Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 3, Problem 3.4P
An electric field in free space is
V/m. Find the total charge contained within a sphere of 3-m radius, centered at the origin.
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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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- An electric field in free space is E = 5 z 3 ε 0 a z(V/m). Find the total charge (in C) contained within a sphere of 2-m radius, centered at the origin.arrow_forwardA charge of −1 nC is located at the origin in free space. What charge must be located at (2, 0, 0) tocause the ?-component of the electric field to be zero at (3, 1, 1)?arrow_forwardA solid copper sphere of radius 20 cm carries a charge of 50 nC. Using Gauss' Law find the electric field (a) 16 cm, (b) 20 cm, and (c) 100 cm from the center of the sphere.arrow_forward
- An 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_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_forwardConsider a solid sphere inside a spherical conducting shell as shown. The solid sphere has a charge of +4Q and the spherical shell has charge +5Q. What is the electric field in the region between the sphere and the shell?arrow_forward
- A charge ring of radius is characterized by a positive linear charge density P?has been. The ring is located in empty space and is in the ? - ? plane as shown in Figure 6.is positioned. A = (0, 0, ℎ) along the axis of the ring, ℎ above its centerDetermine the electric field strength at the point.arrow_forwardIn free space, q1 = 3nC and q2 = 4nC charges are placed at 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_forwardIf a line of charge with uniform density ρl extends between z=-L/2 and z=L/2 along the z-axis, obtain an expression for the electric field intensity at any point P(r, ϕ ,0) on the x-y plane. Investigate the case when L becomes infinite.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 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_forward1. Determine the total charge contained in a line extending from Cartesian point (3, 2, 1)to (5, 4, 7) carrying line charge of density p1(x, y,z)=2x +3y -5z C/m. note: this question is EMT ( electromagnetic field )arrow_forward
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