4. A uniform line charge density of 5 nC/m is at y = 0, z = 2 m in free space, while -5 nC/m is located at y = 0, z = -2 m. A uniform surface charge density of 0.3 nC/m² is at y = 0.2 m, and -0.3 nC/m² is at y = -0.2 m. Find El at the origin.
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- Q3. An infinite line charge density of p, = 5nC/m is distributed over the line x = 1, y = 2 and a surface charge density of p, = -10 nC/m² is distributed over x -2 plane. Find the E vector at P(0,0,1) %3D Q4. A finite line charge density of p 5nC/m is distributed between z=0 and z=-4 as shown in the figure. Find the E-field vector at P(3,4,0). z=0 "P(3,4,0) Pi z=-4 Q5. A circular annular ring of inner radius a = 1 and outer radius b = 5 has a non-uniform surface charge density of p, =nc/m2. Find the following 1. The total charge on the ring. 2. The E-field at P(0,0,2) 3. The E-field at P(0,0,0) %3D PsProblems 11-13 refer to the following situation. A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: Problem 11: What is the constant po? Q πR³ a. Po and R are positive constants. The total charge of the distribution is Q. Problem 12: What is the E-field for r R? 1 Q b. 4περ 12 a. p(r) = {Po (7) . 20 πR³ 1 Qr² 4περ R4 1 QR 4περ 13 C. C. r R C. 30 πR³ 1 Qr³ 4περ R5 QR² 1 4περ 14 d. d. d. 4Q πR³ 1 Qr4 4πεο R6 QR³ 1 Απο 15Find E at the origin if the following charge distributions are present in free : point charge. 12 nC P(2, 0, 6) uniform line charge density 3nC / m at x = - 2 . y = 3 uniform surface charge density. 0.2nC / (m ^ 2) at x = 2
- = Three uniform charge distributions are present in a region: an infinite sheet of charge, a finite line charge, and a ring of charge. The infinite sheet of charge at (x, -3, z), where x and z spans from negative to positive infinity, has a charge density Ps 5 nC/m². The finite line charge at (0, -1, z), where z ranges from -2 to 2, has a charge density -4 nC/m. Finally, the ring of charge, with a radius of 3m and charge density PL 2 nC/m, is parallel to the xz-plane centered at (0, 4, 0). All coordinates are in meters. Use the value k = 9 x 10⁹ in your solutions and = answers. Question: Determine the magnitude the electric field due to the infinite sheet charge only at (0, 2, 0).Density, density, density. (a) A charge -328e is uniformly distributed along a circular arc of radius 6.00 cm, which subtends an angle of 72°. What is the linear charge density along the arc? (b) A charge -328e is uniformly distributed over one face of a circular disk of radius 3.50 cm. What is the surface charge density over that face? (c) A charge -328e is uniformly distributed over the surface of a sphere of radius 2.00 cm. What is the surface charge density over that surface? (d) A charge -328e is uniformly spread through the volume of a sphere of radius 3.30 cm. What is the volume charge density in that sphere? (a) Number Units (b) Number Units (c) Number Units (d) Number UnitsA uniform volume charge density of 0.3 µC/m³ is present throughout the spherical shell extending from r = 2 cm to r = 4 cm. If Py = 0 elsewhere: find the total charge present throughout the shell find r, if half the total charge is located in the region 2 cmFigure 1 shows a uniform square line charge with the line charge density, P₁ = 27C/m at z = 0. All four sides are symmetrical to x-y plane and have equal length of a m. Let a = 6 m, find E at origin, P(0,0,-0.5) and P(0,0,0.5). Compare and explain the results. P(0,0,h) a Figure 1 a ²,An infinitely long cylinder in free space is concentric with the z-axis and has radius a. The net charge density p in this cylinder is given in cylindrical coordinates by, 1 a² +r² where A is a constant. (a) Show that the total charge per unit length, λ in the cylinder is λ = πA ln 2. p(r) = A- Hint: you may find the following integral useful. 1 2 J for r a) and inside the cylinder (r< a). (d) The cylinder is composed of a material in which the polarisation P is given by P = P₁² in (1 +5²) e₁₁ er, r where Po is a constant. Determine the bound charge density pb in the cylinder. Hence, or otherwise, determine a relation between A and Po such that the free charge density of in the cylinder vanishes.A cube structure having pv=(x^2)(y)(e^-z) [c/m^3] charge density distribution is being used to represent a discrete charge element Q. If edge of cube is 1 mm, answer the following question. m m im w n m w w w a) Derive Coulombs Law from Gauss Law. b) Calculate value of Q. c) If 2Q, 3Q, and -Q charges are placed on xy plane to (-1, –1,0), (2,0,0), (-3,1,0) points respectively, calculate the force due to electric field on a charge with 4Q at (1, -1,3) pointA solid insulating cylinder having a radius a = 1m and length L = 3m is inside and concentric with a conducting cylindrical shell having an inner radius b = 2m and outer radius c = 3m. If the charge density on the solid cylinder is 1C/m^3, determine the charge density at a. r = b b. r = cIn free space, a linear charge density > is on the z axis. Get the electric force over a unit charge "q" located at P (1, 2, 3) m if the linear charge density is in -4 m < z < 4m = 2μC m Give the answer in unit vectors terms.A hollow sphere of radui R has a uniform nagative surface charge density -\sigma on its surface and a positive point charge +Q at its center. The charge Q is greater than the absolute magnitude of the total charge on the surface. The direction of the E-field is radially outward both inside and outside the sphere. What is the magnitude of the E-field inside the sphere at a distance r<R from the center? What is the magnitude of the E-field outside the sphere at a distance r<R from the center?SEE MORE QUESTIONS