Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Question
Chapter 3, Problem 3.29P
To determine
(a)
The volume integral side of the divergence theorem for the defined volume.
To determine
(b)
The surface integral side for the corresponding closed surface.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A loop located in space with segments whose coordinates are A(1,-4,5); B(-2,3,-1); C(2,-1,2) and D(4,-3,2). Determine H at the point P(5,-3,2) due to segment AB of the loop.
Q1. In free space, there are 2 concentric spherical surfaces with radii a and b. There is a constant volume charge density between 2 surfaces such that:a) Find the electric potential everywhere using Poisson’s equation. b) Find the electric field vector everywhere using Poisson’s equation.
In free space, there are 2 concentric spherical surfaces with radii a and b. There is a constant volume charge density between 2 surfaces such that: ρ= { 0; ρb [ ? ?3 ] a) Find the electric potential everywhere using Poisson’s equation. b) Find the electric field vector everywhere using Poisson’s equation
Chapter 3 Solutions
Engineering Electromagnetics
Ch. 3 - Prob. 3.1PCh. 3 - An electric field in space is E=(5z2/C0)azV/m....Ch. 3 - Consider an electric dipole in free space,...Ch. 3 - An electric field in free space is E=(5z3/0)z V/m....Ch. 3 - A volume charge distribution in free space is...Ch. 3 - Prob. 3.6PCh. 3 - Prob. 3.7PCh. 3 - Use Gauss, law in integral form to show that an...Ch. 3 - A sphere of radius a free space contains charge of...Ch. 3 - An infinitely long cylindrical dielectric of...
Ch. 3 - Consider a cylindrical charge distribution having...Ch. 3 - The sun radiates a tota1 power of about 3.86...Ch. 3 - Spherical surfaces at r = 2, 4, and 6 m carry...Ch. 3 - Prob. 3.14PCh. 3 - Volume charge density is located as follows; pv=0...Ch. 3 - An electric flux density is given by D=D0aP, where...Ch. 3 - In a region having spherical symmetry, volume...Ch. 3 - State whether the divergence of the following...Ch. 3 - A spherical surface of radius 3 mm is centered at...Ch. 3 - A radial electric field distribution in free space...Ch. 3 - In a region exhibiting spherical symmetry,...Ch. 3 - (a) A flux density field is given as F1 = 5 az....Ch. 3 - (a) A point charge Q lies at the origin. Show that...Ch. 3 - In a region in free space, electric flux density...Ch. 3 - Within the spherical shell, 3D= 5(r-3)3a,C/m2 .(a)...Ch. 3 - If we have a perfect gas of mass density Px...Ch. 3 - Consider a slab of material containing a volume...Ch. 3 - Repeat Problem 3.8, but use .D= pv and take an...Ch. 3 - Prob. 3.29PCh. 3 - (a) Use Maxwells first equation. �. D=Pv, to...Ch. 3 - Prob. 3.31P
Knowledge Booster
Similar questions
- Spherical surfaces at r = 1, 3, and 6 m carry uniform surface charge densities of 20 nC/m2, −4 nC/m2, and ρS0, respectively. Find D at r = 0.5, 2, 5, and 7 m.arrow_forwardLet E = 2{[(x+1)^2][(y+2)^2][(z+3)^3]} V in free space. At P(2,-1,4). Find V, E, |E|, D, |D|.arrow_forwardThere is an infinitely long cylinder of radius 0.5 cm along the z-axis, and it is filled uniformly with a volume charge density of 3.5 C/m3. Apply Gauss’s Law to find an expression for the electric field in two cases: a) For ρ > 0.5cm b) For 0 <ρ<0.5 cmarrow_forward
- Given point P(—2, 6, 3) and vector A = yax + (x + z)ay, express P and A in cylindricaland spherical coordinates. Evaluate A at P in the Cartesian, cylindrical, and sphericalsystems.arrow_forwardQ1. Uniform line charges of 40nC/m lie along the entire extent of the three coordinate axes.Assuming free space condition, find E̅at P( -2,1, 2). Q2. The work is defined by the equation: ? = 2 cos ? − 4?2?2 . Determine the curl of thegradient of the work and comment on the result.arrow_forwardPlease answer and write neatly. (Show your complete solution.) Volume charge density is located in free space as ρν = 2e−1000r nC/m3for 0 < r < 1 mm, and ρν = 0elsewhere.(a) Find the total charge enclosed by the spherical surface r = 1 mm.(b) By using Gauss’s law, calculate the value of Dr on the surface r = 1 mm.arrow_forward
- 6. If D=3y²a, + 3x²ya, + 5a, C/m², find the total charge enclosed within the region 0 < x,y,z <2 by evaluating one or more surface integrals.arrow_forwardIn empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient er = 8 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: In (x <x1), the electric field vector was observed as E1 =(4.5) ux + (7.5) uy+(8.5) uz.Region II : (x1 <x <x2) de er = 8 by determining the electric field E2,Write the value of the x-component: E2x numerically.arrow_forwardIn empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient er = 8 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: In (x <x1), the electric field vector was observed as E1 =(4.5) ux + (7.5) uy+(8.5) uz.Region II : (x1 <x <x2) de er = 8 by determining the electric field E2, write the value of the x-component: E2x numericallyarrow_forward
- I need a solution within 15 minutes Q2) A coaxial cable has voltage of 0.7 V on its inner conductor with a diameter of 4 cm and a voltage of -0.7 V on its outer conductor with a radius of 8 cm. Use Laplace equation to find:1) The general expression for the voltage at the dielectric.2) The general expression for the electric field intensity at the dielectric.3) The surface at which the voltage equals 0.1 V. *arrow_forwardThere are point loads Q1= 4, Q2=9 and Q3=4 at points A(-7,0), O(0,0) and B (4,0) in the OXY plane, respectively. Write the value of the y-component of the electric field in terms of ke numerically at the point P(0, 13) on the-axis.arrow_forwardA hollow sphere, with inner radius a and outer radius b, has a volumetric charge distribution p = kr^2, where r is the distance from the center of the sphere outwards and k is a known constant. Using Gauss's law, find the electric field at r < a, a < r < b, and r > b, and graph the electric field as a function of r.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSON
Delmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage Learning
Programmable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill Education
Electric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSON
Engineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,