Find the electric field due to infinitely long cylindrical volume charge density (P,) and a cylindrical surface charge density (p,) for p
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- An infinite cylinder of radius R = 11.9 m, has a volume charge density of p(r) 3.4 x 10-12 C/m³ Using Gauss's law, what is the electric field (in N/C) at a distance of r = 4.8 m from the cylinder's axis.Flux and nonconducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of nonconducting material. Figure (a) shows a cross section. Figure (b) gives the net flux through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by = 6.0 x 105 N-m²/C. (a) What is the charge of the central particle? What are the net charges of (b) shell A and (c) shell B? (a) B (105 N·m²/C) e -Os rA hollow sphere made from a non-conducting material is shown below in cross-section. The inner radius is R1, and the outer radius is R2. The material is charged uniformly -ρ.(a) Using Gauss’ Law, find an expression in terms R1, R2, and ρ of the magnitude(measured in N/C) and the direction (away from or towards the center) of the electricfield at a distance r from the center of the sphere, for values R1 < r < R2? (Do all thiswork symbolically - don't use the values of part (b) for this part.) (b) The inner radius is R1 = 1.00 cm, and the outer radius is R2 = 4.00 cm. Thematerial is charged uniformly ρ = -1.70 nC/m3. If the electric potential is 0V infinitely faraway, what is the electric potential at the outer surface (r = R2) of the sphere? Please show full work Thank you!
- A long, thin straight wire with a linear charge density λwire = +3.17 nC/m runs down the center of a thin, hollow metal cylindrical shell of radius 1.55 cm. The cylindrical shell has a linear charge density λshell = +6.97 nC/m.(Figure 1) What is the electric field strength at a radius of 1.04 cmcm inside the cylindrical shell? What is the electric field strength at a radius of 2.29 cmcm outside the cylindrical shell?The volume charge density of a spherical charge distribution is given by rho(r) = rho0 e^(-ar), where rho0 and a are constants. What is the electric field produced by this charge distribution? (Enter the radial component of the electric field. Use the following as necessary: rho0, a, r, and E0.)Question 1: Gauss' Law: Electric field from surface charge For this problem assume constants are all in SI units that are not shown. An electric field given by E = (3z³+5)k. Calculate the flux through surface S, with side length a = 2, shown below if the surface is at the following heights: (a) z = 0 (b) z = -2 (c) z = 2 E 2.0 m 1.5 m a (d) The electric field in a region is given by E= a/(b + cx)î, where a = 500N m/C, b = 4.0m, and c 1.0. What is the net charge enclosed by the shaded volume shown below? 1.0 m a 425 y