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Chapter 2 Solutions
Fundamentals of Electromagnetics with Engineering Applications
- 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_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_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
- Charge Q=20 μC is located at the origin in free space. Determine the flux density at point (2, -1, -2) marrow_forwardT:16) 2. A point charge is placed at a distance d from an infinitely large grounded conductive surface (x = 0, y = d, z = 0). There is a conductive half spherical bump (radius a = d/2) on top of this surface. (see figure 2) Assume D = 3a (a) What is the potential at location (x = 0, y = D, z = 0)? (b) What is surface charge density at locations A (x = 0, y = a, z = 0) and B (x = −D, y = 0, z = 0)?arrow_forward1.) a charge Q is at the center of the sphere having radius=aa.) Determine the flux density and the electric intensity at the surfaceb.) Find the relationship between D at the surface at radius=a and at radius=b, where a<barrow_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 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_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
- 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_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_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_forward
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