Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 3, Problem 3.10P
An infinitely long cylindrical dielectric of radius b contains charge within as volume of density
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There is an infinitely long cylinder of radius 0.5 cm along the z-axis, and it is filled uniformly with a volume charge density of 3.5 C/m3. Apply Gauss’s Law to find an expression for the electric field in two cases:
a) For ρ > 0.5cm
b) For 0 <ρ<0.5 cm
A finite line charge located at (0, y, 0)m, where a≤y≤b , has a line charge density of ρL = ycosy C/m. Determine the integral that will solve for the electric field at the origin.
In empty space there is (-∞, 0) semi-infinite linear uniform and constant charge density ρl = 3 [C / m] on the z-axis. Calculate the electrostatic field that this charge density will create at point B (0,0,4). ke = 1 / 4πε
Chapter 3 Solutions
Engineering Electromagnetics
Ch. 3 - Prob. 3.1PCh. 3 - An electric field in space is E=(5z2/C0)azV/m....Ch. 3 - Consider an electric dipole in free space,...Ch. 3 - An electric field in free space is E=(5z3/0)z V/m....Ch. 3 - A volume charge distribution in free space is...Ch. 3 - Prob. 3.6PCh. 3 - Prob. 3.7PCh. 3 - Use Gauss, law in integral form to show that an...Ch. 3 - A sphere of radius a free space contains charge of...Ch. 3 - An infinitely long cylindrical dielectric of...
Ch. 3 - Consider a cylindrical charge distribution having...Ch. 3 - The sun radiates a tota1 power of about 3.86...Ch. 3 - Spherical surfaces at r = 2, 4, and 6 m carry...Ch. 3 - Prob. 3.14PCh. 3 - Volume charge density is located as follows; pv=0...Ch. 3 - An electric flux density is given by D=D0aP, where...Ch. 3 - In a region having spherical symmetry, volume...Ch. 3 - State whether the divergence of the following...Ch. 3 - A spherical surface of radius 3 mm is centered at...Ch. 3 - A radial electric field distribution in free space...Ch. 3 - In a region exhibiting spherical symmetry,...Ch. 3 - (a) A flux density field is given as F1 = 5 az....Ch. 3 - (a) A point charge Q lies at the origin. Show that...Ch. 3 - In a region in free space, electric flux density...Ch. 3 - Within the spherical shell, 3D= 5(r-3)3a,C/m2 .(a)...Ch. 3 - If we have a perfect gas of mass density Px...Ch. 3 - Consider a slab of material containing a volume...Ch. 3 - Repeat Problem 3.8, but use .D= pv and take an...Ch. 3 - Prob. 3.29PCh. 3 - (a) Use Maxwells first equation. �. D=Pv, to...Ch. 3 - Prob. 3.31P
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- 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.arrow_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_forwardHW: A spherical charge of (pv= 6 C/m3 ) and radius ( 4). Its center is at (1,2,3). Find settings(E) at point (3,-2,4). *note and drawarrow_forward
- In free space, q1 = 3nC charges are placed on y = 1 and y = 6, respectively, on the y-axis as shown in the figure. Accordingly, what is the electric potential value at y = 4?arrow_forwardA volume charge density is known to be Delta(n, deg, z) in cylindrical coordinates. What is the appropriate expression to evaluate the total charge (for an arbitrary geometry)arrow_forwardWithin the sphere defined by r ≤ 8 cm, the volume charge density is ρv = 6.8 x 10-7 C/m3 . (i) Find an expression for electric field intensity for region r < 8 cm. Hence, calculate the electric field intensity at a point having rectangular coordinates of (x, y, z) = ( 3 cm, 2cm, 0 ). (ii) Assume that all of the electric charge is removed from a spherical region centered at (x, y, z) =(3 cm, 0, 0) and having a radius of 1 cm. Calculate the total electric field intensity at point (x,y,z) = (3 cm, 2 cm, 0).arrow_forward
- In empty space there is (-∞, 0) semi-infinite linear uniform and constant charge density ρl = 4 [C / m] on the z-axis. Calculate the electrostatic field that this charge density will create at point A (5,0,0). ke = 1 / 4πεWrite numerically the components of the electrostatic field in terms of the given quantities.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_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 uniform volume charge density of 100ρ2 nC/m3 is present throughout the region ρ > 1.8 cm and ρv = 0 elsewhere. Find the total charge (in nC) inside the cylindrical surface in the region 1.8 < ρ < 9.7, -9 < z < 9.arrow_forwardIn a material medium with relative dielectric constant LaTeX: \ varepsilon_r = 3 & varepsilon; r = 3, LaTeX: 5 \ mu C5μC load LaTeX: R = 2mR = 2m radius is uniformly distributed over the sphere volume. Accordingly, which of the following is the expression of electric field outside the sphere.arrow_forwardA 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^2arrow_forward
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Demos: Dielectric breakdown; Author: Caltech's Feynman Lecture Hall;https://www.youtube.com/watch?v=2YrHh1ikefI;License: Standard Youtube License