Concept explainers
CALC A Nonuniformly Charged Slab. Repeat Problem 22.54, but now let the charge density of the slab be given by ρ(x) = ρ0(x/d)2, where ρ0 is a positive constant.
22.54 A Uniformly Charged Slab. A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = −d. The y- and z-dimensions of the slab are very large compared to d; treat (hem as essentially infinite. The slab has a uniform positive charge density ρ. (a) Explain why the electric field due to the slab is zero at the center of the slab (x = 0). (b) Using Gauss’s law, find the electric field due to the slab (magnitude and direction) at all points in space.
Want to see the full answer?
Check out a sample textbook solutionChapter 22 Solutions
University Physics (14th Edition)
Additional Science Textbook Solutions
Physics (5th Edition)
The Cosmic Perspective Fundamentals (2nd Edition)
The Cosmic Perspective
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
The Cosmic Perspective (8th Edition)
College Physics: A Strategic Approach (4th Edition)
- There is a thick wall that extends infinitely in the yz plane. The wall is made of insulating material and has a thickness of D in the x direction. The wall has a charge density of +ρ. At an arbitrary distance x (where x is less than half of D), we need to find the magnitude of the electric field inside the wall.arrow_forwardA hollow conducting sphere has an inner radius of r1 = 1.4 cm and an outer radius of r2 = 3.5 cm. The sphere has a net charge of Q = 2.9 nC. a. What is the magnitude of the electric field in the cavity at the center of the sphere, in newtons per coulomb? b. What is the magnitude of the field, in newtons per coulomb, inside the conductor, when r1 < r < r2? c. What is the magnitude of the field, in newtons per coulomb, at a distance r = 7.6 m away from the center of the sphere?arrow_forwardWhat is wrong with this?arrow_forward
- Please asaparrow_forwardCan you help me answer the first two questions, I don't know what the answer is.arrow_forwardAn insulating sphere with radius 0.120 m has +0.900 nC (nano coulumb) of charge uniformly distributed throughout its volume. The center of the sphere is 0.240 m above a large uniform sheet that has a charge density -8.00 nC/m². Find all points inside the sphere where the electric field is zero. Or, show that there are no such points.arrow_forward
- A thin, horizontal, 11-cm-diameter copper plate is charged to -2.9 nC. Assume that the electrons are uniformly distributed on the surface What is the strength of the electric field 0.1 mm above the center of the top surface of the plate? Answer: 1.7*104N/C What is the direction of the electric field 0.1 mm above the center of the top surface of the plate? Answer: toward the plate What is the strength of the electric field at the plate's center of mass? Answer:170311.8N/C What is the strength of the electric field 0.1 mm below the center of the bottom surface of the plate? Answer:1.7*104N/C What is the direction of the electric field 0.1 mmmm below the center of the bottom surface of the plate? toward the plate with this problem I just want you to show me the steps how to solvearrow_forwardTwo 1.20m nonconducting wires form a right angle. One segment has charge q1=4.0 nC uniformly distributed along its length, the other segment has charge q2 = –6.0 nC uniformly distributed along its length. Point P lies on the central axis of each wire and is 60.0 cm apart. a. The horizontal component of the net electric field at point P is:______N/C. in i or -i. b. The vertical component of the net electric field at point P is:______ N/C. in j or -j. c. The magnitude of the net electric field at point P is:______N/C. d.its direction measured with respect to the x-axis is:_____.arrow_forwardA single isolated, large conducting plate has acharge per unit area σ on its surface. Because the plate is a conductor, the electric field at its surface is perpendicular to the surface and has magnitude E = σ/εo a.The field from a large, uniformly charged sheet with charge per unit area σ has magnitude E = σ/2εo. Why is there a difference? b.Regard the charge distribution on the conducting plate as two sheets of charge (one on each surface), each with charge per unit area σ. Find the electric field inside and outside the plate.arrow_forward
- A flat wire of infinite length has width W and charge density sigma. If we align the wire so that it is everywhere at y=0 and extends in x from x=d to x=d+L, then calculate the electric field at x=0. Hint: Treat the wire as an the sum of the contributions of many "long wires" where the linear charge density satisfies: lambda=sigma*L.arrow_forwardYou are working for the summer at a research laboratory. Your research director has devised a scheme for holding small charged particles at fixed positions. The scheme is shown. An insulating cylinder of radius a and length L >> a is positively charged and carries a uniform volume charge density ρ. A very thin tunnel is drilled through a diameter of the cylinder and two small spheres with charge q are placed in the tunnel. These spheres are represented by the blue dots in the figure. They find equilibrium positions at a distance of r on opposite sides of the axis of the cylinder. Your research director has had great success with this scheme. (a) Determine the specific value of r at which equilibrium exists. (b) Your research director asks you see if he can extend the system as follows. Determine if it is possible to add transparent plastic tubes as extensions of the tunnel and have the small spheres be in equilibrium at a position for which r > a.arrow_forwardA small mass charged sphere (q= 3 µC ) is attached by an insulating string to the surface of a very large conductor with a surface charge density of o = 44.4 µC. Given that the string makes an angle with the surface equal to 30 degrees, find the tension ( in N) in the string. use ɛo = 8.8542x10-12 F-m-1. String b. Select one: O A. 59.44 OB. 17.37 OC. 45.13 OD. 15.04 OE. 30.09 ) ENG 7:56 +++ + + + + +arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning