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
Videos
Textbook Question
Chapter 4, Problem 62P
Conducting wires above a conducting plane carry currents I1 and I2 in the directions shown in Fig. P4.62. Keeping in mind that the direction of a current is defined in terms of the movement of positive charges, what are the directions of the image currents corresponding to I1 and I2?
Figure P4.62 Currents above a conducting plane (Problem 4.62).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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.
B) Define the permeability (ur) of the material. If you are required to design IH and IpH inductors,
what type of core will you use in your design and why? support your answer by equations.
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.
1
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
- 4.46 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_forwardBoth the Biot-Savart and Coulomb's laws exhibit an inverse-square relationship between field and source.? True O Falsearrow_forwarda) A conductor has polymers and metals around it. What are the functions of these materials bounded or covering around it? b) What is the major difference between semi-conductor materials and insulating materials? 1 c)Briefly explain the classification of polymers based on molecular forcesarrow_forward
- 4G 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_forward4) We usually think of wires as perfect (R=0) conductors, which is not quite accurate. Real wires have resistance albeit small - usually less than an ohm. With this in mind: a. Consider a uniform cylindrical copper wire that has diameter of 1 mm and is 10 m long. What is the resistance of this wire? The resistivity of copper is 1.72 x 10-8 9-m. b. This wire is cut in half, and the two strands are used to connect an electric heater to an outlet supplying 1500 W at 120 V. Draw a simple circuit diagram, including the voltage source, resistances of the connector wires, and the calculated resistance for the heater. C. How much of the total 1500 W is absorbed by the connector wires, not by the electric heater? d. If the specific heat and density of copper are 385 J/kg°C and 8940 kg/m³ respectively, how much will the connector wires heat up after 1 minute of use? (Assume all energy absorbed by the connector wires is converted to heat and remains in the copper wire.) Remember that E cmAT,…arrow_forward4. Define the continuity equation, then discuss the relaxation time in dielectric and conducting materials. Page 2 of 2arrow_forward
- Q.3 (a) A capacitor's structure is made up of two conductors that are separated by a dielectric material. Describe the phenomenon that allow the flow of current through the dielectric material. Include in the description relevant mathematical derivation of the abovementioned phenomenon. (b) A capacitor such as illustrated in Figure Q.3 is constructed using copper as plate A and plate B plus a dielectric material with ɛ, 3.8 and o = 4 S/m between the plates. Potential difference plates A across is VAB (t) = Vo cos(2n x 10°t) V. Assume that Plate A and plate B carry charges +Q(t) and and -Q(t) respectively as well as fringing field at the edge of the plates can be ignored, determine: (i) Q(t) if the capacitance is 2.135 x 10-11 F (ii) M(t) if electric field within the capacitor, E(t) = M(t) fV/m Based on Q.3(b)(ii), examine: (iii) Conduction current density and conduction current. UNIVE (iv) Displacement current density and displacement current. arch ASUS VivoBookarrow_forwardGiven that the potential V = 2x²y³ + 4xyz² mv. Find E at (4,5,8). Give expression for pr c/m³.arrow_forwardTwo long straight current-carrying wires are lined up parallel to one another in vacuum at a distance d. Currents of I and I2 flow through the wires, both in the same direction generating the field of BM at a midpoint between them. Write down an expression for BM in terms of the 1. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the currents running in each of the wires. Assume vacuum permeability Ho 1 usual "+" and "-" signs as appropriate. For use 1/(A*B). For Greek letters such as å or n use lambda and pi. Please use the "Display A*B response" button to check you entered the answer you expect. Вм-arrow_forward
- Conductors, 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_forward4. Use this information to answer Question 4-6: Below is the capacitance-voltage curve measured for a Schottky contact made on n-type GaAs at T = 300 K. In this plot, the capacitance has the unit of F/cm² and voltage is in unit of V. 1/C² x 1015 3.0 → Va -2.0 0.9 What is the built-in potential, oi, in unit of V? Answers within 5% error will be considered correct. Enter answer here 5. Calculate doping densiy in GaAs, Np, in unit of cm 3. Answers within 5% error will be considered correct. Enter answer herearrow_forward1. Pure germanium has (4 x 1022) atom. cm-3 doped by indium atoms, the impurity is add to the extent of 1 part in (10) germanium atoms, if the intrinsic concentration of germanium 2.5 x 1013 cm-3, note that Un = 3800 cm2 (V s)-1 and Hp = 1800 cm2(V s)-1. %3D (a) Find the conductivity and the resistivity before the doping? (b) Find the conductivity and the resistivity after the doping? (c) What can you conclude from 1 and 2?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: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