Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Question
Chapter 3, Problem 3.31P
To determine
The total charge within the region
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Q1) Evaluate both sides of stoke's theorem if the magnetic flux density is given by 37.7r aphi(vector) uWb/m^2 in a free space area defined byr = 3; 0
Q. If G(r) = l0 e-2z (ρ aρ + az), determine the flux of G out of the entire surface of the cylinder ρ = l, 0 ≤ z ≤ 1. Confirm the result using the divergence theorem.
The current density in a very long hollow cylindrical conductor of radius a and b, with a < b, has the direction of the cylinder axis, with modulus given by
J = J0(r2/ab)
where J0 is a positive constant and r is the distance from the axis of the conductor. Calculate the magnetic field for a < r < b.
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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- Consider an infinitely large sheet lying in the xz-plane at the origin, the extent of the sheet in thex, and z direction is infinite. The sheet carries surface current J = J0ˆk, where J0 is the current per unit width perpendicular to the flow. Calculate the magnetic field everywhere (y > 0 and y < 0) due to J. Sketch the Amperian loop.arrow_forwardConsider a transmission line of three wires (infinite length). Each of the wires has a radius of 2 cm. Wire #1 whose center is at the point (0.0) cm flows a current of 3 A, through wire #2 centered at (0.10) cm a current of 5 A flows in the same direction as conductor 1 and Wire #3 centered at (0,-10) cm carries a current of 7 A in the opposite direction from conductors #1 and #2. Find the intensity and density of the magnetic field at the point P(3,0).arrow_forwardThe magnetic flux density in all of space is given by B=(3z)ax+(8x2−x2y)ay+(y+x2z)az Wb/m2. Let S denote the paraboloidal surface defined by y=x2+z2,0≤y≤64. Find the net magnetic flux Φ passing through S in the direction away from the xz-plane. Hint: Think about whether there is another way to solve this, such as by using a capping surface.arrow_forward
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