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 4.30P
To determine
The equation of the surface on which
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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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- Example: A 31/4dipole is radiating into free-space. Input power to the dipole is 100 W. Assuming an overall efficiency of 50%, find the power density (in W/m?) at (r = 500 m, 8 = 60°, ¢ = 0)? Solution:arrow_forwardA dipole is composed of a pair of point charges ±?, separated by a distance ?d and aligned parallel with the ?-x-axis, as shown in the figure. Find the expression for the potential ? on the ?-axis at point F located at ?=3.77×10−8 cm, where ?≫?. Then, evaluate the potential for a dipole moment of ?=8.00×10−30 C·m. The Coulomb force constant is ?=1/(4??0)=8.99×109 N·m2/C2.arrow_forwardConsider the dipole in the figure below with the charge magnitude of q = 3.0 nC and separation distance d = 4.0 cm. What is the potential at the following locations in space? (a) (0, 0, 1.0 cm); (b) (0, 0, –5.0 cm); (c) (3.0 cm, 0, 2.0 cm).arrow_forward
- A line with uniform charge density PL forms a semicircle of radius r in the first half of the xy charge plane. Determine the amplitude and direction of the electric field intensity at the center of the semicircle.arrow_forwardAn electric dipole with a dipole moment P = 2qai is placed in an electric field given by E = E0x1. Which of the following is the magnitude of the force acting on the dipole?arrow_forwardA horizontal infinitesimal electric dipole of constant current I0 is placed symmetrically about the origin and directed along the x-axis. Derive the(a) far-zone fields radiated by the dipole(b) directivity of the antennaarrow_forward
- A 1-m long dipole antenna is driven by a 150 MHz source having a source resistance of 50 ohms and a voltage of 100 V. If the ohmic resistance of the antennas is given by RL = 0.625 ohms, find the:(a) Current going into the antenna (Iant)(b) Power dissipated by the antenna(c) Power radiated by the antenna(d) Radiation efficiency of the antennaarrow_forwardExample: A 31/4 dipole is radiating into free-space. Input power to the dipole is 100 W. Assuming an overall efficiency of 50%, find the power density (in W/m) at (r = 500 m, 0 = 60°, o = 0)?arrow_forwardA nonmagnetic medium has an intrinsic impedance of 250∠30 Ω. Find a) Loss tangent b) Dielectric constant c) Complex permittivity d) Attenuation constant at 1 MHz?arrow_forward
- A dipole having a moment p = 3ax − 5ay + 10az nC · m is located atQ(1, 1,−4) in free space. Find V at P(6, 3, 4).arrow_forwardAn antenna radiates a total power of 100W in the direction of maximum radiation, the field strength at a distance of 10Km was found to be 12mV/m. What is the gain of the antenna? Assume free space propagation. If η=90% find directivity.arrow_forward3. With a operational frequency of 30GHz, what is the effective length of a half-wave dipole?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