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 2.40P
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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.
The spherical surfaces r = 1, 2, and 3 carry surface charge densities of 20, -9, and 2 nC/m², respectively. (a) How much electric flux leaves the surface r = 5? (b) Find D at P(1,-1,2).
In the 0<r<1mm cubic region, it is given as ρ_v=2e^(-100r) nC/m^3. In other places, the charge density is given as 0.a) Find the total charge inside the spherical surface r=1mm.b) Calculate the expression Dr on the r=1mm surface using Gauss's law.
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
- Given a 60-uC point charge located at the origin, find the total electric flux passing through: (a) that portion of the spherer= 26 cm bounded by 0 < 0 < and = 0 <0< (b) the closed surface defined by p = 26 cm and := ±26 cm; (c) the plane := 26 cm.arrow_forwardUniform line charge density of 5 nC/m is at y=0, z=2m in free-space while -5 nC/m is located at y=0, z=-2. A uniform surface charge density 0.3 nC/m2 is at y=0.2m, and - 0.3 nC/m is at y=-0.2. Find E at origin?arrow_forwardI = 7 A current flows from the infinitely long wire along the y axis that intersects the z axis at the point C (0,0,8) in the upper half space, which is the empty space. If z <0 half space, it is made of material with relative magnetic permeability µr = 7. Write the sum of the components( Hx + Hy + Hz )of the magnetic field H [A / m] vector at point A (-2, -4,0-) (in half space z <0) in terms of the given magnitudesnumerically.arrow_forward
- 2. Point charges of 15 nC each are symmetrically located at (4,4,0), (4,-4,0), (-4,4,0), and (-4,-4,0), and a uniform line charge of 50 nC/m lies at x = 0, y = 8, all z. (a) Find D at the origin. (b) How much electric flux crosses the y = 0 plane? (c) How much electric flux leaves the surface of a sphere of radius 5 m centered at (0,6,0)?arrow_forwardQ3/Given the current density J = 60 pa, A/m in cylindrical coordinates: (a) Determine the magnetic field H, where H varies with p only and has only a 0 component; (b) integrate J over the circular surface p = 1,0< 0< 2n, z 0, to determine the total current passing through that surface in the a, direction ; (c) find the total current using a line integral around the circular path p = 1, 0< 0< 2n, z = 0.arrow_forwardGiven the field: D = 20 [-sinØ ap + sin 2Ø aØ] Find the total charge lying within the volume 1<p < 2,0 < Ø < π, and 0 < z < 1 by evaluating both sides of the Divergence Theorem equationarrow_forward
- A 5-nC póint charge is located at A(2, -1, -3) in free space. (a) Find E at the origin.(b) Plot E(x, 0,0)| vs. x, -10<x<10 m.(c) What is |E(x,0,0)|max.?arrow_forwardA line charge, P-50 nC/m, is located along the line x2, y = 5, in free space. (a) Find E at P(1,3,-4). (b) If the surface x = 4 contains a uniform surface charge density, pg 18 nC/m², at what point in the z- 0 plane is E-0?arrow_forwardCharge Q=20 μC is located at the origin in free space. Determine the flux density at point (2, -1, -2) marrow_forward
- A volume charge in a form of a cube, 2m on an edge, parallel to the axes and centered at the origin is enclosed by a closed spherical surface with radius 3m centered at the origin. Determine the net flux crossing the closed surface given the volume charge density below Pv = x² + y c/m³arrow_forwardVolume 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.arrow_forwardA 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_forward
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