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 3.16P
An electric flux density is given by D=D0aP, where D 0 is a given constant, (a) what charge density generates this field? (b) for the specified field, what total chatge is contained whithin a cylinder of radius a and height b, where the cylinder axis is the z axis?
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Consider a line charge of density 5 nC/m located at x = 1, y = 3. Determine the amount of flux, in nC, passing through a sphere with center on the origin and radius 13 m. All coordinates are measured in meters.
The cylindrical surface ρ = 8 cm contains the surface charge density, ρS = 5e−20|z| nC/m2. (i) What is the total amount of charge present? (ii) How much electric flux leaves the surface ρ = 8 cm, 1 cm< z < 5 cm, 30◦ < φ < 90◦?
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as (), where ρo, a and b are positive constants and r is the distance from the axis of the cylinder. Use Gauss’s law to determine the magnitude of the electric field at radial distances (a) r < R and (b) r > R
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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- Which of the following is true regarding the electric flux density? a. It always has the same direction as the electric field present in the region.b. The electric flux density of any uniform charge distribution is always uniform.c. The electric flux density is related to the surface charge density of the Gaussian surface, giving it the same unit of measurement, C/m2. d. The electric flux density always passes perpendicular through the Gaussian surface.arrow_forwardA sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. 1. Use Gauss's law to find an expression for the magnitude of the electric field strength E inside the sphere, r≤R, and r>- (more or equal) in terms of Q and R.arrow_forwardhe electric field in the region of space shown is given by: E = (5i + 2j+6k) N/C, What is the magnitude of the electric flux through the Top face of the cube shown? Given that the length of the cube (L) = 6 m.arrow_forward
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- The cylindrical surfaces ρ = 1, 2, and 4 cm carry uniform surface charge densities of 20, −8, and 5 nC/m2, respectively. How much electric flux passes through the closed surface ρ = 5 cm, 0 < z < 2 m? Find D at P(-1 cm, 2 cm, 4 cm).arrow_forwardConsider a long wire in the air (a thin perfectly conducting cylinder ofinfinite length) of radius r0 and charge per unit length q Cm−1.(a) State Gauss’ law for the electric flux density D.(b) The electric flux density D outside the wire varies with the radial distance rfrom the center of the wire. Use Gauss’ law to calculate the electric flux density Das a function of r for r larger than the radius of the wire.(c) What is the equation relating electric field E to electric flux density D in air?What is the electric field E as a function of r for r larger than r0?(d) Suppose we measure voltages relative to a point g outside the wire that is a radialdistance rg from the center of the wire. Write down an integral for the voltage V ofthe wire relative to the point g.(e) The capacitance of the wire per unit length is defined as q/V . If the radius r0of the wire increases, how does the capacitance per unit length change? Explain.arrow_forwardGiven a 60-uC point charge located at the origin, find the total electric flux passing through: (a) that portion of the spherer= 26 cm bounded by 0 < 0 < and = 0 <0< (b) the closed surface defined by p = 26 cm and := ±26 cm; (c) the plane := 26 cm.arrow_forward
- A solid sphere with radius R carrying uniformly surface charge Q and surface density charge σ a) find the electric field E outside the sphere ( r > R ) b) derive the electric potential V outside the sphere ( r > R ) by using the relation between the electric field and the potential Varrow_forward(a) Using Gauss’ law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density a C/m2. Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative. (b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 µC/m2. Calculate the (i) charge on the sphere (ii) total electric flux passing through the spherearrow_forwardElectric flux density is given as:?⃗ = (?2 + ?)? ? + (3? − 5?2)? ? − (2??)? ?a) Determine the volume charge density at point (1,1,1).b) The flux through the cube defined by: 0 ≤ ? ≤ 1, 0 ≤ ? ≤ 1, 0 ≤ ? ≤ 1.c) Find the total charge enclosed by the cube.arrow_forward
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