2. Suppose the electric field in some region is found to be E = kr³, in spherical coordinates (k is one constant). c. Find the charge density p d. Find the total charge in the sphere of radiu R, centered at the origin. (Do it using the Gauss's Law and create a Gaussian surface and evaluate the flux manually)

2. Suppose the electric field in some region is found to be E = kr³, in spherical coordinates (k is one constant). c. Find the charge density p d. Find the total charge in the sphere of radiu R, centered at the origin. (Do it using the Gauss's Law and create a Gaussian surface and evaluate the flux manually)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

6. An infinite line is uniformly charged with a linear charge density A.Find a formula describing the electric field at a distance z from the line.
2. In free space, let D = 8xyz*ā, + 6x²z*ā, + 16x²yz°ā, pC/m². a. Find the total electric flux passing through the rectangular surface z = 2, 0
1. The electric field at all points on a closed spherical surface is 226 N/C outwards. If the area of the surface is 4.2 m², what is the net charge (in nC) enclosed inside the surface? C. 8.40 b. 4.00 2. Imagine two gaussian surfaces in the shape of concentric hollow spheres, A and B. They enclose two point charges of magnitudes, 5 C and 3 C, as shown below. The ratio of the two electric fluxes DA : DB d. c. 12.4 d. 16.0 a. 5:3 b. 3:5 8:8 5:8 +5C +3C B
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 conducting spherical shell has an inner radius Rj and an outer radius Ro. 1) A charge Q is placed on the shell. Calculate the electric field E(r): a) for r> R. b) for R;
1. A total charge +Q is distributed over a plastic line in square shape with sides are equal to 2a. The line is so thin that thickness is negligible. The square is positioned to the center. Find the electric field (E =?) at point P which is positioned away from the center (Tp = xpî + ypj ,Xp > av2, yp > av2 and xp, Yp are constant). d, ip = xpi + yPj 2a 0,0 2a
7. Please show the full solution of the problem
2. Find the electric field at a distance z above the center of a ring of radius a that has a uniform linear charge density A. Compute (only) the Er and Ez components of a cylindrical coordinate system.
4. Use the Gauss law to calculate the magnitude of the electric field from scratch. For the closed surface of integration (the "Gaussian box"), use a shape with two faces, the "caps," parallel and side or to the charged sheets. Explain all the assumptions you have to make for the electric field and back them up with symmetry arguments. sides perpendicular (a) Make a clear sketch of the system and your Gaussian box, including representative area vectors dA and electric field vectors. (b) Calculate the flux integral ƒE•dA. Include an explanation of your reasoning. (c) Calculate Qenc. Include an explanation of your reasoning. (d) Use the Gauss law to calculate the magnitude of the electric field at any point in space.
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.
1. If a Gaussian sphere encloses no charge, does it follow that E = 0 on the surface of the Gaussian sphere? Justify your answer with 1–2 sentences. 2. Charge is uniformly distributed on the surface of a non-conducting spherical shell. The sphere is then dented. Is the electric field inside of the shell different after it is dented? Justify your answer with 1–2 sentences.
1. A flat rectangle is placed in a uniform electric field with a magnitude of 7.8 x 103 N/C. The electric flux through the rectangle when its face is 45º to the field lines is 89.75 Nm2/C. Find the width of the flat rectangle with a length of 9. 45cm. 3. A hollow sphere has an unknown charges distributed uniformly over its surface. At a distance of 0.63 m from the center of the sphere, the electric field points radially inward and has magnitude of 4.56 x103 N/C. How much charge is on the sphere?