Fundamentals of Electromagnetics with Engineering Applications
5th Edition
ISBN: 9780471263555
Author: Stuart M. Wentworth
Publisher: John Wiley & Sons
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Chapter 2, Problem 2.37P
To determine
The equations of electric flux density for all
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A coaxial cable of consists of two concentric cylindrical conductors. The region between the conductors is completely filled with polyethylene plastic. The radius of the inner conductor is 0.50 cm, the radius of the outer conductor is 1.75 cm, and the length of the cable is 15 cm. The resistivity of the plastic is 1013 Ω • m. Calculate the resistance of the plastic if the electric field is applied across the ends of the conductor.
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The charge per unit length on the thin rod shown below is ?. What is the electric field at the point P? (Hint: Solve this problem by first considering the electric field
dE
at P due to a small segment dx of the rod, which contains charge
dq = ? dx.
Then find the net field by integrating
dE
over the length of the rod. Use the following as necessary: L, a, ?, and ?0. Enter the magnitude. Assume that ? is positive.)
E
The region between the conductors of a coaxial cable with inner conductor radius a=2m and outer conductor radius b=3m is filled with a material with dielectric constant E. If the charge per unit length of the inner conductor is q, which of the following is the capacitance of the unit length of the coaxial cable.
Chapter 2 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 2 - Given P(4, 2, 1) and APQ=2ax+4ay+6az, find the...Ch. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Suppose Q1(0.0,-3.0m,0.0)=4.0nC,...Ch. 2 - Prob. 2.5PCh. 2 - Suppose 10.0nC point charges are located on the...Ch. 2 - Four 1.00nC point charges are located at...Ch. 2 - A 20.0nC point charge exists at...Ch. 2 - Prob. 2.9PCh. 2 - Convert the following points from Cartesian to...
Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - A 20.0–cm–long section of copper pipe has a...Ch. 2 - A line charge with charge density 2.00nC/m exists...Ch. 2 - You are given two z–directed line charges of...Ch. 2 - Suppose you have a segment of line charge of...Ch. 2 - A segment of line charge L=10.nC/m exists on the...Ch. 2 - In free space, there is a point charge Q=8.0nC at...Ch. 2 - Prob. 2.20PCh. 2 - Sketch the following surfaces and find the total...Ch. 2 - Consider a circular disk in the x–y plane of...Ch. 2 - Suppose a ribbon of charge with density S exists...Ch. 2 - Sketch the following volumes and find the total...Ch. 2 - You have a cylinder of 4.00–in diameter and...Ch. 2 - Consider a rectangular volume with...Ch. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Given D=2a+sinazC/m2, find the electric flux...Ch. 2 - Suppose the electric flux density is given by...Ch. 2 - Prob. 2.31PCh. 2 - A cylindrical pipe with a 1.00–cm wall thickness...Ch. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - A thick–walled spherical shell, with inner...Ch. 2 - Prob. 2.37PCh. 2 - Determine the charge density at the point...Ch. 2 - Given D=3ax+2xyay+8x2y3azC/m2, (a) determine the...Ch. 2 - Suppose D=6cosaC/m2. (a) Determine the charge...Ch. 2 - Suppose D=r2sinar+sincosaC/m2. (a) Determine the...Ch. 2 - Prob. 2.42PCh. 2 - A surface is defined by the function 2x+4y21nz=12....Ch. 2 - For the following potential distributions, use the...Ch. 2 - A 100nC point charge is located at the origin. (a)...Ch. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Suppose a 6.0–m–diameter ring with charge...Ch. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - The typical length of each piece of jumper wire on...Ch. 2 - A 150–m length of AWG–22 (0.644 mm diameter)...Ch. 2 - Determine an expression for the power dissipated...Ch. 2 - Find the resistance per unit length of a stainless...Ch. 2 - A nickel wire of diameter 5.0 mm is surrounded by...Ch. 2 - Prob. 2.57PCh. 2 - A 20nC point charge at the origin is embedded in...Ch. 2 - Suppose the force is very carefully measured...Ch. 2 - The potential field in a material with r=10.2 is...Ch. 2 - In a mineral oil dielectric, with breakdown...Ch. 2 - Prob. 2.62PCh. 2 - For z0,r1=9.0 and for z0,r2=4.0. If E1 makes a 300...Ch. 2 - Prob. 2.64PCh. 2 - Consider a dielectric–dielectric charge–free...Ch. 2 - A 1.0–cm–diameter conductor is sheathed with a...Ch. 2 - Prob. 2.67PCh. 2 - For a coaxial cable of inner conductor radius a...Ch. 2 - Prob. 2.69PCh. 2 - Prob. 2.70PCh. 2 - A parallel–plate capacitor with a 1.0m2 surface...Ch. 2 - Prob. 2.72PCh. 2 - Prob. 2.73PCh. 2 - Given E=5xyax+3zaZV/m, find the electrostatic...Ch. 2 - Suppose a coaxial capacitor with inner radius 1.0...
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- It is viewed from the cross-section of a coaxial cable consisting of a cylindrical conductive tube with an internal radius R and an outer radius of Rz wrapped around a cylindrical conductive wire with a RADIUS of R. r to indicate the radial distance from the center, the inner cylindrical conductor,if it is j1 = Gr and the outer conductive tube, j2 = Car has improper current densities. Here, the two conductors carry the same I flow in zit directions. What is the size of the B2 magnetic fields at r=1 cm and B2 at r= 8 cm?(R=4 cm; R=7 cm, R3=9 cm; Io=2 A; uo=47.10-7 T.m/A and our aquani-positive forehead outward from the page plane).arrow_forwardTwo lengths of conductors are made from, i) a single solid copper wire of radius 5 mm, and, ii) a bundle of 25 solid copper wires each of radius 1 mm. For each conductor, estimate the resistance per unit length at a frequency of 1 MHz. You may assume a conductivity of σ = 6.7 × 107 Ω −1m−1 and that the skin depth, δ, is given by δ = r 2 µ0σω .arrow_forwardAn image taken from the cross-sectional area of a coaxial cable consisting of a solid inner conductor of Radius R, surrounded by a concentric cylindrical tube of inner radius R, and outer radius Rg is given in the figure. The inner conductor and outer conductor (cylindrical tube) have the current density j1 = Cr and ja = Cyr respectively, for which r is the radial distance from the center. Each conductor carries the same total 1, in opposite directions. What is the magnitude of the magnetic field B, at a distance 11 = 2 cm and B, at a distance 12 = 9 cm? (R = 5 cm; R2 = 8 cm; Rg = 10 cm: 1, = 4 A; Ho = 47x10-?T.m/A. Take the sign of the current coming out from the page plane as positive).arrow_forward
- Given a coaxial capacitor with the length of L which has two coaxial conductors with radius a=1 cm and b= 4 cm for inner and outer conductor, respectively. The inner conductor carries the total charge of –Q C whilst the outer carries +Q C. If the length of the coaxial, L = 100m and the coaxial is filled with the lossy Teflon (εr = 2.2 and σ = 4 Sm-1), determine: i. Potential Different between r = 3cm and r = 6cm ii. Energy in region a<r<b Note: In dielectric material, permittivity ε=εoεr and D=εEarrow_forward: A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points Aand B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to bemoved from A to B, determine the following:a. The potential at A; b. The electric potential energy at B; c. The work done in moving the test charge; d. The rate of change of the potential with respect to length or displacement in the conductor Assuming the dielectric of each capacitor is air and the network is connected to Vab = 30V supply, calculate thefollowing:a. The equivalent capacitance between a and b. b. The charge on each capacitor. c. The potential difference on each capacitor d. Energy stored on each capacitorarrow_forwardA spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points A and B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to be moved from A to B, determine the following: a. what is the work done in moving the test charge? b. what is the rate of change of the potential with respect to length or displacement in the conductor?arrow_forward
- Problem 1: A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points Aand B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to bemoved from A to B, determine the following:a. The potential at Aarrow_forwardplease show diagram and complete solution. A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points A and B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to be moved from A to B, determine the following: a. The potential at A; b. The electric potential energy at B; c. The work done in moving the test charge; d. The rate of change of the potential with respect to length or displacement in the conductorarrow_forwardDetermine the capacitance of: (a) a 1-ft length of 35B/U coaxial cable,which has an inner conductor 0.1045 in. in diameter, a polyethylene dielectric(r = 2.26 from Table C.1), and an outer conductor that has an inner diameter of0.680 in.; (b) a conducting sphere of radius 2.5 mm, covered with a polyethylenelayer 2 mm thick, surrounded by a conducting sphere of radius 4.5 mm; (c) tworectangular conducting plates, 1 cm by 4 cm, with negligible thickness, betweenwhich are three sheets of dielectric, each 1 cm by 4 cm, and 0.1 mm thick, havingdielectric constants of 1.5, 2.5, and 6.arrow_forward
- The inner conductor of a long coaxial cable has radius a. The inner radius of the outer conductor is b. Inner conductor V0, outer conductor at 0 potential. Determine the electric potential and electric field strength in the insulating material.arrow_forwardA spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points Aand B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to bemoved from A to B, determine the following:The potential at A; The electric potential energy at B;arrow_forward
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