Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4, Problem 4.16P
A spherically symmetric charge distribution in free space (with a < r < so) is known to have a potential function V(r) = V0a2/r2, where V0 and a are constants, (a) Find the electric field intensity. (b) Find the volume charge density. (c) Find the charge contained inside radius a. (d) Find the total energy stored in the charge (or equivalently, in its electric field).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A 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.
In empty space there is (-∞, 0) semi-infinite linear uniform and constant charge density ρl = 4 [C / m] on the z-axis. Calculate the electrostatic field that this charge density will create at point A (5,0,0). ke = 1 / 4πεWrite numerically the components of the electrostatic field in terms of the given quantities.
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.
Chapter 4 Solutions
Engineering Electromagnetics
Ch. 4 - Given E = Exax + Eyay + Ez3z V/m, where EX, Ey,...Ch. 4 - A positive point charge of magnitude q1 lies at...Ch. 4 - Given E=Epap+Ea+Ez+azV/m, where Ep, E and E2 are...Ch. 4 - An electric field in free space is given by...Ch. 4 - Consider the vector field G = (A/p) aa where A is...Ch. 4 - A electric field in free space is given as...Ch. 4 - Prob. 4.7PCh. 4 - Given E=-xax+yay,(a) find the work involved in...Ch. 4 - An electric field intensity in spherical...Ch. 4 - A sphere of radios a carries a surface density of...
Ch. 4 - At large distances from a dipole antenna (to be...Ch. 4 - Prob. 4.12PCh. 4 - Thee identical point charges of 4 pC each are...Ch. 4 - Given the electric field E=(y+1)ax+(x1)ay+2az find...Ch. 4 - Two uniform lines, 8 nC/m, are located at x=1, z=2...Ch. 4 - A spherically symmetric charge distribution in...Ch. 4 - Uniform surface charge densities of 6 and 2 nC/m2...Ch. 4 - Find the potential at the origin produced by a...Ch. 4 - Volume charge density is given as pv=poer/C/m3,...Ch. 4 - En a certain medium, the electric potential is...Ch. 4 - Prob. 4.21PCh. 4 - A Line charge of infinite length lies along the z...Ch. 4 - Prob. 4.23PCh. 4 - A certain spherically symmetric charge...Ch. 4 - Consider an electric field intensity in free space...Ch. 4 - Let us assume that we have a very thin, square,...Ch. 4 - By performing an appropriate Line integral from...Ch. 4 - Prob. 4.28PCh. 4 - A dipole having a moment P=3ax-5ay+10aznC.m is...Ch. 4 - Prob. 4.30PCh. 4 - A potential field in free space is expressed as...Ch. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - A sphere of radius a contains volume charge of...Ch. 4 - Four 0.8 nC point charge are located in free space...Ch. 4 - Surface charge of uniform density ps lies on a...
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
- In free space, q1 = 3nC charges are placed on y = 1 and y = 6, respectively, on the y-axis as shown in the figure. Accordingly, what is the electric potential value at y = 4?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_forwardA solid metallic sphere of radius a carries total chargeQ. No other charges are nearby. The electric fieldjust outside its surface is keQ /a2 radially outward. Atthis close point, the uniformly charged surface of thesphere looks exactly like a uniform flat sheet of charge.Is the electric field here given by s/P0 or by s/2P0?arrow_forward
- Within the sphere defined by r ≤ 8 cm, the volume charge density is ρv = 6.8 x 10-7 C/m3 . (i) Find an expression for electric field intensity for region r < 8 cm. Hence, calculate the electric field intensity at a point having rectangular coordinates of (x, y, z) = ( 3 cm, 2cm, 0 ). (ii) Assume that all of the electric charge is removed from a spherical region centered at (x, y, z) =(3 cm, 0, 0) and having a radius of 1 cm. Calculate the total electric field intensity at point (x,y,z) = (3 cm, 2 cm, 0).arrow_forwardThe 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 empty space there is (-∞, 0) semi-infinite linear uniform and constant charge density ρl = 3 [C / m] on the z-axis. Calculate the electrostatic field that this charge density will create at point B (0,0,4). ke = 1 / 4πεarrow_forward
- A 500nC point charge, an infinite line charge of ρL = 50 nC/m and an infinite surface charge of ρS = 5 nC/m^2 are located at (-2, 4, 5) , (4, -3, 0) and (0, 3, 0) respectively, find the electric field intensity at A ( 1, 2, 3)( Draw the diagram )arrow_forwardFind the electric potential difference V12 between two points in free space at radial distances r1and r2 from an infinite line of charge with density ρl along the z-axis,where the electric field due to an infinite line of charge is: ~E= ˆrρl/2e0rarrow_forwardThe electric potential V in a region of space is given by V(x,y,z)=A(x^2−3y^2+z^2)where A is a constant. Derive an expression for the electric field E→ at any point in this region. The work done by the field when a 1.50-μC test charge moves from the point (x,y,z)=(0,0,0.250m) to the origin is measured to be 6.00×10−5J. Determine A. Determine the electric field at the point (0, 0, 0.250 m). Show that in every plane parallel to the xz-plane the equipotential contours are circles.arrow_forward
- Two uniform line charges, 6 nC/m each, are located at x = 2, z = 3, and at x = -2, y = 2 in free space. If the potential at the origin is 137V, find V at P(1, 3, -4)arrow_forwardA sphere with a radius of 1 relative dielectric constant 0 = 10 has a volumetric charge distribution varying only by "r" (independent of θ and Φ). (Here r is the distance measured from its origin in spherical coordinates.). The region outside the sphere that opens to infinity is the void. The electric field vector in the region (r <1) inside the sphere is as in the photo. Find the explicit expression of the electric field vector outside the sphere.arrow_forwardIn the 0<r<1mm cubic region, it is given as ρ_v=2e^(-100r) nC/m^3. In other places, the charge density is given as 0.a) Find the total charge inside the spherical surface r=1mm.b) Calculate the expression Dr on the r=1mm surface using Gauss's law.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:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering 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