Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Textbook Question
Chapter 4, Problem 4.14P
Given the electric field
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In a certain region of space, the electrical potential is given by the relationship
V (x, y, z) = Axy- Bx² + Cy
where A, B and C are constant. Calculate as x, y and z components of the electric field. (b) in which points (x, y, z) is the electric field equal to zero?
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
Given the potential field in cylindrical coordinates, V = 100 + 50ρ + 150ρ sinΦ volts, and point P at ρ = 1 m, Φ = 600, z = 0.5 m, find the electric field intensity E at P.
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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- 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?arrow_forwardIf the electric field in the region is given as E = 2 (z ax - y ay + x az) V/m. Determine the potential at point A(9, 5, 6) m, in volts, if the potential at point B(3, -7, -8) m is 78 volts.arrow_forwardThe points A(2,0,0) B(1,0,0), C(0,1,0), D(0,2,0) are inside the E^= ar^ r SinΦ + aΦ^ r2 CosΦ (V/m) Electric field. find the VAB over the B, C, D, A path?arrow_forward
- Three infinite uniform sheets of charge are located in free space as follows: -7 nC/m2 at y = 3, -4 nC/m2 at y = -4, and 9 nC/m2 at y = 0. Find magnitude of E at the point PA(9, 14,-7).arrow_forwardElectrical Engineering 1. The point charges of +Q at (-1,0), +Q at (1,0), and -2Q at (0,1) lie in a plane where z = 0, respectively. At this time, find the electric flux density at (0,0).arrow_forwardElectrostatic field at point A (2, -2.9) in empty space Observed as E = 4ke*ux. Determine the location (xs, ys, zs) of the point Q = -3 [C] that is likely to form this area. It shows the constant ke = 1 / (4πε).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_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_forwardA sheet of charge, ρS = 2nC/m2, is pressed at the plane x = 3 in free space, and a line charge, ρL = 20nC/m, is located at x = 1, z = 4. Find the magnitude of the electric field intensity at the origin. (Hint: E = ES + EL)arrow_forward
- A 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_forwardThe charges and locations of four point charges in free space are as follows: Charge 1: 500 pC at (-1, 2, 3)Charge 2: -40 nC at (4, 3, -1)Charge 3: 300 nC at (2, 2, 2)Charge 4: -2 nC at (-2, 1, 0) In this coordinate system, one unit of distance is 1 m; that is, (1, 0, 0), (0, 1, 0) and (0, 0, 1) are each 1 m away from (0, 0, 0). Calculate the magnitude of the electric field at (0, -3, 0). Express in V/m.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_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