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 2, Problem 2.16P
Within a region of free space, charge density given as
where P0 and a are constants. Find the total charge lying within (a) the sphere, (b) the cone, r≤a, 0≤θ≤0.1đ�œ‹. (c) the region. r≤a,0≤θ≤01đ�›‘,0≤0.2đ�›‘.
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(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 sphere
Determine the magnitude of the Electric Field Intensity at the origin given the following charge distributions in free space: point charge, 7 nC at P(2, 0, 3); uniform infinite line charge, 3 nC/m at x = -2, y = 5; uniform surface charge density, 0.8 nC/m^2 at x = 4. Use k = 9 x 10^9.
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 2 Solutions
Engineering Electromagnetics
Ch. 2 - Three point charges of equal magnitude q, that...Ch. 2 - Point charges of 1nC and -2 nC are located...Ch. 2 - Point charges of 50 nC each are located at...Ch. 2 - Eight identical point charges of Q C each are...Ch. 2 - A point charge of 3 nC is located at the point...Ch. 2 - Two point charges of equal magnitude q are...Ch. 2 - Point charges of equal magnitude but of opposite...Ch. 2 - A crude device for measuring charge consists of...Ch. 2 - A 100-nCpoint charges is located at A(-1,1,3)in...Ch. 2 - A configuration of point charges consists of a...
Ch. 2 - A charge Q0 located at the origin in free product...Ch. 2 - Electrons are in random in a fixed region in...Ch. 2 - A uniform volume charge density of 0.2 μC/m3 is...Ch. 2 - The electron beam in a certain cathode ray tube...Ch. 2 - A spherical volume having a 2-/μm radius contains...Ch. 2 - Within a region of free space, charge density...Ch. 2 - A length d of the charge lies on the Z-axis infree...Ch. 2 - (a) Find E in the plane z=0 that is produced by a...Ch. 2 - A line having charge density p0|C|C/m and of...Ch. 2 - A line charge of uniform charge density p0 C/m and...Ch. 2 - A charged filament forms a circle of radius a in...Ch. 2 - Prob. 2.22PCh. 2 - A disk of radius a in the xy plane carries surface...Ch. 2 - (a) Find the electric field on the z-axis produced...Ch. 2 - A disk of radius a in the xy plane carries surface...Ch. 2 - (a) Find the electric intensity on the z- axis...Ch. 2 - Given the electric field E=(4x2y)ax(2x+4y)ay, find...Ch. 2 - An electric dipole (introduced in Problem 2.7, and...Ch. 2 - If E=20e5y(cos5xaxsin5xay) ,find (a)...Ch. 2 - For fields that do not vary with z in cylindrical...
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- A uniform volume charge distribution Pv=3 (nC/m3) exists in a sphere that has a radius of 3 cm. What is the value of E at a distance R=1 cm? (Use Gauss’s Law)arrow_forwardThe 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◦?arrow_forwardAn isolated charged soap bubble of radius ?0=5.15 cmR0=5.15 cm is at a potential of ?0=287.0 volts.V0=287.0 volts. If the bubble shrinks to a radius that is 39.0%39.0% of the initial radius, by how much does its electrostatic potential energy ?U change? Assume that the charge on the bubble is spread evenly over the surface, and that the total charge on the bubble remains constant.arrow_forward
- Planes x = 1, y = 4 and z =5, respectively, carrying charges of 15nC/m2, 18nC/m2 and 23nC/m2. If the line charges of 10nC/m, 15nC/m and 20nC/m at x = 2, y = -3; y=-4, z = 6 and x= 9, z = 6, respectively. Calculate the total electric flux density at the following locations:a. P1(1,1,5)arrow_forwardConsider a solid sphere of radius 5cm having volume charge density of 20 C/m^3. Calculate the electric flux density at 10cm from the outer surface of sphere.arrow_forwardAn insulating solid sphere of radius a has a uniform volume charge density ρ and carries a total positive charge Q. (A) Calculate the magnitude of the electric field at a point outside the sphere. (B) Find the magnitude of the electric field at a point inside the sphere.arrow_forward
- 9 9 - The electric field on a non-uniform conductor surface ranges from 5.6.10^4 N/C to 2.8.10^4 N/C. Calculate the surface charge density at the surface point where the radius of curvature of the surface is greatest. {ε0=8,85.10^(-12)C^2/Nm^2} a) -4,96.10^(-7) C/m^2 B) -2,8.10^(-7) C/m^2 NS) 2.8.10^(-7) C/m^2 D) 0 TO) 4,96.10^(-7) C/m^2arrow_forwardThe magnitude of the surface charge density of two large conducting plates that carry an equal and opposite charges is 9.5 x 10^(-7) C/m^2. The separation distance between plates is 8.0 mm. Calculate the electric field between the plates. (k = 9.00 x 10^9 N.m^2/C^2; eo = 8.85 x 10^(-12) C^2/Nm^2)arrow_forwardPlease answer in 4 decimal points Two bidirectionally infinite line charges exist in vacuum. One has a charge density of -9 nC/m at x = -1, y = -9, while the other has a charge density of 5 nC/m at y = -3, z = -8. Determine the y-component of the electric field in V/m at (2, 9, 4). All coordinates are measured in meters.arrow_forward
- An electric field is given by Ex = 3.5x^3 kN/C. Find the potential difference between the points on the x axis at x = 1 m and x = 4 m. kV Find the maximum surface charge density sigma max that can exist on the surface of any conductor before dielectric breakdown of a gas with a dielectric strength of 3.95 MV/m occurs. C/m^2arrow_forwardThere are 3 thin conducting spherical shells with radiuses of R, 2R, and 3R. Each shell has a charge of +2Q and the shells are concentric. Draw a graph of E vs R. Note: Make sure to show the values of E(3R), E(2R), and E(R). Also, put R on the x axis.arrow_forwardA solid sphere of radius 0.5 m is uniformly charged with a charge density of 1.127×10-8 C/m3. If the chosen Gaussian sphere has a radius of 0.2 m, determine the total electric flux through the Gaussian sphere.arrow_forward
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