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
Want to see the full answer?
Check out a sample textbook solutionChapter 21 Solutions
Essential University Physics (3rd Edition)
Additional Science Textbook Solutions
Tutorials in Introductory Physics
Sears And Zemansky's University Physics With Modern Physics
University Physics Volume 2
Lecture- Tutorials for Introductory Astronomy
University Physics with Modern Physics (14th Edition)
An Introduction to Thermal Physics
- A non-uniform electric field directed along the x-axis penetrates a cubical surface oriented as shown in the figure. The cube has an edge length of L=0.79 m and the field varies from E1=2000 N/C at x=0 to E2=5000 N/C at x=L. Find the total charge (in nC) enclosed by the cube.arrow_forwardA 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_forwardAn infinite plane in the xz plane carries a uniform surface charge density ?1 = 66 nC/m2. A second infinite plane carrying a uniform charge density ?2 = 43 nC/m2 intersects the xz plane at the z axis and makes an angle of 30° with the xz plane as shown in the figure below. Find the electric field in the xy plane at each of the following locations.arrow_forward
- a) 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_forwardConsider 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_forward
- 2r 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_forwardA long, straight wire has fixed negative charge with a linear charge density of magnitude 3.6 nC/m. The wire is to be enclosed by a coaxial, thin-walled nonconducting cylindrical shell of radius 1.5 cm.The shell is to have positive charge on its outside surface with a surface charge density s that makes the net external electric field zero. Calculate s.arrow_forwardA -198.7 mC charge is placed at the center of a hollow conducting sphere. Find the Charge density (in C/m²) on the outside of the sphere if its radius is 6.47 cm and if it Contains zero net charge.arrow_forward
- A very thin spherical shell of radius a has a total charge of Q distributed uniformly over its surface . Find the electric field at points inside and outside the shell.arrow_forwardQ4. (a) For an infinitely long wire with uniform line-charge density, along the z-axis, find the electric field at a point (a,b,0) away from the origin. (b) A uniform line charge, infinite in extent, having charge per unit length 10 nC/m lies along the z-axis. Find the magnitude of electric field E at (6,8,3) m.arrow_forwardA slab of insulating material has a uniform positive charge density ρ, as shown in the figure below. The slab is infinite in the y and z directions. Derive expressions for the field for the following regions. (Use the following as necessary: ε0, ρ, d, and x as necessary.) (a) the exterior regions (x > d/2)E = _____ in the +x +y +z direction(b) the interior region of the slab (0 < x < d/2) E = _____ in the +x +y +z directionNote: your answers should be the same when x = d/2arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning