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 solid conducting sphere of radius 2.00 cm has a charge 8.00 μC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a total charge −4.00 μC. Find the electric field at (a) r = 1.00 cm, (b) r = 3.00 cm, (c) r = 4.50 cm, and (d) r = 7.00 cm from the center of this charge configuration.arrow_forward1.Charge is uniformly distributed around a ring of radius R = 2.40 cm, and the resulting electric field magnitude E is measured along the ring's central axis (perpendicular to the plane of the ring).At what distance from the ring's center is E maximum?arrow_forwardA 9 nC charge is distributed uniformly along the y axis from y = 0 to y = 5 m. Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?arrow_forward
- A non-conducting sphere of radius R = 7.0 cm carries a charge Q = 4.0 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere, does the electric field reach a value equal to half its maximum value?arrow_forwardA nonconducting sphere with uniform charge density has a radius a and a total charge +2q; a nonconducting spherical shell (with uniform charge density) has an inner radius b, outer radius c, and total charge −q. Find expressions for the electric field in the regions (a) r < a, (b) a < r < b, (c) b < r < c, and (d) r > c. For parts (e) through (h), now assume the sphere and shell are conductors, though with their net charges unchanged; find expressions for the electric field in the regions (e) r < a, (f) a < r < b, (g) b < r < c, and (h) r > c.arrow_forwardfind the electric field 23 cm from the center of a thin, spherical shell of radius 16.0 cm with a total charge of 33.8 mC distributed uniformly on its surface. What is the magnitude and the directionarrow_forward
- Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of -2.00 nC is at the center of the sphere. If a = 2.00 m and b = 2.40 m, find the electric field at (a) r = 1.50 m, (b) r = 2.20 m, and (c) r = 2.50 m. (d) What is the charge distribution on the sphere?arrow_forwardIn the figure a sphere, of radius a = 14.2 cm and charge q = 1.00×10-5 C uniformly distributed throughout its volume, is concentric with a spherical conducting shell of inner radius b = 48.3 cm and outer radius c = 50.3 cm . This shell has a net charge of -q. a) Find expressions for the electric field, as a function of the radius r, within the sphere and the shell (r < a). Evaluate for r = 7.1 cm. b) Find expressions for the electric field, as a function of the radius r, between the sphere and the shell (a < r < b). Evaluate for r=31.2 cm. c) Find expressions for the electric field, as a function of the radius r, inside the shell (b < r < c). Evaluate for r = 49.3 cm. d) Find expressions for the electric field, as a function of the radius r, outside the shell (r > c). Evaluate for r = 51.3 cm. e) What is the charge on the outer surface of the shell?arrow_forwardThe figure shows a closed Gaussian surface in the shape of a cube of edge length 2.40 m. It lies in a region where the electric field is given by E→ = (1.60x + 5.85)î + 4.53 ĵ + 5.44 k̂ N/C, with x in meters. What is the net charge contained by the cube?arrow_forward
- We have a nonconducting solid sphere of radius 2.6 cm carrying a uniformly distributed positive charge of 8.7 nC. What is the magnitude of the electric field at a point 4.2 cm from the center of the conducting sphere?arrow_forwardA certain region of space bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface?arrow_forwardA non-uniformly charged semicircle of radius R=10.9 cm lies in the xy plane, centered at the origin, as shown. The charge density varies as the angle θ (in radians) according to λ=1.15θ, where λ has units of μC. What is the y component of the electric field at the origin? I have already found the total charge to be 6.186E-7 C.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning