Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3, Problem 3.11P
Consider a cylindrical charge distribution having infinite length in Z, but which has a radial dependence in charge density given by the Gaussian, pv=p =p0 exp[-(p/b)2] (a) Find the electric field intensity, E, at large radii, p>>b This enables the enclosed charge integral in Gauss’s law so be approximated using an infinite upper limit in radius. (b) Compare your result to the field outside a charged cylinder of radius b containing uniform charge density P0.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Volume charge density is located in free space as ρν = 2e−100r nC/m3 for 0 < r < 3 mm, and ρν = 0 elsewhere.
Find the total charge enclosed by the spherical surface r = 2 mm.
By using Gauss’s law, calculate the value of Dr on the surface r = 2 mm.
Q1. 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.
A uniform line charge and a uniform sheet charge, both infinite in extent, are located in free space along the y-axis and at x = -1 respectively. Determine E at point M(2, -1, 1) if the line charge density is 15 nc/m and the sheet charge density is 2 nC/m^2
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
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
- The structure in the figure has 4 concentric spherical media,which have;0<r<a free spacea<r<b ρv (C/m3) constant volume charge densityb<r<c εr relative permittivityc<r free spaceFind ?⃗ , ?⃗ and ?⃗ in these 4 regions and also plot themarrow_forwardIn free space, let Q1 = 10 nC be at P1 (0,-4, 0). Find the work required done in moving a 2-microC charge along a straight line path from A(1, 2, 3) to B(3, 1, 2).arrow_forwardA charge located at the origin in free space produces a fields for which Ez=2kV/m at point P(-2, 4, -1) Find E at D(3, 4, 2) in spherical coordinates system.arrow_forward
- A thin circular ring of radius a=5 mm lies in the x-y plane and is centered at the origin as shown in Figure . Assume that the ring is in air and carries a uniform line charge density The electric potential at point P(0,0,4) cm is equal toarrow_forwardConsider the surface charge distributed along the disk with an inner radius of 1m, an outer radius of 2m, and a charge density of 3[μC/m2] shown in the figure. Since the medium is empty space, (a) Find the total charge on the disk. (b) If a 2[μC] load is placed at point P1 10m above the axis of the load, find the force acting on this load.arrow_forwardUniform line charges of 114 nC/m lie along the entire extent of the three coordinate axes. Assuming free space conditions, find Ez at P(-8, -1,4).arrow_forward
- 19. A life charge density of 24 nC/m is located in free space on the line y=1, z=2. (a) Find E at P(6,-1,3), (b) What point charge Q, should be located at Q(-34,1) to cause E, to be equal to zero at P?arrow_forwardA charge ring of radius is characterized by a positive linear charge density P?has been. The ring is located in empty space and is in the ? - ? plane as shown in Figure 6.is positioned. A = (0, 0, ℎ) along the axis of the ring, ℎ above its centerDetermine the electric field strength at the point.arrow_forwardcan you please solve this question, thanks. A sheet of charge, m , is present at the plane x = 3 in free space, and a line charge of rL = 20 nC/m , is located at x = 1, z = 4. (a) Find the magnitude of the electric field intensity at the origin. (b) Find the direction of E at P(4,5,6)arrow_forward
- Consider two concentric spherical shells--one conducting and one non-conducting. The conducting spherical shell has radius 3 cm and total charge of -8 nC, while the non-conducting spherical shell, which is outside the conducting shell, has inner radius 8 cm, outer radius 14 cm, and total charge 5 nC. Determine how strong the electric field is, in kV/m, 10 cm from the center of the conducting shell.arrow_forwardA solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net charge. (a) What is the charge on the inner surface of the hollow sphere? On the outer surface? (b) Sketch the electric field lines of the system. (c) Derive expressions for the electric field magnitude and for the electric potential interms of the distance r from the center for the regions r < a, a < r < b, b < r < c, and r > c. (Take the electric potential to vanish at r = ∞.)(d) Graph the magnitude of the electric field and the electric potential as a function of r from r = 0 to r = 2c.arrow_forwardIn 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 equationarrow_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,
Electric Charge and Electric Fields; Author: Professor Dave Explains;https://www.youtube.com/watch?v=VFbyDCG_j18;License: Standard Youtube License