Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 23, Problem 51CP
A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar2, where A is a constant and r < R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR5/5ϵ0r2. (b) Show that the magnitude of the electric field inside (r < R) the sphere is E = Ar3/5ϵ0. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The 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?
The volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant.
(a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A?b) Calculate the electric field for a point outside the cylinder, r > Rc) Calculate the electric field for a point inside the cylinder, r<R.d) Sketch Exr
Positive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric
field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere.
a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p.
b) Determine the electric field, E(r), for r > R (outside the sphere).
c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere
(r = R)?
d) What is the energy stored in this electric charge configuration?
Chapter 23 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 23.2 - Suppose a point charge is located at the center of...Ch. 23.3 - If the net flux through a gaussian surface is...Ch. 23 - A negatively charged rod of finite length carries...Ch. 23 - A positively charged disk has a uniform charge per...Ch. 23 - A uniformly charged ring of radius 10.0 cm has a...Ch. 23 - The electric field along the axis of a uniformly...Ch. 23 - Example 23.3 derives the exact expression for the...Ch. 23 - A uniformly charged rod of length L and total...Ch. 23 - A continuous line of charge lies along the x axis,...Ch. 23 - A thin rod of length and uniform charge per unit...
Ch. 23 - (a) Consider a uniformly charged, thin-walled,...Ch. 23 - A vertical electric field of magnitude 2.00 104...Ch. 23 - A flat surface of area 3.20 m2 is rotated in a...Ch. 23 - A nonuniform electric field is given by the...Ch. 23 - An uncharged, nonconducting, hollow sphere of...Ch. 23 - Find the net electric flux through the spherical...Ch. 23 - Four closed surfaces, S1 through S4 together with...Ch. 23 - A charge of 170 C is at the center of a cube of...Ch. 23 - (a) Find the net electric flux through the cube...Ch. 23 - A particle with charge of 12.0 C is placed at the...Ch. 23 - A particle with charge Q = 5.00 C is located at...Ch. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Find the net electric flux through (a) the closed...Ch. 23 - Figure P23.23 represents the top view of a cubic...Ch. 23 - Determine the magnitude of the electric field at...Ch. 23 - Prob. 25PCh. 23 - Prob. 26PCh. 23 - A large, flat, horizontal sheet of charge has a...Ch. 23 - A nonconducting wall carries charge with a uniform...Ch. 23 - A uniformly charged, straight filament 7.00 m in...Ch. 23 - You are working on a laboratory device that...Ch. 23 - Consider a long, cylindrical charge distribution...Ch. 23 - Assume the magnitude of the electric field on each...Ch. 23 - A solid sphere of radius 40.0 cm has a total...Ch. 23 - A cylindrical shell of radius 7.00 cm and length...Ch. 23 - You are working for the summer at a research...Ch. 23 - You are working for the summer at a research...Ch. 23 - Find the electric flux through the plane surface...Ch. 23 - Prob. 38APCh. 23 - Prob. 39APCh. 23 - Show that the maximum magnitude Emax of the...Ch. 23 - A line of positive charge is formed into a...Ch. 23 - Prob. 42APCh. 23 - A sphere of radius R = 1.00 m surrounds a particle...Ch. 23 - A sphere of radius R surrounds a particle with...Ch. 23 - A slab of insulating material has a nonuniform...Ch. 23 - A sphere of radius 2a is made of a nonconducting...Ch. 23 - Prob. 47CPCh. 23 - Prob. 48CPCh. 23 - Review. A slab of insulating material (infinite in...Ch. 23 - Identical thin rods of length 2a carry equal...Ch. 23 - A solid insulating sphere of radius R has a...
Additional Science Textbook Solutions
Find more solutions based on key concepts
Whether two metal foil leaves an electroscope get opposite charge when the electroscope is charged.
The Physics of Everyday Phenomena
Is Earths inner core solid and the outer core liquid because the inner core is cooler than the outer core? Expl...
Conceptual Integrated Science
Choose the best answer to each of the following. Explain your reasoning. Which of these star clusters is oldest...
Cosmic Perspective Fundamentals
An aluminum calorimeter with a mass of 100 g contains 250 g of water. The calorimeter and water are in thermal ...
Physics for Scientists and Engineers, Technology Update (No access codes included)
2. Which of the following is the best example of the use of a referent? _
a. A red bicycle
b. Big as a dump tru...
Physical Science
Why is physics the most basic science?
Conceptual Physics: The High School Physics Program
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- The surface charge density on a long straight metallic pipe is . What is the electric field outside and inside the pipe? Assume the pipe has a diameter of 2a.arrow_forwardThe electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?arrow_forwardTwo infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .arrow_forward
- An insulating solid sphere of radius a has a uniform volume charge density and carries a total positive charge Q. A spherical gaussian surface of radius r, which shares a common center with the insulating sphere, is inflated starting from r = 0. (a) Find an expression for the electric flux passing through the surface of the gaussian sphere as a function of r for r a. (b) Find an expression for the electric flux for r a. (c) Plot the flux versus r.arrow_forwardThe volume charge density ρ for a spherical charge distribution of radius R= 6.00 mm is not uniform. (Figure 1) shows ρ as a function of the distance r from the center of the distribution. a)Calculate the electric field at r = 1.00 mm. b)Calculate the electric field at r = 1.00 mm.arrow_forwardA thick insulating spherical shell of inner radius a=2.4R and outer radius b=6.1R has a uniform charge density p. pR What is the magnitude of the electric field at r=5.6 R ? Express your answer using one decimal place in units of €oarrow_forward
- An insulating solid sphere of radius a has a uniform volume charge density ρ and carries a total positive charge Q (as shown). (A) Calculate the magnitude of the electric field at a point outside the sphere. (B) Find the magnitude of the electric field at a point inside the sphere.arrow_forwardA thick insulating spherical shell of inner radius a=2.1R and outer radius b=9.9R has a uniform charge density p. pR What is the magnitude of the electric field at r=4.5 R ? Express your answer using one decimal place in units ofarrow_forwardA thick insulating cylindircal shell of inner radius a-1.5R and outer radius b=5.1R has a uniform charge density p. What is the magnitude of the electric field at r=9.4 R ? Express your answer using one decimal place in units of PR :?arrow_forward
- A thick insulating spherical shell of inner radius a=1.2R and outer radius b=5.5R has a uniform charge density p. b. What is the magnitude of the electric field at r=8.9 R ? Express your answer using one decimal place in units of pR €oarrow_forwardA thick insulating cylindircal shell of inner radius a=2.9R and outer radius b=6.8R has a uniform charge density p. PR What is the magnitude of the electric field at r=8.3 R ? Express your answer using one decimal place in units ofarrow_forwardThe bulk density of charge on a sphere of radius a is given by ρ = ρ0(1 + r/a), where ρ0 is a constant, and r is the radial distance measured from the center of the sphere. (a) Determine the total charge present on the sphere.(b) Calculate the electric field for points inside the sphere.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY