Loose Leaf For Engineering Electromagnetics
9th Edition
ISBN: 9781260472370
Author: John A. Buck, William H. Hayt
Publisher: McGraw-Hill Education
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Chapter 7, Problem 7.10P
To determine
(a)
The total current flowing.
To determine
(b)
The magnetic field H at origin.
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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).
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
Within the sphere defined by r ≤ 8 cm, the volume charge density is ρv = 6.8 x 10-7 C/m3
. (i) Find an expression for electric field intensity for region r < 8 cm. Hence, calculate the electric field intensity at a point having rectangular coordinates of (x, y, z) = ( 3 cm, 2cm, 0 ).
(ii) Assume that all of the electric charge is removed from a spherical region centered at (x, y, z) =(3 cm, 0, 0) and having a radius of 1 cm. Calculate the total electric field intensity at point (x,y,z) = (3 cm, 2 cm, 0).
Chapter 7 Solutions
Loose Leaf For Engineering Electromagnetics
Ch. 7 - Find H in rectangular components at P(2,3,4) if...Ch. 7 - Prob. 7.2PCh. 7 - Prob. 7.3PCh. 7 - Prob. 7.4PCh. 7 - The parallel filamentary conductors shown in...Ch. 7 - A disk of radius a lies in the xy plane, with z...Ch. 7 - Prob. 7.7PCh. 7 - For the finite-length current element on the z...Ch. 7 - Prob. 7.9PCh. 7 - Prob. 7.10P
Ch. 7 - A solenoid of radius a and of length. L is...Ch. 7 - Prob. 7.12PCh. 7 - Prob. 7.13PCh. 7 - Prob. 7.14PCh. 7 - Prob. 7.15PCh. 7 - A current filament carrying I in the -az direction...Ch. 7 - Prob. 7.17PCh. 7 - Prob. 7.18PCh. 7 - Prob. 7.19PCh. 7 - A solid conductor of circular cross section with a...Ch. 7 - Prob. 7.21PCh. 7 - Prob. 7.22PCh. 7 - Prob. 7.23PCh. 7 - Prob. 7.24PCh. 7 - Prob. 7.25PCh. 7 - Prob. 7.26PCh. 7 - The magnetic field intensity is given in a certain...Ch. 7 - Given H=(3r2/sin)a+54rcosa A/m in free space: (a)...Ch. 7 - Prob. 7.29PCh. 7 - Prob. 7.30PCh. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - Use an expansion in rectangular coordinates to...Ch. 7 - A filamentary conductor on the z axis carries a...Ch. 7 - A current sheet K = 20 az A/m, is located at p =...Ch. 7 - Let A= (3y-z)ax+2xzayWb/m in a certain regin of...Ch. 7 - Let/N=1000, I=.08 A, p0=2 cm and a=.08 cm for the...Ch. 7 - A square filamentary differential current loop, dL...Ch. 7 - Prob. 7.39PCh. 7 - Show that the line integral of the vector...Ch. 7 - Prob. 7.41PCh. 7 - Show that 2(1/R12)=1(1/R12)=R21/R312.Ch. 7 - Compute the vector magnetic potential within the...Ch. 7 - Prob. 7.44P
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- Inside a sphere of radius a is a volumetric charge distribution with a density expressed in spherical coordinates as pv = k0 / r2 [C / m3]. Show that the equation div(D) = pv is satisfied by calculating div(D) inside and outside the sphere.arrow_forwardA 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 finite line charge located at (0, y, 0)m, where a≤y≤b , has a line charge density of ρL = ycosy C/m. Determine the integral that will solve for the electric field at the origin.arrow_forward
- 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_forwardA line charge of uniform charge density ρ0 C/m and of length L is oriented along the z axis at −L/2 < z < L/2. (a) Find the electric field strength, E, in magnitude and direction at any position along the x axis. (b) With the given line charge in position, find the force acting on an identical line charge that is oriented along the x- axis at L/2 < x < 3L/2.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
- Within the cylinder ρ = 2, 0 < z < 1, the potential is given by V=50+100ρ+150ρsinϕV. (a) Find V, E, D, and ρ at P(√3/2, 1/2, 1/2) in free space. (b) How much charge lies within the cylinder?arrow_forwardFind 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 = 2arrow_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_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_forwardIn free space, q1 = 3nC charges are placed on y = 1 and y = 6, respectively, on the y-axis as shown in the figure. Accordingly, what is the electric potential value at y = 4?arrow_forwardIn empty space there is (-∞, 0) semi-infinite linear uniform and constant charge density ρl = 4 [C / m] on the z-axis. Calculate the electrostatic field that this charge density will create at point A (5,0,0). ke = 1 / 4πεWrite numerically the components of the electrostatic field in terms of the given quantities.arrow_forward
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