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Fundamentals of Electromagnetics with Engineering Applications
- Given 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_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_forwardI = 7 A current flows from the infinitely long wire along the y axis that intersects the z axis at the point C (0,0,8) in the upper half space, which is the empty space. If z <0 half space, it is made of material with relative magnetic permeability µr = 7. Write the sum of the components( Hx + Hy + Hz )of the magnetic field H [A / m] vector at point A (-2, -4,0-) (in half space z <0) in terms of the given magnitudesnumerically.arrow_forward
- 2. Point charges of 15 nC each are symmetrically located at (4,4,0), (4,-4,0), (-4,4,0), and (-4,-4,0), and a uniform line charge of 50 nC/m lies at x = 0, y = 8, all z. (a) Find D at the origin. (b) How much electric flux crosses the y = 0 plane? (c) How much electric flux leaves the surface of a sphere of radius 5 m centered at (0,6,0)?arrow_forwardQ3/Given the current density J = 60 pa, A/m in cylindrical coordinates: (a) Determine the magnetic field H, where H varies with p only and has only a 0 component; (b) integrate J over the circular surface p = 1,0< 0< 2n, z 0, to determine the total current passing through that surface in the a, direction ; (c) find the total current using a line integral around the circular path p = 1, 0< 0< 2n, z = 0.arrow_forwardGiven 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_forward
- A 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_forwardA line charge, P-50 nC/m, is located along the line x2, y = 5, in free space. (a) Find E at P(1,3,-4). (b) If the surface x = 4 contains a uniform surface charge density, pg 18 nC/m², at what point in the z- 0 plane is E-0?arrow_forwardCharge Q=20 μC is located at the origin in free space. Determine the flux density at point (2, -1, -2) marrow_forward
- A 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_forwardVolume 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_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_forward
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