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 4.32P
To determine
(a)
The energy stored in dipole field in the region
To determine
(b)
The reason for not letting an approach to be zero as a limit.
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1. Which dipole pair in the figure below has the lower energy, the parallel pair in (a) or the antiparallel pair in (b)?
2. If you double the distance between the dipole centers by what factor does each pair interaction change? Does it increase of decrease?
An 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?
An electric dipole of 50 az pC.m is located at the (0,0,1). Find the V and E at (0,0,-5) and (2, π/2, π/3).
Please remember the dipole is not at the origin and we have spherical coordinates for the second part.
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Consider a finite line charge of length L and linear charge density λ that lies along the dipole axis of an ideal dipole with dipole moment p →. The end of the line charge nearest to the dipole is at a distance d from the center of the dipole. Draw a clearly labelled Figure showing the setup. Calculate the electrical force between the two. Show all work in clear steps with justification. Show that the force reduces to an expected result when d >> L. Show all work in clear steps with justification.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_forwardExample: 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_forward
- An 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_forwardAn electric dipole of 50 az pC.m is located at the (0,0,1). Find the V and E at (0,0,-5) and (2, π/2, π/3).arrow_forwardAn electric dipole p=6ax-3ay+2ax nC-m is located at (-1,2,-3). Find the potential at point (3,-9,4).arrow_forward
- Example: 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 dipole having a moment p = 3ax − 5ay + 10az nC · m is located atQ(1, 2,−4) in free space. Find V at P(6, 3, 4).arrow_forwardA slab of dielectric material has a relative dielectric constant of 3.8 and contains a uniform electric flux density of 8nC/m^2. If the material is lossless; find: The average number of dipoles per cubic meter (n) if the average dipole moment is p=10^-29Cmarrow_forward
- A dipole with charges of ±q, where q = 3.9e-05, and a separation d = 0.0001 has what magnitude field strength along the z (dipole) axis at a distance 1 away?arrow_forwardA 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_forwardA circular loop antenna with cross-sectional area 10 cm2 is absorbing power from electromagnetic radiation with a frequency of 2 GHz and generating an rms electric current of 50 μA in the electric circuit connected to the antenna. If the antenna is 5 km away from the source of the electromagnetic radiation, and the source is assumed to be a “point particle” radiating energy equally in all directions, what is the power (in kW) of the radiation emitted by the source? Assume that the antenna is in vacuum and is absorbing power with its maximum effective area.arrow_forward
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