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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.Q2) A disk of radius 0.1 m is oriented with its normal unit vector n at 30° to a uniform electric field of magnitude 2 x 103 N/C. (Since this isn't a closed surface, it has no "inside" or "outside." That's why we have to specify the direction of n in the figure.) (a) What is the electric flux through the disk? (b) What is the flux through the disk if it is turned so that n is perpendicular to E? (c) What is the flux through the disk if n is parallel to E?c) For the same cylindrical shell as in the previous problem, draw and label a Gaussian surface and use Gauss's Law to find the radial electric field in the region r > R2. You may take the positive direction as outward. 0 E (r > R2) =
- 9A. A metal sphere of radius R and charge Q is surrounded by concentric metallic spherical shell of inner radius R1 > R, outer R1 > R1 and load Q1 . This system is surrounded by another concentric metallic spherical shell of inner radius R2 > R1, outer R2 > R2 and of load Q2 . Using suitably chosen Gaussian spherical surfaces, find the charge on the spherical surfaces with radii R, R1, R1, R2, R2Multiple Choice.2. A uniform electric field ai + bj intersects a surface of area A. What is the flux through this area if the surface lies in the yz plane
- 1. A thin sheet of sides 2a and 2b lying in the xy plane and centered at the origin has a uniform charge density o (see figure). a. Using the result of Example 1 in the Chapter 23 slides, show that the electric field on the z-axis is given by of ab E = 4k,o arctan | zva² + b² + z². To get full credit you must show an appropriate differential of charge dq and explain any symmetry arguments you might have use to arrive to this result. b. What is the field in the limit a and b going to infinity? Compare your answer with the result of the What If? in Example 3 in the Chapter 23 slides. c. Using the results of part (a), find an integral expression for the electric field at an arbitrary point on the x-axis created by a cube of side 2a centered at the origin with uniform volume charge density p. You do not need to solve this integral.Determine the net charge inside a cube placed in a region with an electric field E = [6.00î + 7.00ĵ + ((2.80 m-¹)z + 4.00)Ê] N/C. Each side of the cube has a length L = 3.56 m. X What is the direction of the normal for each face of the cube? What is the flux through each face of the cube? Review Gauss's law. nC8. 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 b