Elements of Electromagnetics
Elements of Electromagnetics
7th Edition
ISBN: 9780190698669
Author: Sadiku
Publisher: Oxford University Press
bartleby

Videos

Question
Book Icon
Chapter 7, Problem 41P

(a)

To determine

Find whether the given field D is electrostatic or magnetostatic field in free space.

(a)

Expert Solution
Check Mark

Answer to Problem 41P

The vector D is possibly a magnetostatic field.

Explanation of Solution

Calculation:

Given field is,

D=y2zax+2(x+1)yzax(x+1)z2az

Generally, the vector is a magnetostatic field if its dot product is zero and the vector is an electrostatic field if its cross product is zero. That is,

For magnetostatic field, (vector)=0

For electrostatic field, ×(vector)=0

Substitute y2zax+2(x+1)yzax(x+1)z2az for D to find D.

D=xDx+yDy+zDz=x(y2z)+y(2(x+1))+z((x+1))=0+0+0=0

Substitute y2zax+2(x+1)yzax(x+1)z2az for D to find ×D.

×D=|axayazxyzDxDyDz|=|axayazxyzy2z2(x+1)yz(x+1)z2|=[(y((x+1)z2)z(2(x+1)yz))ax(x((x+1)z2)z(y2z))ay+(x(2(x+1)yz)y(y2z))az]=[((0)2(x+1)y(1))ax(((1)z2+0)y2(1))ay+((2(1)yz+0)(2y)z)az]

Simplify the above equation.

×D=(2(x+1)y)ax(z2y2)ay+(2yz2yz)az=(2(x+1)y)ax+(z2+y2)ay+(0)az=2(x+1)yax+(z2+y2)ay0

Therefore, for the field D,

D=0×D0

Conclusion:

Thus, the vector D is possibly a magnetostatic field.

(b)

To determine

Find whether the given field E is electrostatic or magnetostatic field in free space.

(b)

Expert Solution
Check Mark

Answer to Problem 41P

The vector E is possibly a magnetostatic field.

Explanation of Solution

Calculation:

Given field is,

E=(z+1)ρcosϕaρ+sinϕρaz

Substitute (z+1)ρcosϕaρ+sinϕρaz for E to find E.

E=1ρρ(ρEρ)+1ρϕEϕ+zEz=1ρρ(ρ((z+1)ρcosϕ))+1ρϕ(0)+z(sinϕρ)=1ρρ((z+1)cosϕ)+0+0=0

Substitute (z+1)ρcosϕaρ+sinϕρaz for E to find ×E.

×E=1ρ|aρρaϕazρϕz(z+1)ρcosϕρ(0)sinϕρ|=1ρ|aρρaϕazρϕz(z+1)ρcosϕ0sinϕρ|=1ρ[(ϕ(sinϕρ)z(0))aρ(ρ(sinϕρ)z((z+1)ρcosϕ))ρaϕ+(ρ(0)ϕ((z+1)ρcosϕ))az]=1ρ[ϕ(sinϕρ)aρ(ρ(sinϕρ)z((z+1)ρcosϕ))ρaϕϕ((z+1)ρcosϕ)az]

Simplify the above equation.

×E=1ρ[cosϕρaρρ(sinϕ(1ρ2)(cosϕρ)(1+0))aϕ(z+1)ρ(sinϕ)az]=1ρ[cosϕρaρρ(sinϕρ2(cosϕρ))aϕ+(z+1)sinϕρaz]=cosϕρ2aρ(sinϕρ2(cosϕρ))aϕ+(z+1)sinϕρ2az0

Therefore, for the field E,

E=0×E0

Conclusion:

Thus, the vector E is possibly a magnetostatic field.

(c)

To determine

Find whether the given field F is electrostatic or magnetostatic field in free space.

(c)

Expert Solution
Check Mark

Answer to Problem 41P

The vector F is neither electrostatic nor magnetostatic field.

Explanation of Solution

Calculation:

Given field is,

F=1r2(2cosθar+sinθaθ)=2r2cosθar+1r2sinθaθ

Substitute 2r2cosθar+1r2sinθaθ for F to find F.

F=1r2r(r2Fr)+1rsinθθ(sinθFθ)+1rsinθϕ(Fϕ)=1r2r(r2(2r2cosθ))+1rsinθθ(sinθ(1r2sinθ))+1rsinθϕ(0)=1r2r(2cosθ)+1rsinθθ(1r2sin2θ)+0=1r2(0)+1r3sinθ(2sinθcosθ)

Simplify the above equation.

F=0+1r3(2cosθ)=2cosθr30

Substitute 2r2cosθar+1r2sinθaθ for F to find ×F.

×F=1r2sinθ|arraθrsinθaϕrθϕ2r2cosθr(1r2sinθ)0|=1r2sinθ|arraθrsinθaϕrθϕ2r2cosθ1rsinθ0|=1r2sinθ[(θ(0)ϕ(1rsinθ))ar(r(0)ϕ(2r2cosθ))raθ+(r(1rsinθ)θ(2r2cosθ))rsinθaϕ]=1r2sinθ[(0(0))ar(0(0))raθ+(sinθ(1r2)(2r2)(sinθ))rsinθaϕ]

Simplify the above equation.

×F=1r2sinθ[0+0+rsinθ(1r2sinθ+2r2sinθ)aϕ]=rsinθr2sinθ(1r2sinθ+2r2sinθ)aϕ=1r3(sinθ)aϕ0

Therefore, for the field F,

F0×F0

Conclusion:

Thus, the vector F is neither electrostatic nor magnetostatic field.

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
I need help with a MATLAB code. I am trying to solve this question. Based on the Mars powered landing scenariosolve Eq. (14) via convex programming. Report the consumed fuel, and discuss the results with relevant plots. I am using the following MATLAB code and getting an error. I tried to fix the error and I get another one saying something about log and exp not being convex. Can you help fix my code and make sure it works.   The error is CVX Warning:  Models involving "log" or other functions in the log, exp, and entropy  family are solved using an experimental successive approximation method.  This method is slower and less reliable than the method CVX employs for  other models. Please see the section of the user's guide entitled      The successive approximation method  for more details about the approach, and for instructions on how to  suppress this warning message in the future.Error using  .*  (line 173)Disciplined convex programming error:   Cannot perform the operation:…
Note: please  use integration for parabolic volume (Vp) of the fluid displaced due to rotation. (Make it simpe as possible to follow in the working out). Provide a clear, step-by-step simplified handwritten solution (with no extra explanations) that is entirely produced by hand without any AI help. I require an expert-level answer, and I will assess it based on the quality and accuracy of the work, referring to the attached image for additional guidance. Make sure every detail is carefully verified for correctness before you submit. Thanks!.
Note: use centroid method please  Provide a clear, step-by-step simplified handwritten solution (with no extra explanations) that is entirely produced by hand without any AI help. I require an expert-level answer, and I will assess it based on the quality and accuracy of the work, referring to the attached image for additional guidance. Make sure every detail is carefully verified for correctness before you submit. Thanks!.
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Lesson 2: Thermodynamic Properties; Author: The Thermo Sage;https://www.youtube.com/watch?v=qA-xwgliPAc;License: Standard Youtube License