Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4, Problem 4.9P
An electric field intensity in spherical coordinates is given as
where V0 and a are constants, and where the field exists everywhere, (a) Find the potential field V(r), using a zero reference at infinity. (b) What is the significance of V0?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these 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?
Given the potential field in cylindrical coordinates, V = 100 + 50ρ + 150ρ sinΦ volts, and point P at ρ = 1 m, Φ = 600, z = 0.5 m, find the electric field intensity E at P.
Within the cylinder ρ=5 (m), 0≤z≤1 (m), the potential field is given by V=100+50ρ+150ρ sin Φ
Determine the electric field intensity at P(1, π/3, 0.5) in free space and in CCS.
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 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.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 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
- Within the cylinder ρ=5 (m), 0≤z≤1 (m), the potential field is given by V=100+50ρ+150ρ sin Φ Determine the potential (in V) at P(1, π/3, 0.5) in free space.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_forwardAn electric field intensity Ez =1kV/m at point P(-2,1,-1) in free space is caused by a charge Qo located at the origin. Solve for Qoarrow_forward
- A ring and a disk both are centered at (7, 6, 5) and are both lying on the plane y = 6. The ring has a radius of 7 m, while the disk has a radius of 9 m, so that the ring is around the disk. Determine the magnitude of the electric field in kV/m at point (7, -7, 5) if the ring has a total charge of -5 mC and the disk has a total charge of 7 mC. All coordinates are measured in meters.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_forward4) Develop an electromagnetic field environment equation for the electric field intensity, E provided the electric potential at a fixed radius from the point charge kept at the origin is given as V=Q/(4πɛ˳r), after developing the equation compute the vector value of electric field intensity for a Charge density of pv =10Nc/m3 , provided dv=r² sinθ dr dθ d∅ , and the distance r in magnitude is given as 1m from the origin.arrow_forward
- A charge QA = −20µC is located at A(−6, 4, 7), and a charge QB = 50µC is at B(5, 8, −2) in free space. If distances are given in meters, find: a. RAB; b. |RAB|. Determine the vector force exerted on QA by QB if E0 = c. 10−9/(36π) F/m; d. 8.854 × 10−12 F/m.arrow_forwardThere are point loads ,Q1 = 5, Q2 = 8 and Q3 = 6 at points A(-8,0), O(0,0) and B (6,0) in the OXY plane, respectively.Write the value of the x-component of the electric field in ke numerically at the point P(0, 10) on the-axis.arrow_forwardA charge q = 2 x 105 is located in free space at a point Pc(1, 3, −1) in Cartesian coordinate system . Calculate the electric field at P (3, 1, −2) in Cartesian coordinate system using Coulombs Lawarrow_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