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The plane y = O separates two magnetic media. Medium
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Fundamentals of Electromagnetics with Engineering Applications
- The magnetic flux density in all of space is given by B=(3z)ax+(8x2−x2y)ay+(y+x2z)az Wb/m2. Let S denote the paraboloidal surface defined by y=x2+z2,0≤y≤64. Find the net magnetic flux Φ passing through S in the direction away from the xz-plane. Hint: Think about whether there is another way to solve this, such as by using a capping surface.arrow_forwardA rectangular loop carrying current I is placed on the xy-plane. Assume that the corners of the loop are at (0,0),(a,0), (0,b), (a,b). Find the magnetic field intensity above the loop. Specifically, let a=2, b=1: A.) Find the magnetic field intensity H at any point in the region 0<x<a, 0<y<b, 0<z<2.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
- In the upper half space, which is the empty space, I = 7 A current flows from the infinitely long wire along the y axis that intersects the z axis at the point C (0,0,10). Half-space z <0 is from a material with relative magnetic permeability µr = 5. Magnetic field in terms of given magnitudes Hx + Hy + Hz =? write it numerically.arrow_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_forwardA rectangular loop carrying current I is placed on the xy-plane. Assume that the corners of the loop are at (0,0),(a,0), (0,b), (a,b). Find the magnetic field intensity above the loop. Specifically,let a=2,b=1: B.) Plot the magnitude of H when 0<x<a, 0<y<b, z=0,1,2arrow_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_forwardIf a line of charge with uniform density ρl extends between z=-L/2 and z=L/2 along the z-axis, obtain an expression for the electric field intensity at any point P(r, ϕ ,0) on the x-y plane. Investigate the case when L becomes infinite.arrow_forwardElectrostatic field at point A (2, -2.9) in empty space Observed as E = 4ke*ux. Determine the location (xs, ys, zs) of the point Q = -3 [C] that is likely to form this area. It shows the constant ke = 1 / (4πε).arrow_forward
- A current sheet vector J = 10 Uy A/m lies on the dielectric interface x = 0 between two dielectric media with ɛr1 = 1, µr1 = 1 in region-1 ( X < 0 ) and ɛr2 = 2, µr2 = 2 in region-2 (X > 0 ). If the magnetic flied in region 2 is H2 = 3Ux + 30Uy A/m, then find the magnetic field in region 1.arrow_forwardIn the upper half space, which is the empty space, I = 7 A current flows from the infinitely long wire along the y axis that intersects the z axis at the point C (0,0,10). Half-space z <0 is from a material with relative magnetic permeability µr = 5. 1. Write numerically the sum of the components (Hx + Hy + Hz) at the point A (-5, -5,0+) of the magnetic field H [A / m] vector in terms of the given magnitudes (in the half space z> 0). 2.Write numerically the sum of the components (Hx + Hy + Hz) at the point A (-2, -4,0-) of the vector magnetic field H⃗[A / m] in terms of the given magnitudes (in the half-space z <0).arrow_forwardCalculate D at point (12, -2, 7), produced by a uniform line charge 20 mC/m on x axis.arrow_forward
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