1. A flat, square surface with sides of length L is described by the equations x = L (0 ≤ y ≤L,0 ≤z ≤ L). (a) Draw this square and show the x-, y-, and z-axes. (b) Find the electric flux through the square due to a positive point charge q located at the origin (x = 0, y = 0, z = 0). Hint: Think of the square as part of a cube centered on the origin.

1. A flat, square surface with sides of length L is described by the equations x = L (0 ≤ y ≤L,0 ≤z ≤ L). (a) Draw this square and show the x-, y-, and z-axes. (b) Find the electric flux through the square due to a positive point charge q located at the origin (x = 0, y = 0, z = 0). Hint: Think of the square as part of a cube centered on the origin.

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter24: Gauss’s Law

Section: Chapter Questions

Problem 24.63CP: A dosed surface with dimensions a = b= 0.400 111 and c = 0.600 in is located as shown in Figure...

See similar textbooks

Similar questions

The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r R)?
Two positively charged spheres are shown in Figure P24.70. Sphere 1 has twice as much charge as sphere 2. If q = 6.55 nC, d = 0.250 m, and y = 1.25 m, what is the electric field at point A?
1. A 30 cm long thin-walled cylinder of radius R = 3.5 cm, has charge of 1 x 108 C uniformly spread on it. a. Draw the Gaussian surfaces for radius values of r = R/2, r = R, r = 2R and r = 4R. (Draw to scale as much as possible) b. Calculate the magnitude of the electric field at each of the radial distance r = R/2, r = R and r = 2R. c. Graph E versus r for range r from 0 to 4R.
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
6. A cylinder with radius R and infinite length is centered on the z-axis and has a uniform charge density r R p= Po 0 where po is a constant. a) Using Gauss's law find the electric field for r R. Express your answer in terms of the charge per unit length of the cylinder (you'll have to think about how to define it). Hint: in terms of symmetry, this case is very similar to an infinite line charge. b) Now a uniform surface charge density o is pasted onto the surface of the cylinder such that the electric field outside the cylinder is zero. What is o in terms of R, po, and numerical factors?
2. A charge Q is uniformly distributed over a rod of length 1. Consider a hypothetical cube of edge I with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.
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.
2. In free space, let D = 8xyz*āz + 6x²z*ā, + 16x²yz°ã; pC/m². a. Find the total electric flux passing through the rectangular surface z = 2, 0
1. Figure shows a non-conducting hollow sphere with inner radius a and outer radius b. It has non-uniform positive volume charge density p P. d that is a function of radial distance r from its center p = ar where a is a constant with the units of C/m*. a. Find the electrical flux through the spherical Gaussian surface with radius r for a b) element of a sphere Express your answers in term of a, b, d,r, a, e, and n.
Calculate the absolute value of the electric flux for the following situations (In all case provide your answer in N m2/C): a. A constant electric field of magnitude 300 N/C at a 30 degrees angle with respect to the flat rectangular surface shown in the Figure above. b. A uniform electric field E = (70 i + 90 k) N/C through a 4 cm ×5 cm in the x-y plane. c. A uniform electric field E = (−350 i + 350 j + 350 k) N/C through a disk of radius 3 cm in the x-z plane.
1. A very large flat insulating sheet with uniform charge per area n (SI units: C/m²) sits in the y-z plane at x = 0. We want to find the electric field at a point Pa distance x from the sheet. Assume P is far from the edges and x is small compared to the size of the sheet. Assume that is positive. From symmetry, the electric field must point directly away from the sheet. We choose to draw the Gaussian surface as a cylinder of radius R that extends a distance x on both sides of the sheet. а. Which statement is true regarding the flux through the Gaussian surface? Choose one answer below! The electric flux through all the surfaces is zero. The flux through the endcaps is zero and the flux through the curved section is positive. The flux through the endcaps is zero and the flux through the curved section is negative. R The flux through the curved section is zero. The flux through the right endcaps is positive and through the left endcaps is negative. The flux through the curved section…
Here’s one more model of an electron. Here e is the magnitude of the charge of an electron, and R is a constant parameter characterizing the electron’s size: rho=-e (105/4pi)r2(R-r)2/R7 , rho = 0 for r >R. a. Use the problem's symmetry to evaluate the electric field at all points in space, it r >R and r<R. b. Sketch the electric field magnitude versus r for all values of r. d. evaluate the electric potential at all points in space and sketch its magnitude as a function of r.