Concept explainers
A charged slab extends infinitely in two dimensions and has thickness d in the third dimension, as shown in Fig. 21.36. The slab carries a uniform volume charge density ρ. Find expressions for the electric field (a) inside and (b) outside the slab, as functions of the distance x from the center plane. (Although the infinite slab is impossible, your answer is a good approximation to the field of a finite slab whose width is much greater than its thickness.)
59. INTERPRET The infinitely large slab has plane symmetry, and we can apply Gauss’s law to compute the electric field.
DEVELOP When we take the slab to be infinitely large, the electric field is everywhere normal to the slab's surface and symmetrical about Die center plane we follow the approach outlined in example 21.6 to compute the electric field. As the Gaussian surface, we choose a box that has area A on its top and bottom and that extends a distance x both up and down from the center of the slab. See figure below.
EVALUATE (a) For points inside the slab |x| ≤ d/2, the charge enclosed by our Gaussian box is
qenclosed = ρVenclosed = ρA(2x)
Thus, Gauss’s law gives
The direction of
(b) For points outside the slab |x| > d/2. the enclosed charge is
qenclosed = ρVenclosed = ρA(d)
Applying Gauss’s law again gives
Learn your wayIncludes step-by-step video
Chapter 21 Solutions
Essential University Physics
Additional Science Textbook Solutions
Essential University Physics: Volume 1 (3rd Edition)
Physics (5th Edition)
Sears And Zemansky's University Physics With Modern Physics
The Cosmic Perspective (8th Edition)
An Introduction to Thermal Physics
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
- A very large nonconducting plate lying in the xy-plane carries a charge per unit area of 3?. A second such plate located at z = 2.40 cm and oriented parallel to the xy-plane carries a charge per unit area of −2?. Find the electric field for the following. (a) when z<0 (b) when 0 < z < 2.40 cm (c) when z > 2.40 cmarrow_forward18. A uniform volume charge density of 10 C/m³ is present in the spherical shell 0.9 1 m that is identical to the field that would be produced by a point charge Qt at the origin. Find E in spherical coordinates for r> 1 m.arrow_forwardA hollow cylindrical shell has an inner radius of 2.0 cm, an outer cylinder of radius 5.0 cm, and a length of 5.0 m. The shell is charged with a total of 10.0 nC distributed uniformly throughout its volume. Use this context for the following two questions. Determine the magnitude of the electric field of the cylindrical shell at a radial distance of 5.4 cm, measured from the center of the shell perpendicular from its axis. Give your answer in units of N/C. Determine the magnitude of the electric field of the cylindrical shell at a radial distance of 4.7 cm, measured from the center of the shell perpendicular from its axis. Give your answer in units of N/C.arrow_forward
- Problems 11-13 refer to the following situation. A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: Problem 11: What is the constant po? Q πR³ a. Po and R are positive constants. The total charge of the distribution is Q. Problem 12: What is the E-field for r R? 1 Q b. 4περ 12 a. p(r) = {Po (7) . 20 πR³ 1 Qr² 4περ R4 1 QR 4περ 13 C. C. r R C. 30 πR³ 1 Qr³ 4περ R5 QR² 1 4περ 14 d. d. d. 4Q πR³ 1 Qr4 4πεο R6 QR³ 1 Απο 15arrow_forwarda) A very long (almost infinitely long) cylindrical wire of radius R carries a uniform charge density Po. Find the line charge density. Find the electric field inside and outside the wire. b) If a long cylindrical cavity of radius b is created at a distance a in the wire maintaining same charge density as part (a) (see Fig. 2). Find the line charge density. Find the electric field inside the cylindrical cavity. 01 Fig. 2arrow_forwardThe Earth has an inwardly directed electric field that varies slightly depending on location and altitude. Make the simplifying assumption that this field is a constant 135 N/C and directed toward Earth’s center. What is the net charge, in Coulombs, on the Earth’s surface?arrow_forward
- Consider a thin-shelled hollow tube of length L, radius R with a uniform surface charge of density ? and with the x axis as its central axis. This can be described by: y2+z2=R2 and 0<= x <= L. What is the elctric field at x0 along the x axis, where x0 > L?arrow_forwardThe charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs 1.0 m; p(r)= Po(1-4r/3) For r> 1.0 m; p(r)= 0, where r is in meters. What is the value of r in meters for which the electric field is maximum? 0.25 0.50 0.75 1.00 2.00 Other:arrow_forwardConsider two infinite planes of charge. One coincides with the x-y plane and has a charge density of +9.5 x 10-12 C/m2. The second plane coincides with the y-z plane and has a charge density of -9.5 x 10-12 C/m2. Calculate the magnitude of electric field, in N/C, at any location that is not on the x-y or y-z planes. Use ε 0 = 8.9 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forward
- A thick insulating cylindircal shell of inner radius a=2.5R and outer radius b=5.2R has a uniform charge density p . What is the magnitude of the electric field at r=8.2 R ? Express your answer using one decimal place in units of ?arrow_forward2r 3. Suppose that a sphere of radius 2r and uniform volume charge density p is composed of a nonconducting material (charges remain in place). A cavity of radius r is then carved out as shown above. Show that the net electric field is given by TP 360 (Problem 64, chapter 24, Physics for Scientists and Engineers)arrow_forwardThis is a four-part problem. A nonconducting uniformly charged sphere has a radius R and volume charge density “rho”. Find the electric field: a) outside the sphere r>R b) inside the sphere rarrow_forward
- 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