Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Chapter 4, Problem 4.6P
A electric field in free space is given as
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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
If V(x, y, z)= 3x²ye^2 is the scalar electric potential given as V, what is the magnitude of the electric field E at the point P(1,-1,0)?
In free space, q1 = 4nC 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?
Chapter 4 Solutions
Engineering Electromagnetics
Ch. 4 - Given E = Exax + Eyay + Ez3z V/m, where EX, Ey,...Ch. 4 - A positive point charge of magnitude q1 lies at...Ch. 4 - Given E=Epap+Ea+Ez+azV/m, where Ep, E and E2 are...Ch. 4 - An electric field in free space is given by...Ch. 4 - Consider the vector field G = (A/p) aa where A is...Ch. 4 - A electric field in free space is given as...Ch. 4 - Prob. 4.7PCh. 4 - Given E=-xax+yay,(a) find the work involved in...Ch. 4 - An electric field intensity in spherical...Ch. 4 - A sphere of radios a carries a surface density of...
Ch. 4 - At large distances from a dipole antenna (to be...Ch. 4 - Prob. 4.12PCh. 4 - Thee identical point charges of 4 pC each are...Ch. 4 - Given the electric field E=(y+1)ax+(x1)ay+2az find...Ch. 4 - Two uniform lines, 8 nC/m, are located at x=1, z=2...Ch. 4 - A spherically symmetric charge distribution in...Ch. 4 - Uniform surface charge densities of 6 and 2 nC/m2...Ch. 4 - Find the potential at the origin produced by a...Ch. 4 - Volume charge density is given as pv=poer/C/m3,...Ch. 4 - En a certain medium, the electric potential is...Ch. 4 - Prob. 4.21PCh. 4 - A Line charge of infinite length lies along the z...Ch. 4 - Prob. 4.23PCh. 4 - A certain spherically symmetric charge...Ch. 4 - Consider an electric field intensity in free space...Ch. 4 - Let us assume that we have a very thin, square,...Ch. 4 - By performing an appropriate Line integral from...Ch. 4 - Prob. 4.28PCh. 4 - A dipole having a moment P=3ax-5ay+10aznC.m is...Ch. 4 - Prob. 4.30PCh. 4 - A potential field in free space is expressed as...Ch. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - A sphere of radius a contains volume charge of...Ch. 4 - Four 0.8 nC point charge are located in free space...Ch. 4 - Surface charge of uniform density ps lies on a...
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- If 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_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 nonuniform electric field is given by the expression D=2y ax+z ay-3x az C/m^2. Determine the electric flux through a rectangular surface in the xy plane, extending from x = 0 to x = 5 and from y = 0 to y = 6.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_forwardAn 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 disk of radius a in the xy plane carries surface charge of density ρs = ρs0 /ρ C/m2 where ρs0 is a constant. Find the electric field intensity E everywhere on the z axis.arrow_forward
- Given 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_forwardSince the potential of a perfect conducting sphere with a radius of 2.7 cm in empty space is 10 V, calculate the strength of the electric field at a distance of 16.3 cm from the center of the sphere as V / m in ke.arrow_forwardFind the charge density in a region for which the electric field in spherical coordinates is given byarrow_forward
- Gauss’ law relates the electric fields at points on a (closed) _______ to the net charge enclosed by that surface. Select one: a. Plane surface b. Gaussian surface c. Voltage surface d. Coulomb’s surfacearrow_forwardAn electric field in free space is E = (5z3/ε0) az V/m. Find the total charge contained within a sphere of 2-m radius, centered at the origin.arrow_forwardIn 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 / 4πεarrow_forward
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