Fundamentals Of Applied Electromagnetics
7th Edition
ISBN: 9781292082448
Author: Fawwaz T Ulaby Umberto Ravaioli
Publisher: Pearson Education Dorling Kindersley
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4, Problem 51P
Figure P4.51 shows three planar dielectric slabs of equal thickness but with different dielectric constants. If E0 in air makes an angle of 45° with respect to the z axis, find the angle of E in each of the other layers.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Conducting planes at z = 2 cm and z = 8 cm are held at potentials of
-3 V and 9 V, respectively. The region between the plates is filled with a perfect dielectric with ϵ = 15 ϵ0, voltage at z = 1CM?
A conducting cylinder with a radius of 1 cm and at a potential of 20 V is parallel toa conducting plane which is at zero potential. The plane is 5 cm distant from thecylinder axis. If the conductors are embedded in a perfect dielectric for which ?* =4.5, find:(a) the capacitance per unit length between cylinder and plane;(b) ?# R4S on the cylinder.
The linear dielectric material has a uniform free charge density ρ when embedded in a sphere of radius R. Find the potential at the center of the sphere?
Chapter 4 Solutions
Fundamentals Of Applied Electromagnetics
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
- We have a long straight coaxial cable consisting of a cylindrical conducting wire surrounded by an insulating layer surrounded by a concentric pipe-like conducting sheath. If the inner wire has uniform charge per unit length, list the direction of the electric field.arrow_forwardThe charge densities of the 2 layers are given in the figure. These layers are perpendicular to the z-axis and the distance between them is d. both layers extend to infinity in the x and y directions, and their thickness is negligibly small. Take the electric potential as 0 at the starting point.Draw equipotential surfaces.arrow_forwardTwo coaxial conducting cylinders are located at ρ = 2 cm and ρ = 4 cm in free space and have a length of 100 m. The region between the cylinders contains a layer of dielectric from ρ = 2 cm to ρ = 3.69 cm with εr = 2. The capacitance in nF is?arrow_forward
- Find the work done in moving a point charge Q = -20 μC from the origin to (4, 2, 0)m in the fieldarrow_forwardTwo conducting cylinders at ρ = 2 cm and ρ = 8 cm in free space are held at potentials of 60 mV and -30 mV, electric field at ρ = 4 cmarrow_forwardtwo conducting coaxial cylinders are located at rho =1 cm and rho = 1.5 cm. The inner conductor is maintained at 50 V while the outer one is grounded. If the cylinders are separated by a dielectric material with e = 4eo, find the surface charge density on the inner conductor.arrow_forward
- Hey I was wondering if you can help me with this problem plz Figure shows a plastic rod with a uniform charge −Q. It is bent in a 120° circular arc of radius r and symmetrically placed across an x axis with the origin at the center of curvature P of the rod. In terms of Q and r, what is the electric field E ⃗ due to the rod at point P?arrow_forwardThe charge distribution in a region is given by ρ(~r) = ρ0ra where ρ0 and a areconstants of appropriate dimensions.Find the expression for electric field E(~r) due to ρ(~r).arrow_forwardUse Gauss’s law to derive the expression for the electric field between two uniformly charged large parallel sheets with surface charge densities a and -a respectively.arrow_forward
- Determine the work done, in mJ, in moving a 8-nC charge against the electric field due to a point charge 8 mC at (1, 3, 4) m from A(-3, 0, -1) m to B(0, -4, -3) m.arrow_forwardGauss’ law relates the electric fields at points on a (closed) _______ to the net charge enclosed by that surface. Select one: a. Plane surface b. Gaussian surface c. Voltage surface d. Coulomb’s surfacearrow_forwardQuestion: Consider a point charge near a grounded metal plate. Could the field around it be approximated by Coulomb’s Law for an isolated point charge? Yes, or No? Explain your Answer. If no, what sort of field should we consider instead?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,
Demos: Dielectric breakdown; Author: Caltech's Feynman Lecture Hall;https://www.youtube.com/watch?v=2YrHh1ikefI;License: Standard Youtube License