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Fundamentals of Electromagnetics with Engineering Applications
- Please answer and write neatly. (Show your complete solution.) Volume charge density is located in free space as ρν = 2e−1000r nC/m3for 0 < r < 1 mm, and ρν = 0elsewhere.(a) Find the total charge enclosed by the spherical surface r = 1 mm.(b) By using Gauss’s law, calculate the value of Dr on the surface r = 1 mm.arrow_forwardA. In free space, find the electric field intensity for these cases of infinite uniform sheet of charges: 1. (3 nC/m2) at z = −4 2. (6 nC/m2) at z = 1 3. (−8 nC/m2) at z = 4 B. Infreespace,apointcharge(Q=55mC)at(-2,3,-6),findtheelectricfluxdensity(D)atpoint P(2, -3, 6)?arrow_forwardcan you please solve this question, thanks. A sheet of charge, m , is present at the plane x = 3 in free space, and a line charge of rL = 20 nC/m , is located at x = 1, z = 4. (a) Find the magnitude of the electric field intensity at the origin. (b) Find the direction of E at P(4,5,6)arrow_forward
- A disk of radius a in the xy plane carries surface charge of density ρs = ρs0 /ρ C/m2 where ρs0 is a constant. Find the electric field intensity E everywhere on the z axis.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_forwardWithin the cylinder ρ=5 (m), 0≤z≤1 (m), the potential field is given by V=100+50ρ+150ρ sin Φ Determine the electric field intensity at P(1, π/3, 0.5) in free space and in CCS.arrow_forward
- A sheet of charge, ρS = 2nC/m2, is pressed at the plane x = 3 in free space, and a line charge, ρL = 20nC/m, is located at x = 1, z = 4. Find the magnitude of the electric field intensity at the origin. (Hint: E = ES + EL)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_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_forward
- If 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_forwardAn infinitely long uniform line charge is located at y = 3, z = 5 if ρL = 30nC/m, find E at: (a) the origin; (b) PB(0,6,1); (c) PC(5,6,1).arrow_forwardWithin the cylinder ρ = 2, 0 < z < 1, the potential is given by V = 100+50ρ+150ρsin ϕ V. Find V, E, D, and ρv at P(1,60°,0.5) in free space.arrow_forward
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