρ,Aϕ,Az are the components of the field A in ρ,ϕ,z directions and Bρ,Bϕ,Bz are the components of the field B in ρ,ϕ,z directions.

Calculation:

Substitute 1 for Aρ , 2 for Aϕ , 4 for Az , 2 for Bρ , 0 for Bϕ and 6 for Bz in equation (2).

  A×B=| a ρ a ϕ a z 1 2 4 2 0 6|=aρ(120)aϕ(68)+az(04)=12aρ+2aϕ4az

Conclusion:

Thus, the cross product of the two vectors is 12aρ+2aϕ4az .

(c)

Expert Solution
Check Mark
To determine

The cross product of the two fields.

Answer to Problem 3.1P

The cross product of the two vectors is 15ar5aθ5aϕ .

Explanation of Solution

Given:

The field A is 2ar+5aθ+1aϕ .

The field B is ar+3aϕ .

Concept used:

Write the expression for the cross-product of the two fields.

  A×B=| a r a θ a ϕ A r A θ A ϕ B r B θ B ϕ| ........(3)

Here, Ar,Aθ,Aϕ are the components of the field A in r,θ,ϕ directions and Br,Bθ,Bϕ are the components of the field B in r,θ,ϕ directions.

Calculation:

Substitute 2 for Ar , 5 for Aθ , 1 for Aϕ , 1 for Br , 0 for Bθ and 3 for Bϕ in equation (3).

  A×B=| a r a θ a ϕ 2 5 1 1 0 3|=ar(150)aθ(61)+aϕ(05)=15ar5aθ5aϕ

Conclusion:

Thus, the cross product of the two vectors is 15ar5aθ5aϕ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
5 A Moving to another question will save this response. Quèstion 31 The angle that vector A=2a,+3a, +4a, makes with z-axis is 68.19 56.14 76.82 42.03 A Moving to another question wvll save this response.
None
1. Plot the complex number as a point and vector once the following are evaluated. a. 7+7 (727°) 1+1 7L7° →7c0s 7 + j(75in 7) 6.9478 +jo.8531 = (7+7₁) (6.9478 +jo.8531) J+7 2 48-6346 + j5-9717 +j48.63467 5.917) ² J+7 = 48-6346 + 54.6063i + 5.9717 (-1) it t = 42.6629 + 54-60631 1+7 (1 + 2i) b. 526° 31+4

Chapter 3 Solutions

Fundamentals of Electromagnetics with Engineering Applications

Ch. 3 - A solenoid has 200 turns, is 10.0 cm long, and has...Ch. 3 - For the solenoid of the previous problem, plot the...Ch. 3 - Prob. 3.13PCh. 3 - Two infinite extent current sheets exist at z=2.0m...Ch. 3 - An infinite extent current sheet with K=6.0ayA/m...Ch. 3 - Given the field H=3y2ax, find the current passing...Ch. 3 - Given a 3.0–mm–radius solid wire centered on...Ch. 3 - Given a 2.0–cm–radius solid wire centered on...Ch. 3 - An infinitesimally thin metallic cylindrical shell...Ch. 3 - A cylindrical pipe with a 1.0–cm wall thickness...Ch. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - Consider the toroid in Figure 3.55 that is tightly...Ch. 3 - Find A for the following fields: A=3xy2/zax...Ch. 3 - Find J at (3m,60,4m) for H=(z/sin)a(2/cos)azA/mCh. 3 - Suppose H=y2ax+x2ayA/m .(a) Calculate HdL around...Ch. 3 - Prob. 3.27PCh. 3 - Suppose you have the field H=rcosaA/m. Now...Ch. 3 - Prob. 3.29PCh. 3 - Suppose an infinite extent sheet of current with...Ch. 3 - Prob. 3.31PCh. 3 - A 1.0nC charge with velocity 100.m/s in the y...Ch. 3 - A 1.0nC charge with velocity 100.m/s in the z...Ch. 3 - A 10.nC charged particle has a velocity...Ch. 3 - What electric field is required so that the...Ch. 3 - An electron (with rest mass Me=9.111031kg and...Ch. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Suppose you have a pair of parallel lines each...Ch. 3 - In Figure 3.57, a 2.0-A line of current is shown...Ch. 3 - Modify MATLAB 3.4 to find the differential force...Ch. 3 - Prob. 3.43PCh. 3 - A square loop of 1.0-A current of side 4.0 cm is...Ch. 3 - A current sheet K=100axA/m exists at z=2.0cm. A...Ch. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - A solid nickel wire of diameter 2.0 mm evenly...Ch. 3 - Prob. 3.49PCh. 3 - The plane y = O separates two magnetic media....Ch. 3 - Prob. 3.52PCh. 3 - Prob. 3.53PCh. 3 - Prob. 3.54PCh. 3 - Prob. 3.55PCh. 3 - Prob. 3.56PCh. 3 - Prob. 3.57PCh. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - In Figure 3.59, a 2.0-cm-diameter toroidal core...Ch. 3 - Suppose the 2.0-cm-diameter core of the toroid in...Ch. 3 - Prob. 3.64PCh. 3 - Consider a 1.0-mm air gap in Figure 3.49a. The...
Knowledge Booster
Background pattern image
Electrical Engineering
Learn more about
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Text book image
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Text book image
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Text book image
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Text book image
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,
Y Parameters - Admittance Parameters; Author: Electrical Engineering Authority;https://www.youtube.com/watch?v=MLqqa8YbVrA;License: Standard Youtube License