3.11 i In cylindrical coordinates, let p, = 0 for p < 1 mm, p, = 2 sin(2000 Tp) nC/m' for 1 mm < p < 1.5 mm, and p, = 0 for p > 1.5 mm. Find D everywhere. %3D
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- hello, i’m studying coordinate system from electromagnetics. In the cartesian coordinate system, the coordinate variables x, y, and z are already length dimensions, so the scaling factors to convert them to length are hx=1, hy=1, and hz=1. In the cylindrical coordinate system, the scaling factors to convert the rho and z into length , are hrho=1 and hz=1. A) what is the hpi that changes coordinate pi into the length? B) in terms of spherical coordinates, what is the hr, htheta , hpi that changes ( r, theta, pi ) of spherical coordinate into the length?The structure in the figure has 4 concentric spherical media,which have;0<r<a free spacea<r<b ρv (C/m3) constant volume charge densityb<r<c εr relative permittivityc<r free spaceFind ?⃗ , ?⃗ and ?⃗ in these 4 regions and also plot themPlease write to text format The charge per unit length on the thin rod shown below is ?. What is the electric field at the point P? (Hint: Solve this problem by first considering the electric field dE at P due to a small segment dx of the rod, which contains charge dq = ? dx. Then find the net field by integrating dE over the length of the rod. Use the following as necessary: L, a, ?, and ?0. Enter the magnitude. Assume that ? is positive.) E
- a long straight cylindrical wire of radius r meter, in a medium of permittivity e is parallel to a horizontal plane conducting sheet. The axis of the wire is it expr metres above the sheet (a) Derive an expression of the capacitance per unit length between the wire and the sheet (b) If r = 0.3 x 10-2 m, h.= 0.12 m find the capacitance per metre length (c) If the potential difference betweenthe wire and sheet is 5 kV, find the magnitude and direction of electric stress in the medium at theupper surface of the sheet at a distance 20 cm from the axis of the wire. Take e = 1/36π x 10-9 F/m [(a) C = 2πe/ln 2h - r/r F/m (b) 0.0127 x 10-9 F/rn (c) 6.85 kV/m acting vertically downward]Find 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 ??/?/.Find the total capacitance C of the spherical capacitors shown in the figure, where a= 1 mm, b= 2 mm and c= 3 mm; and therelative electric permittivity of the mediums are Er1= 3.5 and Er2= 2.5
- Specify Maxwell’s equations in free space.It is viewed from the cross-section of a coaxial cable consisting of a cylindrical conductive tube with an internal radius R and an outer radius of Rz wrapped around a cylindrical conductive wire with a RADIUS of R. r to indicate the radial distance from the center, the inner cylindrical conductor,if it is j1 = Gr and the outer conductive tube, j2 = Car has improper current densities. Here, the two conductors carry the same I flow in zit directions. What is the size of the B2 magnetic fields at r=1 cm and B2 at r= 8 cm?(R=4 cm; R=7 cm, R3=9 cm; Io=2 A; uo=47.10-7 T.m/A and our aquani-positive forehead outward from the page plane).In a spherical electrode system, gas material with the most favorable arrangement in terms of puncture resistance, outer radius r2 = 3.2 cm, puncture field strength Ed=75kV/cm and dielectric constant Ergas=1 is used. According to this;a) Calculate the inner radius of the electrode and the puncture voltage of the system according to the geometrical characteristics of the most suitable arrangement in terms of puncture resistance.b) Draw the puncture curve in the p-Emax plane for a voltage of U=40kV provided the outer radius is kept constant and indicate the boundaries of the inner sphere radii on the curve.c) Briefly interpret the electrode system in terms of discharge events in the geometric characteristics of p=0.8, p=1.8 and p=5 on the puncture curve.
- 6. If D=3y²a, + 3x²ya, + 5a, C/m², find the total charge enclosed within the region 0 < x,y,z <2 by evaluating one or more surface integrals.Q1. Uniform line charges of 40nC/m lie along the entire extent of the three coordinate axes.Assuming free space condition, find E̅at P( -2,1, 2). Q2. The work is defined by the equation: ? = 2 cos ? − 4?2?2 . Determine the curl of thegradient of the work and comment on the result.Describe the surfaces, in the spherical coordinates, defined by the following equations:a) ρ=13b) θ=2π/3c) φ=π/4