Fundamentals of Electromagnetics with Engineering Applications
1st Edition
ISBN: 9780470105757
Author: Stuart M. Wentworth
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2, Problem 2.23P
Suppose a ribbon of charge with density
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Volume charge density is located in free space as ρν = 2e−100r nC/m3 for 0 < r < 3 mm, and ρν = 0 elsewhere.
Find the total charge enclosed by the spherical surface r = 2 mm.
By using Gauss’s law, calculate the value of Dr on the surface r = 2 mm.
Using Gauss’ law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point
(i) outside and
(ii) inside the shell.
Plot a graph showing variation of electric field as a function of r > R and r < R (r being the distance from the centre of the shell)
A uniform line charge and a uniform sheet charge, both infinite in extent, are located in free space along the y-axis and at x = -1 respectively. Determine E at point M(2, -1, 1) if the line charge density is 15 nc/m and the sheet charge density is 2 nC/m^2
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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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
- Find |E| at the origin in free space if a uniform line charge of 30 nC/m lies along the line (y = 3, z = 5).arrow_forwardAn infinitely long uniform line charge lies along the x-axis. If the line charge has a density of 12 nC/m, determine E at point (7, 3, -4)marrow_forwardPlease answer and write neatly. (Show your complete solution.) Volume charge density is located in free space as ρν = 2e−1000r nC/m3for 0 < r < 1 mm, and ρν = 0elsewhere.(a) Find the total charge enclosed by the spherical surface r = 1 mm.(b) By using Gauss’s law, calculate the value of Dr on the surface r = 1 mm.arrow_forward
- A 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_forwardA spherical charge of radius 3 cm and a volume charge density given below. How much is the D-field at a distance of 8 cm from the center of the spherical charge and in uC/(m^2) and 3-decimal places? note: PV = 20 mC/m^3arrow_forward6. If D=3y²a, + 3x²ya, + 5a, C/m², find the total charge enclosed within the region 0 < x,y,z <2 by evaluating one or more surface integrals.arrow_forward
- A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. 1. Use Gauss's law to find an expression for the magnitude of the electric field strength E inside the sphere, r≤R, and r>- (more or equal) in terms of Q and 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_forwardCalculate the electric field intensity E at M(3, -4, 2) in free space caused by: a. Charge Q1 = 2 µC at P1(0, 0, 0) b. Charge Q2 = 3 µC at P2(-1, 2, 3) c. Charge Q3 = 4 µC at P3(-3, -2, 4) d. The total field intensity of the 3 charges ( please provide complete solutions, thank you )arrow_forward
- The structure in the figure has 4 concentric spherical media,which have;0<r<a free spacea<r<b ρv (C/m3) constant volume charge densityb<r<c εr relative permittivityc<r free spaceFind ?⃗ , ?⃗ and ?⃗ in these 4 regions and also plot themarrow_forwardA 20-nC point charge is at the origin in free space. Calculate V1 if pointP1 is located at P1(2, 3,−1) and V = 0 at (6, 5, 4).arrow_forwardA circular ring with uniform charge density of ρL=10 nC/m with radius 2m lies in the z=0 with center at the origin. Find the point charge Q at the origin which would produce the same electric field E at (0,0,5)arrow_forward
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