Concept explainers
The general form of Gauss’s law describes how a charge creates an electric field in a material, as well as in vacuum:
where ϵ = κϵ0 is the permittivity of the material. (a) A sheet with charge Q uniformly distributed over its area A is surrounded by a dielectric. Show that the sheet creates a uniform electric field at nearby points with magnitude E = Q/2Aϵ. (b) Two large sheets of area A, carrying opposite charges of equal magnitude Q, are a small distance d apart. Show that they create uniform electric field in the space between them with magnitude E = Q/Aϵ. (c) Assume the negative plate is at zero potential. Show that the positive plate is at potential Qd/Aϵ. (d) Show that the capacitance of the pair of plates is given by C = Aϵ/d = κAϵ0/d.
Trending nowThis is a popular solution!
Chapter 25 Solutions
Physics for Scientists and Engineers
- Consider the charge distribution shown in Figure P19.74. (a) Show that the magnitude of the electric field at the center of any face of the cube has a value of 2.18 keq/s2. (b) What is the direction of the electric field at the center of the top face of the cube?arrow_forwardTwo solid spheres, both of radius 5 cm, carry identical total charges of 2 C. Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume. (i) How do the magnitudes of the electric fields they separately create at a radial distance of 6 cm compare? (a) EA EB = 0 (b) EA EB 0 (c) EA = EB 0 (d) 0 EA EB (e) 0 = EA EB (ii) How do the magnitudes of the electric fields they separately create at radius 4 cm compare? Choose from the same possibilities as in part (i).arrow_forwardA circular ring of charge with radius b has total charge q uniformly distributed around it. What is the magnitude of the electric field at the center of the ring? (a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) none of those answersarrow_forward
- A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown in Figure P19.75. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r a. (b) From this value, find the magnitude of the electric field for r a. (c) What charge is contained within a sphere of radius r when a r b? (d) From this value, find the magnitude of the electric field for r when a r b. (e) Now consider r when b r c. What is the magnitude of the electric field for this range of values of r? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density?arrow_forwardIs it possible for a conducting sphere of radius 0.10 m to hold a charge of 4.0 C in air? The minimum field required to break down air and turn it into a conductor is 3.0 106 N/C.arrow_forwardConsider a thin, spherical shell of radius 14.0 cm with a total charge of 32.0 C distributed uniformly on its surface. Find the electric field (a) 10.0 cm and (b) 20.0 cm from the center of the charge distribution.arrow_forward
- Rank the electric fluxes through each gaussian surface shown in Figure OQ19.7 from largest to smallest. Display any cases of equality in your ranking. Figure OQ19.7arrow_forwardaA plastic rod of length = 24.0 cm is uniformly charged with a total charge of +12.0 C. The rod is formed into a semicircle with its center at the origin of the xy plane (Fig. P24.34). What are the magnitude and direction of the electric field at the origin? Figure P24.34arrow_forwardA circular ring of charge of radius b has a total charge q uniformly distributed around it. Find the magnitude of the electric field in the center of the ring. (a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) None of these answers is correct.arrow_forward
- A uniformly charged insulating rod of length 14.0 cm is bent into the shape of a semicircle as shown in Figure P 19.21. The rod has a total charge of 7.50 C. Find (a) the magnitude and (b) the direction of the electric field at O, the center of the semicircle.arrow_forwardThe electric field at a point on the perpendicular bisector of a charged rod was calculated as the first example of a continuous charge distribution, resulting in Equation 24.15:E=kQy12+y2j a. Find an expression for the electric field when the rod is infinitely long. b. An infinitely long rod with uniform linear charge density also contains an infinite amount of charge. Explain why this still produces an electric field near the rod that is finite.arrow_forwardConsider the electric dipole shown in Figure P19.20. Show that the electric field at a distant point on the + x axis is Ex 4 keqa/x3.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- 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 LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning