Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 21, Problem 54P
A thick, spherical shell of inner radius a and outer radius b carries a uniform volume charge density ρ. Find an expression for the electric field strength in the region a < r < b, and show that your result is consistent with liquation 21.5 when a = 0.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents 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?
Q: A long thin wire carrying a uniform line charge density +λ runs down the center of a long cylindrical tube of radius R carrying a line charge density -2λ distributed uniformly over its surface. Find expressions for the electric field as a function of radial distance r from the axis of the wire for (a) r<R and (b) r>R. Use a minus sign to indicate a field pointing inward.
In this question would area, A=2πrL where L is the length of the wire and why is that?
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 21 Solutions
Essential University Physics (3rd Edition)
Ch. 21.1 - Which figure represents the electric field of a...Ch. 21.2 - The figure shows a cube of side s in a uniform...Ch. 21.3 - A spherical surface surrounds an isolated positive...Ch. 21.4 - A spherical shell carries charge Q distributed...Ch. 21.5 - (1) If you're close to a finite line of charge...Ch. 21.6 - (1) If you're close to a finite line of charge...Ch. 21 - Can electric field lines ever cross? Why or why...Ch. 21 - The electric flux through a closed surface is...Ch. 21 - If the flux of the gravitational field through a...Ch. 21 - Under what conditions can the electric flux...
Ch. 21 - Right field lines emerge from a closed surface...Ch. 21 - If a charged particle were released from rest on a...Ch. 21 - In Gausss law, EdA=q0does the field E necessarily...Ch. 21 - In a certain region the electric field points to...Ch. 21 - A point charge is located a fixed distance outside...Ch. 21 - The field of an infinite charged line decreases as...Ch. 21 - Why cant you use Gausss law to determine the field...Ch. 21 - Youre sitting inside an uncharged, hollow...Ch. 21 - Does Gausss law apply to a spherical Gaussian...Ch. 21 - An insulating sphere carries charge spread...Ch. 21 - Why must the electric field be zero inside a...Ch. 21 - The electric field of a flat sheet of charge is...Ch. 21 - In Fig. 21.32, the magnitude of the middle charge...Ch. 21 - Charges +2q and q are near each other. Sketch some...Ch. 21 - The net charge shown in Fig. 21.33 is +Q. Identify...Ch. 21 - A flat surface with area 2.0 m2 is in a uniform...Ch. 21 - Whats the electric field strength in a region...Ch. 21 - A flat surface with area 0.14 m2 lies in the x-y...Ch. 21 - The electric field on the surface of a...Ch. 21 - In the figure with GOT IT? 21.2, take E = 1.75...Ch. 21 - In Fig. 21.8, take the half-cylinders radius and...Ch. 21 - A sock comes out of the dryer with a trillion...Ch. 21 - Whats the electric flux through the closed...Ch. 21 - Interpret This problem involves applying Gauss's...Ch. 21 - A 2.6-C charge is at the center of a cube 7.5 cm...Ch. 21 - The electric field at the surface of a...Ch. 21 - A solid sphere 25 cm in radius carries 14C,...Ch. 21 - A 15-nC point charge is at the center of a thin...Ch. 21 - The electric field strength outside a charge...Ch. 21 - An electron close to a large, Hat sheet of charge...Ch. 21 - Find the field produced by a uniformly charged...Ch. 21 - What surface charge density on an infinite sheet...Ch. 21 - A rod 50 cm long and 1.0 cm in radius carries a...Ch. 21 - Whats the approximate field strength 1 cm above a...Ch. 21 - The disk in Fig. 21.22 has area 0.14 m2 and is...Ch. 21 - What is the electric field strength just outside...Ch. 21 - A net charge of 5.0 C is applied on one side of a...Ch. 21 - A positive point charge q lies at the center of a...Ch. 21 - A total charge of 18 C is applied to a thin,...Ch. 21 - Whats the flux through the hemispherical open...Ch. 21 - An electric field is given byE=E0(y/a)k, where E0...Ch. 21 - The electric field in a certain region is given by...Ch. 21 - A study shows that mammalian red blood cells...Ch. 21 - Positive charge is spread uniformly over the...Ch. 21 - A solid sphere 2.0 cm in radius carries a uniform...Ch. 21 - A point charge of 2Q is at the center of a...Ch. 21 - A friend is working on a biology experiment and...Ch. 21 - A spherical shell of radius 15 cm carries 4.8 C...Ch. 21 - A spherical shell 30 cm in diameter carries 85 C...Ch. 21 - A thick, spherical shell of inner radius a and...Ch. 21 - A long, thin wire carrying 5.6 nC/m runs down the...Ch. 21 - An infinitely long rod of radius R carries a...Ch. 21 - A long, solid rod 4.5 cm in radius carries a...Ch. 21 - If you painted positive charge on the floor, what...Ch. 21 - A charged slab extends infinitely in two...Ch. 21 - A solid sphere 10 cm in radius carries a 40-C...Ch. 21 - A nonconducting square plate 75 cm on a side...Ch. 21 - A 250-nC point charge is placed at the center of...Ch. 21 - An irregular conductor containing an irregular,...Ch. 21 - You measure the electric field strength at points...Ch. 21 - A point charge q is at the center of a spherical...Ch. 21 - A point charge q is at the center of a spherical...Ch. 21 - The volume charge density inside a solid sphere of...Ch. 21 - Figure 21.37 shows a rectangular box with sides 2a...Ch. 21 - The charge density within a charged sphere of...Ch. 21 - Calculate the electric fields in Example 21.2...Ch. 21 - A solid sphere of radius R carries a nonuniform...Ch. 21 - Problem 76 of Chapter 13 explored what happened to...Ch. 21 - An infinitely long solid cylinder of radius R...Ch. 21 - A solid sphere of radius R carries a uniform...Ch. 21 - Repeal Problem 59 for the case where the charge...Ch. 21 - Coaxial cables are widely used with audio-visual...Ch. 21 - A coaxial cable carries equal but opposite charges...Ch. 21 - How does the electric field between the conductors...Ch. 21 - Coaxial cables are widely used with audio-visual...
Additional Science Textbook Solutions
Find more solutions based on key concepts
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective (8th Edition)
19.28 The engine of a Ferrari F355 F1 sports car takes in air at 20.0°C and 1.00 atm and compresses it adiabati...
University Physics with Modern Physics (14th Edition)
Check Your Understanding Identify one way you could decrease the maximum velocity of a simple harmonic oscillat...
University Physics Volume 1
Choose the best answer to each of the following. Explain your reasoning. Which of the following provides eviden...
The Cosmic Perspective Fundamentals (2nd Edition)
Calculate the reactance of a 5.0-mH inductor at (a) 60 Hz, (b) 600 Hz, and (C) 6000 Hz.
University Physics Volume 2
Comparing the visible and the infrared types of light, which would you say has an easier time getting through o...
Lecture- Tutorials for Introductory Astronomy
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
- Problem: An infinitely long cylindrical conductor has radius R and uniform surface charge density Ơ. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forwardProblem: An infinitely long cylindrical conductor has radius R and uniform surface charge density 0. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forwardProblem 4. Exponentially Decaying Charge Density. A spherically symmetric charge distribution is described by a volume charge density given byp = Poe¯"/a, where po and a are both positive constants, and r is the distance from the center of the distribution. (a) Determine the electric field at any value of r. (b) Sketch the graph of the electric field magnitude with r. (c) Describe how the electric field varies with the distance r.arrow_forward
- A spherically symmetric charge distribution produces the electric field E- (3x10 ) N/C along the radial directrion, where r is in m. How much charge (in nC) is inside a 0.2 m radius spherical sphere?arrow_forwardProblem 4. Exponentially Decaying Charge Density. A spherically symmetric charge distribution is described by a volume charge density given by p = Poe-"/a, where po and a are both positive constants, and r is the distance from the center of the distribution. (a) Determine the electric field at any value of r. (b) Sketch the graph of the electric field magnitude with r. (c) Describe how the electric field varies with the distance r.arrow_forwardA nonconducting solid sphere of radius R has a volume charge density that is proportional to the distance from the center. That is, ρ = Ar for r R, where A is a constant. (Use the following as necessary: ε0, A, r, and R, as necessary.) (a) Find the total charge on the sphere. (b) Find the expressions for the electric field inside the sphere (r < R) and outside the sphere (r > R).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_forwardIn the center of a hollow insulating sphere with a volumetric charge densityp and a total charge + Q, there is a point load with + 2Q charge. What is the electric field magnitude in the region Rarrow_forwardYou have been given the following charge density function for r ≤ R elsewhere P Po (1-r/R) 0 This charge density function describes a long cylindrical charge distribution. Please explain your steps and determine the electric field everywhere due to this charge distribution.arrow_forwardA long nonconducting cylinder (radius 6.0 mm) has a nonuniform volume charge density given by ar, where a= 6.2 mC/m' and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis?arrow_forwardA 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_forwardQUESTION 1 Problem: An infinitely long cylindrical conductor has radius R and uniform surface charge density o. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY