Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Textbook Question
Chapter 4, Problem 4.25P
Consider an electric field intensity in free space that exhibits a Gaussian function of radius in spherical coordinates
where pc and a are constants, and where the field exists everywhere, (a) What charge density would produce this field? (b) What total charge is present? (c) What is the potential at the origin? (d) What is the net stored energy in the field?
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2) If the angle the displacement makes with the electric field is 0° it means the charge is moving
along (or parallel to) the field vectors. Is work being done? How will the angle here affect the
work done, explain your answer with a diagram?
Last Revised 12/21/2015
Equipotential Surfaces – 3.1
A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. A proton is traveling in the vicinity of this wire. (a) At the instant the proton is at point P, 4.50 cm above the wire’s center and moving with a speed of 6×104 m/s directly toward it, what is the force (magnitude and direction) that the magnetic field of the current exerts on the proton?(b) explain how you've determined the direction of the force in part (a).(c) What would be the magnetic force (magnitude and direction) if the proton were instead moving parallel to the wire in the same direction as the current?(d) explain how you've determined the direction of the force in part (c).
μ0 = 4π × 10-7 T ∙ m/Ae = 1.6 × 10-19 C
A solid conducting sphere of radius R
carries a charge +Q.
A thick conducting shell is concentric with the sphere
and has an inner radius R2 and outer radius R3.
The shell carries a charge -Q.
The figure shows a cross section.
a) Where are the charges located? Add charge symbols to
the figure.
R1
R3
R2
b) Add a few electric field lines and equipotential lines to the figure. Please label the lines
clearly.
c) Draw a sketch of the potential as a function of distance from the center of the sphere. Please
label all interesting points on the graph.
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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