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Fundamentals of Electromagnetics with Engineering Applications
- 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).arrow_forwardThe spherical surfaces r = 1, 2, and 3 carry surface charge densities of 20, -9, and 2 nC/m², respectively. (a) How much electric flux leaves the surface r = 5? (b) Find D at P(1,-1,2).arrow_forwardAn 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 > Rarrow_forward
- Volume charge density is located in free space as ρν = 2e−100r nC/m3 for 0 < r < 3 mm, and ρν = 0 elsewhere. Find the total charge enclosed by the spherical surface r = 2 mm. By using Gauss’s law, calculate the value of Dr on the surface r = 2 mm.arrow_forwardUniform line charge density of 5 nC/m is at y=0, z=2m in free-space while -5 nC/m is located at y=0, z=-2. A uniform surface charge density 0.3 nC/m2 is at y=0.2m, and - 0.3 nC/m is at y=-0.2. Find E at origin?arrow_forwardA 5-nC póint charge is located at A(2, -1, -3) in free space. (a) Find E at the origin.(b) Plot E(x, 0,0)| vs. x, -10<x<10 m.(c) What is |E(x,0,0)|max.?arrow_forward
- An infinitely long, uniform line charge is located in the x-y plane with an equation 2x – y + 4. If ρL = 30 nC/m. Find the magnitude of E at P(6, -3)arrow_forwardA hollow sphere, with inner radius a and outer radius b, has a volumetric charge distribution p = kr^2, where r is the distance from the center of the sphere outwards and k is a known constant. Using Gauss's law, find the electric field at r < a, a < r < b, and r > b, and graph the electric field as a function of r.arrow_forwardA volume charge in a form of a cube, 2m on an edge, parallel to the axes and centered at the origin is enclosed by a closed spherical surface with radius 3m centered at the origin. Determine the net flux crossing the closed surface given the volume charge density below Pv = x² + y c/m³arrow_forward
- Given the field: D = 20 [-sinØ ap + sin 2Ø aØ] Find the total charge lying within the volume 1<p < 2,0 < Ø < π, and 0 < z < 1 by evaluating both sides of the Divergence Theorem equationarrow_forwardA very large conducting plate lying in the xy plane carries a charge per unit area of +5.0 nC/m2. A second such plate located above the first plate at z = z0 and oriented parallel to the xy plane carries a charge per unit area of -5.0 nC/m2. Find the electric field for (a) z < 0, (b) 0 < z < z0, and (c) z > z0.arrow_forwardLet D = 6xy3z2 ax + 7xyz4 ay + 8x5y4 az PC/m2 in free space, Answer all questions (a)Find the total electric flux passing through the surface y = 4, 0 ≤ x ≤ 3, 0 ≤ z ≤ 2 in a direction away from the origin. (b) Find the force |F| on the charge Q1(30 mC) at P(4,1,6)? (c) Find the total charge contained in an incremental sphere having a diameter of 8 mm centered at P (4, 1, 6)?arrow_forward
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