Concept explainers
The Gaussian cylinder below encloses a portion of two identical large sheets. The charge density of the sheet on the left is
1. Find the net charge enclosed by the Gaussian cylinder in terms of
2. Let
Is
3. Find the net flux through the Gaussian cylinder in terms of
4. Use Gauss’ law to find the electric field a distance
Are your results consistent with the results you would obtain using superposition? Explain.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Tutorials in Introductory Physics
Additional Science Textbook Solutions
Physics: Principles with Applications
Conceptual Integrated Science
An Introduction to Thermal Physics
Life in the Universe (4th Edition)
Introduction to Electrodynamics
Applied Physics (11th Edition)
- Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. What is the direction of the electric field at any point on the z axis? What is the magnitude of the electric field along the positive z axis? Use k in your answer, where k=1/4πϵ0.arrow_forwardConsider a solid uniformly charged dielectric sphere where the charge density is give as ρ. The sphere has a radius R. Say that a hollow of charge has been created within the spherethat is offset from the center of the large sphere such that the small hollow has its center on the x axis where x = R/2. Using a standard frame where the large frame has its center at the origin, find the Electric field vector at the following points. a.The origin b.Anywhere inside the hollow (challenging) c.x = 0, y = R d.x = -R, y =0arrow_forwardE. When E and A were parallel, we called the quantity EA the electric flux through the surface. For the parallel case, we found that EA is proportional to the number of field lines through the surface. By what trigonometric function of 0 must you multiply EA so that the product is proportional to the number of field lines through the area for any orientation of the surface? Rewrite the quantity described above as a product of just the vectors E and A.arrow_forward
- Consider a short cylinder carrying a uniform permanent polarization field P parallel to its axis. a. There are no free charges in this system. Briefly describe what this means. b. Show that the bound charges are confined to the cylinder faces. Find the surface bound charge density in terms of P = P. Sketch the bound charge for this system. %3Darrow_forwardCharge is distributed throughout a spherical shell of inner radius r₁ and outer radius r2 with a volume density given by p= Pori/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r > r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Because the charge density is a function of r, rather than being able to multiply the charge density by the volume, row you need to integrate over the volume. The amount of charge in a spherical shell of radius r and thickness dr is p(r). 4tr²dr; integrate this from r = r₁ to r = r₂ to obtain the total amount of charge. Qencl= (Answer in terms of given quantities, po, 71, 72, and physical constants ke and/or Eo. Use underscore ("") for subscripts, and spell out Greek letters.) b. What is the electric field as a…arrow_forwardA very long, uniformly charged cylinder has radius R and volume charge density p. (a) Draw the electric field lines of this situation assuming the charge density is negative. How can we use the fact that the cylinder is very long to solve the problem? (b) Draw an appropriate Gaussian surface that you can use to find the electric field at any distance r> R. What is the electric flux through the flat parts of the Gaussian surface? How much charge is inside the Gaussian surface? What is the Electric field? R (c) Draw an appropriate Gaussian surface that you can use to find the electric field at any distance r < R. How much charge is inside the Gaussian surface? What is the Electric field? (d) Check that the two expressions give the same answer for points at the surface of the cylinder (e) Plot the Electric field as a function of distance r from the axis of the cylinder.arrow_forward
- Problem 3: Imagine you have a very thin plastic hoop of diameter D, which is charged up to total net electrostatic charge Q. The hoop is thin in the sense that the plastic rod of which it is made has a diameter d D. In each case, give the magnitude and direction of the field. You might need to use words (rather than formulae) to express the direction unambiguously. Assume that there are no other charges anywhere!arrow_forwardFor this question, see Figure 2 below. Consider the electric field of a disk of radius R and surface chargedensity σ along the z-axis as a) Use this expression to find the electric field of the disk very close to the disk i.e. Z << R such that thedisk looks like an infinite plane with surface charge density σ. b) Use a Gaussian cylinder (pill box) to find the electric field of the plate at this limit (Z << R such thatthe disk looks like an infinite plane), and compare it with your answer from part a.arrow_forwardCharge is distributed throughout a spherical shell of inner radius ₁ and outer radius r2 with a volume density given by p= Por1/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r>r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Qencl (Answer in terms of given quantities, po, r1, 72, and physical constants ke and/or Eo. Use underscore ("_") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of r for distances greater than r₂? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r> r₂) c. Now let's work on the "mantle" layer, r₁arrow_forwardA positively charged insulating cylinder (shown in yellow in Figure 3) with radius R has uniform volume charge density ρ0. The cylinder is placed at the centre of a negatively-charged insulating cylinder (shown in grey) with inner radius 2R, outer radius 3R, and volume charge density − ρ0/2 . a) Use Gauss’ Law to find the electric field E outside the cylinders at r > 3R. Express your answer in terms of the parameters defined in the problem. b) What is the electric potential on the surface at r = 3R, considering V = 0 at ∞.arrow_forwardYou're going to find the electric field at a point P due to a line of charge. This line of charge is infinitely long, although you can consider the charges within a length L which has a charge density of λ. Let P be a distance "D" away from the line. If you get confused with any of the steps, see if you can compare with how we found the electric field due to a point charge using Gauss's law. 1. Draw a suitable Gaussian surface on the picture below. Ꭰ P. L 2. Add a little square (or other small area) on the Gaussian surface you drew, and draw the vector perpendicular to it in order to represent a vector for dA somewhere on the gaussian surface. dA is the infinitesimal area element on your drawing. 3. Draw vectors for the electric field caused by L on the Gaussian surface. 4. Write down an equation for the linear charge density 2. 5. Write down Gauss's law, and use #4 to substitute on one side. 6. Simplify the other side of Gauss's law based on the geometry of what you did in #2 and #3.…arrow_forwardConsider a hollow spherical conductive shell of radius (R) 0.2 m with a fixed charge of +2.0 x 10-6 C uniformly distributed on its surface. (figure on the picture) a. What is the electric field at all points inside the sphere? Express your answer as a function of the distance r from the center of the sphere. b. What is the electric field outside the sphere? Express your answer as a function of the distance r from the center of the sphere. What if the sphere is a solid conductive sphere? What is the electric field at all points inside the sphere? Express your answer as function of the distance r from the center of the sphere.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON