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- 2. Consider an insulating spherical shell of inner radius a and outer radius b. a. If the shell has a net charge Q uniformly distributed over its volume, find the vector electric field in all regions of space (r b) as a function of r. b. Now assume that the shell has a non-uniform charge density given by r2 p(r) = Po ab What is the net charge of the shell? c. For the charge distribution in part (b), find the vector electric field in all regions of space (r b) as a function of r.A uniformly charged conducting sphere of 1.2m diameter has a surface charge density of 1.8µC/m?. Find the net charge on the sphere. b. What is the total electric flux leaving the sphere? What is the magnitude of the electric field at point P, 0.7m from the center of the sphere?The Electric Field of a Charged Cylinder and a Concentric Cylindrical Shell. A non-conducting cylinder of radius a is charged with charge density p(r) = p.r, where r is the distance from the cylinder axis. The cylinder is placed inside a shell with cylindrical inner and outer radii b and c, respectively. The outer shell is charged with a uniform charge density p(r) = Po. The cylinder and the shell are concentric (see figure). D B b 0 Derive the formulas for the magnitude of the electric field at points A, B, C, and D. Guidance: 1. If required by the formulas, specify Coulomb's force constant through the Vacuum Permittivity, E = 1/4nk instead of Coulomb's onstant, k. 2. Type epso, rhoo, and pi, if the respective symbols Eo,Po, and n, are required.
- A charge of 22.2 pC is distributed uniformly on a spherical surface (r1 = 2.0 cm), and a second charge of-9.2 pC is distributed uniformly on a concentric thin spherical surface (r2 = 4.0 cm). Determine the magnitude of the electric field ( in units of N/C) at a distance of 5.0 cm from the center of the two surfaces. Select one: O A. 3.90 O B. 46.80 OC. 32.50 OD. 59.80 OE. 113.048. A solid sphere with radius a = 2cm in encased in a spherical shell with inner radius a = 2cm and outer radius b = 4cm. (A cross section is shown on the right). The sphere has charge density Psphere = 1µC and the shell has charge density Pshell = 2µC. Let r measure the dis- tance from the center of the sphere. Answer the following questions: (Note: Your answer can contain a, b, A, B, and r the radial distance you are looking at.) (a) What shape of Gaussian surface will you use to solve this problem? (b) What is the electric field at r = 3cm? a Psphere Pshell bA conducting sphere witha net charge Q and radius a sits inside a hollow conducting sphere with a net charge q, inside radius b and ouside radius c. What is the electric field as a function of position? Include answer for r < a, a < r < b, b < r< c and r>c