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 3, Problem 3.23P
(a) A point charge Q lies at the origin. Show that div D is zero everywhere except at the origin. (b) Replace the point charge with a uniform volume charge density
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HW: A spherical charge of (pv= 6 C/m3 ) and radius ( 4). Its center is at (1,2,3). Find settings(E) at point (3,-2,4).
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" A sheet charge, ρS = 4 nanoC/m2 is present at the plane x = 4m in free space. Find the electric field intensity E in N/C at T(3, 5, -4) ."
Find E at the origin if the following charge distributions are present in free space: point charge, 12 nC at P(2, 0, 6); uniform line charge density, 3nC/m at x =−2, y = 3; uniform surface charge density, 0.2nC/m² at x = 2
Chapter 3 Solutions
Engineering Electromagnetics
Ch. 3 - Prob. 3.1PCh. 3 - An electric field in space is E=(5z2/C0)azV/m....Ch. 3 - Consider an electric dipole in free space,...Ch. 3 - An electric field in free space is E=(5z3/0)z V/m....Ch. 3 - A volume charge distribution in free space is...Ch. 3 - Prob. 3.6PCh. 3 - Prob. 3.7PCh. 3 - Use Gauss, law in integral form to show that an...Ch. 3 - A sphere of radius a free space contains charge of...Ch. 3 - An infinitely long cylindrical dielectric of...
Ch. 3 - Consider a cylindrical charge distribution having...Ch. 3 - The sun radiates a tota1 power of about 3.86...Ch. 3 - Spherical surfaces at r = 2, 4, and 6 m carry...Ch. 3 - Prob. 3.14PCh. 3 - Volume charge density is located as follows; pv=0...Ch. 3 - An electric flux density is given by D=D0aP, where...Ch. 3 - In a region having spherical symmetry, volume...Ch. 3 - State whether the divergence of the following...Ch. 3 - A spherical surface of radius 3 mm is centered at...Ch. 3 - A radial electric field distribution in free space...Ch. 3 - In a region exhibiting spherical symmetry,...Ch. 3 - (a) A flux density field is given as F1 = 5 az....Ch. 3 - (a) A point charge Q lies at the origin. Show that...Ch. 3 - In a region in free space, electric flux density...Ch. 3 - Within the spherical shell, 3D= 5(r-3)3a,C/m2 .(a)...Ch. 3 - If we have a perfect gas of mass density Px...Ch. 3 - Consider a slab of material containing a volume...Ch. 3 - Repeat Problem 3.8, but use .D= pv and take an...Ch. 3 - Prob. 3.29PCh. 3 - (a) Use Maxwells first equation. �. D=Pv, to...Ch. 3 - Prob. 3.31P
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- " A sheet charge, ρS = 4 nanoC/m2 is present at the plane x = 4m in free space. Find the electric field intensity E in N/C at T(3, 5, -4) ." QUICKLY AND NO SHORTCUTS PLEASEarrow_forwardA point charge of 10uC is located x = 3, four infinite line charges of ρL = 50uC/cm and ρL = 20 uC/cm are located at x = ± 2 cm and x = ± 4 cm respectivelyand an infinite surface charge of ρS = 15μC/cm2 located at y = 4.5cm, find the totalcharge bounded by a sphere of radius 5cm with its center at the origin.arrow_forwardCalculate D in rectangular coordinates at point P(2,-3,6) produce by: (a) a point charge QA=55 mC at Q(-2,3,-6); (b) a uniform line charge ρLB=20mCmρLB=20mCm on the x axis; (c) a uniform surface charge density ρSC=120μCm2ρSC=120μCm2on the plane z=-5m.arrow_forward
- A uniform line charge, p = 2 nC/m) lies in the z= 0 plane parallel to the x-axis at y=3 m. Find the potential difference Vab for the points A(2,0,4)m and B(0,0,0)arrow_forwardA) If the electrical potential V=ρ2zcosϕ in free space, find the electric field strength E⃗ at the point (2,60o,1)? B) Find the bulk charge density ρv for the same point?arrow_forwardEmag In free space, let V = 3x^2y + xz V. Finda.Electric field intensity E at points (3,4,5)b.Volume charge density at points (3,4,5)c. Lines of electric force passing through a cube with dimensions0 <= x <= 20 <= y <= 20 <= z <= 2d. Total charge Q inside the cube.arrow_forward
- A uniform surface charge density of 30 nC/m2 is present on the spherical surface r = 0.6 cm in free space. Find the absolute potential at P(r = 1 cm, θ = 25◦, φ = 50◦)arrow_forwardA copper wire of 2mm diameter with conductivity of 5.8*10 7S/m and electron mobility of 0.00032m 2 / V-s is subjected to anelectric field of 20mV/m. Find(i) The charge density of free electrons(ii) The current density(iii) The current flowing in the wire(iv) The electron drift velocityarrow_forwardHW: A spherical charge of (pv= 6 C/m3 ) and radius ( 4). Its center is at (1,2,3). Find settings(E) at point (3,-2,4).arrow_forward
- The outer radius of a coaxial cylindrical electrode system is given in 32 cm. The system is the most suitable sized according to puncture. Penetration of the insulator between the cylindrical layers Its strength is Ed = 72 kV / cm and the relative dielectric constant of the insulator is Er1 = 52 c) -Calculate the actual distance (d) of the system, the utilization factor (n) of the electrode aperture (alpha)? (E0 = 8,854x10-12 F / m)arrow_forwardThree uniform charge distributions are present in a region: an infinite line charge, an infinite sheet of charge, and a finite line charge. An infinite line charge has a charge density pL = -2 nC/m is located at (x, 0, 4); an infinite sheet of charge located at (x, y,-7) with a charge density pS = -3 nC/m 2 ;a finite line charge that spans from (0, -3, 0) to (0, 3, 0) with a charge density of pL = 4 nC/m. Indicate the formulas that you will use. All coordinates are in meters. Use k=9 x 10 9. Determine the electric field due to the infinite line charge at (0, 0, 3). Determine the electric field due to the infinite sheet charge at (0, 0, 3). Determine the electric field due to the finite line charge at (0, 0, 3). Determine the total electric field at (0, 0, 3) due to the three charge distributions.arrow_forwardA point charge, QA = 1μC is at A(0, 0, 1), and QB = −1μC is at B(0, 0, −1).Find Er, Eθ and E∅ at P(2, 3, 1).arrow_forward
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