Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356816
Author: Fawwaz T. Ulaby, Umberto Ravaioli
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
thumb_up100%
Chapter 4, Problem 10P
A line of charge of uniform density ρℓ occupies a semicircle of radius b as shown in Fig. P4.10. Use the material presented in Example 4-4 to determine the electric field at the origin.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
2. The charges are enclosed with in a surface at which neither the charge distribution
nor the potential distribution is known. How do you estimate the Electric and magnetic
fields across the surface? Illustrate with example.
A uniformly charged insulating rod of length 14.0 cm is bent into the shape of a semicircle, as shown in Figure . If the rod has a total charge of -15.0 µC, find the electric potential at O, the center of the semicircle.
4) Electric field of a rod. Consider a nonconducting rod of length L with a charge q
uniformly distributed along its length. We want to know the magnitude of the electric
field a distance x away from one end as shown below.
X
L, with q evenly distributed
Explain why EACH of the four answers below is WRONG. Consider symmetry,
dimensions, unit analysis, behavior in limiting cases, and/or behavior at particular
positions. You SHOULD NOT actually solve the problem and your answer shouldn't be
because the correct answer is this. This is good practice in considering the nature of your
answer...
а) Е:
b) E =
4πε, L(x + L)
4TE,x(x – L)
c) E =
d) E =
4л, (х? + L/4)
4лєрх(2х + L)
5) Electric field of a rod again--this time with calculus and a different geometry
•Part a: A thin nonconducting rod of length L has charge q uniformly distributed along it
as shown in Fig. 22-55 (associated with problem 32). SHOW that the magnitude of the
electric field at point P (on the perpendicular bisector of the…
Chapter 4 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 4.2 - What happens to Maxwells equations under static...Ch. 4.2 - How is the current density J related to the volume...Ch. 4.2 - Prob. 3CQCh. 4.2 - A square plate residing in the xy plane is...Ch. 4.2 - A thick spherical shell centered at the origin...Ch. 4.3 - When characterizing the electrical permittivity of...Ch. 4.3 - If the electric field is zero at a given point in...Ch. 4.3 - State the principle of linear superposition as it...Ch. 4.3 - Four charges of 10 C each are located in free...Ch. 4.3 - Two identical charges are located on the x axis at...
Ch. 4.3 - In a hydrogen atom the electron and proton are...Ch. 4.3 - An infinite sheet with uniform surface charge...Ch. 4.4 - Explain Gausss law. Under what circumstances is it...Ch. 4.4 - How should one choose a Gaussian surface?Ch. 4.4 - Two infinite lines, each carrying a uniform charge...Ch. 4.4 - A thin spherical shell of radius a carries a...Ch. 4.4 - A spherical volume of radius a contains a uniform...Ch. 4.5 - What is a conservative field?Ch. 4.5 - Why is the electric potential at a point in space...Ch. 4.5 - Prob. 11CQCh. 4.5 - Why is it usually easier to compute V for a given...Ch. 4.5 - Prob. 13CQCh. 4.5 - Determine the electric potential at the origin due...Ch. 4.5 - A spherical shell of radius a has a uniform...Ch. 4.6 - What are the electromagnetic constitutive...Ch. 4.6 - Prob. 15CQCh. 4.6 - What is the conductivity of a perfect dielectric?Ch. 4.6 - Prob. 17CQCh. 4.6 - Prob. 18CQCh. 4.6 - Determine the density of free electrons in...Ch. 4.6 - Prob. 13ECh. 4.6 - A 50 m long copper wire has a circular cross...Ch. 4.6 - Prob. 15ECh. 4.7 - What is a polar material? A nonpolar material?Ch. 4.7 - Prob. 20CQCh. 4.7 - What happens when dielectric breakdown occurs?Ch. 4.7 - Find E1 in Fig. 4-19 if E2=x2y3+z3(v/m),1=20,2=80,...Ch. 4.7 - Repeat Exercise 4.16 for a boundary with surface...Ch. 4.8 - What are the boundary conditions for the electric...Ch. 4.8 - Prob. 23CQCh. 4.9 - How is the capacitance of a two-conductor...Ch. 4.9 - What are fringing fields and when may they be...Ch. 4.10 - To bring a charge q from infinity to a given point...Ch. 4.10 - Prob. 27CQCh. 4.10 - The radii of the inner and outer conductors of a...Ch. 4.11 - What is the fundamental premise of the image...Ch. 4.11 - Given a charge distribution, what are the various...Ch. 4.11 - Use the result of Example 4-13 to find the surface...Ch. 4 - A cube 2 m on a side is located in the first...Ch. 4 - Prob. 2PCh. 4 - Find the total charge contained in a round-top...Ch. 4 - If the line charge density is given by l = 24y2...Ch. 4 - Find the total charge on a circular disk defined...Ch. 4 - If J = 4xz (A/m2), find the current I flowing...Ch. 4 - Prob. 7PCh. 4 - An electron beam shaped like a circular cylinder...Ch. 4 - Prob. 9PCh. 4 - A line of charge of uniform density occupies a...Ch. 4 - A square with sides of 2 m has a charge of 40 C at...Ch. 4 - Three point charges, each with q = 3 nC, are...Ch. 4 - Charge q1 = 6 C is located at (1 cm, 1 cm, 0) and...Ch. 4 - A line of charge with uniform density = 8 (C/m)...Ch. 4 - Prob. 15PCh. 4 - A line of charge with uniform density l extends...Ch. 4 - Repeat Example 4-5 for liie circular disk of...Ch. 4 - Multiple charges at different locations are said...Ch. 4 - Three infinite lines of charge, all parallel to...Ch. 4 - Prob. 20PCh. 4 - A horizontal strip lying in the xy plane is of...Ch. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Charge Q1 is uniformly distributed over a thin...Ch. 4 - The electric flux density inside a dielectric...Ch. 4 - Prob. 26PCh. 4 - An infinitely long cylindrical shell extending...Ch. 4 - If the charge density increases linearly with...Ch. 4 - A spherical shell with outer radius b surrounds a...Ch. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - A circular ring of charge of radius a lies in the...Ch. 4 - Prob. 33PCh. 4 - Find the electric potential V at a location a...Ch. 4 - For the electric dipole shown in Fig. 4-13, d = 1...Ch. 4 - For each of the distributions of the electric...Ch. 4 - Two infinite lines of charge, both parallel to the...Ch. 4 - Given the electric field E=R18R2(V/m) find the...Ch. 4 - An infinitely long line of charge with uniform...Ch. 4 - The xy plane contains a uniform sheet of charge...Ch. 4 - A cylindrical bar of silicon has a radius of 4 mm...Ch. 4 - Repeat Problem 4.41 for a bar of germanium with e...Ch. 4 - A 100 m long conductor of uniform cross-section...Ch. 4 - Prob. 44PCh. 4 - Apply the result of Problem 4.44 to find the...Ch. 4 - A 2 103 mm thick square sheet of aluminum has 5 cm...Ch. 4 - A cylinder-shaped carbon resistor is 8 cm in...Ch. 4 - With reference to Fig. 4-19, find E1 if...Ch. 4 - An infinitely long cylinder of radius a is...Ch. 4 - If E=R150(V/m) at the surface of a 5-cm conducting...Ch. 4 - Figure P4.51 shows three planar dielectric slabs...Ch. 4 - Determine the force of attraction in a...Ch. 4 - Dielectric breakdown occurs in a material whenever...Ch. 4 - An electron with charge Qe = 1.61019 C and mass me...Ch. 4 - In a dielectric medium with r = 4, the electric...Ch. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Conducting wires above a conducting plane carry...Ch. 4 - Prob. 63P
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
- (al:Determine E caused by the spherical cloud of electrons with a volume charge density of - 1.68 x 10 -18 for 0 10mm. Clearly mention the surfaces, there differential components and write the equation properly by doing all the steps. (b): For the dielectric composition shown in the figure find out its total capacitance.arrow_forward4G 5:05 B/s 4. The figure shows a plastic rod having a uniform charge distribution -Q. The rod has been bent into a circular arc of radius r. In terms of Q andr, what is the electric field E (magnitude and direction) due to the rod at point P? (You are being asked to derive an equation for E, as we’ve done in lecture for charge distributions.) Show every mathematical step. Plastic rod of charge -Q 60° PY60° Solved: 4. The Figure Shows A Plastic Rod Having A Uniform ... Chegg Images may be subject to copyright. O Zoom Related Images 4 The n lew ref pen e er hael pide al l t apla Apla i a ETe d Whdee pal heof sirodar wt-youd ng Coidthe .. 1 Te y e co padPypng e hdentdid geovarrow_forwardExample 4.15: Given the potential field, V = 2x²y - 5z, and a point P(-4, 3, 6), find several numerical values at point P: the potential V, the electric field intensity E, the direction of E, the electric flux density D, and the volume charge density pv.arrow_forward
- A conducting wire is 2 mm in radius and 100 m in length. When a dc voltage of 9 V is applied to the wire, it results in a current of 0.3 A. Find: (a) the E-field in the wire, (b) the conductivity of the wire.arrow_forwardConductors, Dielectrics, and Capacitance Q4) Assume a 2 V conductor wire with a 3 cm diameter is embedded in silica with a relative permittivity of 2.25. The wire's center is 10 cm away from a 0 V conducting plane. Draw the wire, the conducting plane, and the wire's image. 1) Find the capacitance between the wire and its image per unit length. 2) Find the maximum surface charge density on the wire.arrow_forwardQ4. A finite length wire, which is bent as shown in the below figure, lies in xy-plane and carries a current I. If the magnetic flux density in the region is B = Ba, determine the magnetic force acting on the wire. {a+L) a+Larrow_forward
- INC 6- Two identical ring of radii 1 cm are separated by a distance much greater than their radii as shown in Figure. The rings carry charges of -1 μC and +1 µc uniformly distributed over them. If a point charge of 1 µC moves from the center of the ring on the right to the center of the ring on the left, how much potential energy changes in the point charge-rings system? Note: the potential of a uniformly charged ring of radius a and total charge Q at a point on its perpendicular axis is given by V=k, va'+xarrow_forward4.46 A 2 x 10-3 mm thick square sheet of aluminum has 5 cm x 5 cm faces. Find the following: (a) The resistance between opposite edges on a square face. (b) The resistance between the two square faces. (See Appendix B for the electrical constants of materials.)arrow_forwardPicture attached of question The 1D Poisson equation for the calculation of electrostatic potential can be written as: ?2?(?) ??2 = − ? ?(?) ???0 where q is the change of electron, N is the total charge density, and ε is material permittivity which consists of the relative permittivity εr and the permittivity of a vacuum ε0. Solve the above equation and find the potential for a p-n junction assuming the depletion approximation, i.e., when a concentration of acceptors NA is much larger than a concentration of donors ND so that: ?? ≫ ?? and this lead to ?? ≫ ??.arrow_forward
- QUESTION 1 a) Two conducting plates are separated by three dielectric materials as shown in Figure Q.1(a) The relative permittivity, &, of the materials filled in the two conducting plates are tabulated in Table Q.1. Find the total capacitance, C of the parallel plates in terms of d₁, d2, A₁, and A₂ by neglecting the fringing effects. The symbols of di, d2, A₁, and A2 are the material thickness and material areas, respectively. A₁ A₂ di d₂ 1 3 2 Figure Q. 1(a) Table Q.1 Material Relative permittivity, &r 1 2.2 2 2.8 3 4.2 Hint: The general capacitance formula of two conducting plates is given as: d where E, A, and d are the permittivity of free space, area of the two conducting plates, and distance between the two conducting plates, respectively. 1arrow_forwardPoint charges Q1 = 5 µC and Q2 = -4 µC are placed at (3, 2, 1) and (-4, 0, 6), re- spectively. Determine the force on Qj. 4.1arrow_forwardQ4. A finite length wire, which is bent as shown in the below figure, lies in xy-plane and carries a current I. If the magnetic flux density in the region is B = Ba,, determine the magnetic force acting on the wire. {a+L) a+LLarrow_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