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Consider a dielectric–dielectric charge–free boundary at the plane
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EBK FUNDAMENTALS OF ELECTROMAGNETICS WI
- 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_forwardIn empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient er = 4 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: In (x <x1), the electric field vector is observed as E1 = (- 0.5) ux + (5.5) uy + (-1.5) uz.Region II : By determining (x1 <x <x2) value er = 4 electric field E2,|E2|,write its value numericalarrow_forwardIn empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient er = 4 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: In (x <x1), the electric field vector is observed as E1 = (- 0.5) ux + (5.5) uy + (-1.5) uz.Region II : By determining (x1 <x <x2) value er = 4 electric field E2,|E2|,write its value numericallyarrow_forward
- An 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_forwardConsider region 1 (z<0) contains a dielectric for which ϵr=2.5, and region 2 (z>0) is characterized by ϵr=4 .Let E1=−30ax+50ay+70az V/m. The D2 is given byarrow_forwardIn the 0<r<1mm cubic region, it is given as ρ_v=2e^(-100r) nC/m^3. In other places, the charge density is given as 0.a) Find the total charge inside the spherical surface r=1mm.b) Calculate the expression Dr on the r=1mm surface using Gauss's law.arrow_forward
- Within 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_forwardFind the relative permittivity of the dielectric material present in a parallel-platecapacitor if: (a) S = 0.12 m/, d = 80 μm, V = 12 volt, and the capacitor contains1 ?? of energy; (b)The stored energy density is 100 ?/?/, V = 200 volt, and ? =45 ??; (c) ? = 200 ??/? and ?# = 20 ??/?/.arrow_forwardGiven a 2.215 nC/m2 surface charge at z = – 15. Solve E on point (250, 100, 10) caused by the surface charge in (nC/m).arrow_forward
- Electromagnetic question Consider a hollow cylindrical surface centered on the z-axis with radius r = a, carrying a uniform surface current density Jsa = 5 af A/m. Additionally, there is a second cylindrical surface with radius r = b (b > a), which carries a current density Jsb = 4 az A/m. Calculate the magnetic field intensity H(r) for the following regions: 1. For 0 < r < a: Determine H(r) using the given parameters. 2. For a < r < b: Calculate H(r) using the given parameters. 3. For r > b: Find H(r) using the given parameters.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_forward3.(Part I) A 50 V voltage generator at 20 MHz is connected to the plates of an air dielectric parallel-plate capacitor with a plate area of 2.8 cm^2 and a separation distance of 0.2 mm. Find the maximum value of displacement current density and displacement current. (Part II) A dielectric material with permeability that of free space, permittivity = 9xpermittivity of free space, conductivity = 4 S/m, is placed between the plates of a parallel-plate capacitor. Calculate the frequency at which the conduction and displacement currents are equal.arrow_forward
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