Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 25, Problem 58PQ
A charged rod is placed in the center along the axis of a neutral metal cylinder (Fig. P25.57). The rod has positive charge uniformly distributed. (Ignore the ends.)
- a. Find expressions for the electric fields in all regions: r < a, a < r < b, b < r < c, and r > c.
- b. Plot your expressions on one graph. Is the electric field continuous or discontinuous? Explain.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Time left C
For which of the following charge distributions would Gauss's law not be useful for
calculating the electric field?
a spherical shell of radius R with charge uniformly distributed over its surface
O a.
Ob.
an infinitely long cylinder of radius R with charge uniformly distributed over its
surface
Oc.
a uniformly charged sphere of radius R
d.
an infinite planar sheet having constant surface charge density
Oe a cylinder of radius R and height h with charge uniformly distributed over its surface
NEXT PAGE
A total charge of 4Q is uniformly distributed in a noncunducting sphere with a radius of R. A point charge with a total charge of -Q is at the center of the sphere.
A. Derive an equation for the electric feild strength where r<R (in other words find the electric field strength when you at a radius less that R).
B. Make a diagram and show the gaussian surface that was used to derive the equation
D. Derive an equation for the value of R such that E = 0
Suppose that we know that the electric field created by an infinitely long charged cylindrical rod is axial. Assume that the rod is an insulator and has a uniform positive interior charge density p0 and has a radius R.
a. Find the electric field both inside and outside the rod.
b. Explain why the rod's linear charge density (charge per unit length) is lambda = p0 * pi * R2.
c. Express the rod's external electric field in terms of lambda.
Chapter 25 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 25.1 - a. List all the uppercase letters that have the...Ch. 25.2 - The terms electric force, electric field, and...Ch. 25.2 - Prob. 25.3CECh. 25.3 - Which of the following expressions are correct...Ch. 25.3 - Find the electric flux through the three Gaussian...Ch. 25.4 - Prob. 25.6CECh. 25.7 - Is it possible for the charged solid sphere in...Ch. 25 - Which word or name has the same symmetry as the...Ch. 25 - Prob. 2PQCh. 25 - Prob. 3PQ
Ch. 25 - Prob. 4PQCh. 25 - Prob. 5PQCh. 25 - Prob. 6PQCh. 25 - A positively charged sphere and a negatively...Ch. 25 - A circular hoop of radius 0.50 m is immersed in a...Ch. 25 - Prob. 9PQCh. 25 - If the hemisphere (surface C) in Figure 25.10...Ch. 25 - A Ping-Pong paddle with surface area 3.80 102 m2...Ch. 25 - Prob. 12PQCh. 25 - A pyramid has a square base with an area of 4.00...Ch. 25 - Prob. 14PQCh. 25 - Prob. 15PQCh. 25 - A circular loop with radius r is rotating with...Ch. 25 - A circular loop with radius r is rotating with...Ch. 25 - Prob. 18PQCh. 25 - What is the net electric flux through each of the...Ch. 25 - Prob. 20PQCh. 25 - The colored regions in Figure P25.21 represent...Ch. 25 - Prob. 22PQCh. 25 - Prob. 23PQCh. 25 - Three particles and three Gaussian surfaces are...Ch. 25 - A Using Gausss law, find the electric flux through...Ch. 25 - Three point charges q1 = 2.0 nC, q2 = 4.0 nC, and...Ch. 25 - Prob. 27PQCh. 25 - A very long, thin wire fixed along the x axis has...Ch. 25 - Figure P25.29 shows a wry long tube of inner...Ch. 25 - Two very long, thin, charged rods lie in the same...Ch. 25 - Prob. 31PQCh. 25 - Two long, thin rods each have linear charge...Ch. 25 - Figure P25.33 shows a very long, thick rod with...Ch. 25 - A very long line of charge with a linear charge...Ch. 25 - Two infinitely long, parallel lines of charge with...Ch. 25 - An infinitely long wire with uniform linear charge...Ch. 25 - Prob. 37PQCh. 25 - Prob. 38PQCh. 25 - Prob. 39PQCh. 25 - Prob. 40PQCh. 25 - Two uniform spherical charge distributions (Fig....Ch. 25 - FIGURE P25.41 Problems 41 and 42. Two uniform...Ch. 25 - The nonuniform charge density of a solid...Ch. 25 - Prob. 44PQCh. 25 - What is the magnitude of the electric field just...Ch. 25 - Prob. 46PQCh. 25 - The infinite sheets in Figure P25.47 are both...Ch. 25 - Prob. 48PQCh. 25 - Prob. 49PQCh. 25 - Prob. 50PQCh. 25 - A very large, flat slab has uniform volume charge...Ch. 25 - FIGURE P25.41 Problems 51 and 52. Find the surface...Ch. 25 - Prob. 53PQCh. 25 - Prob. 54PQCh. 25 - If the magnitude of the surface charge density of...Ch. 25 - A spherical conducting shell with a radius of...Ch. 25 - A charged rod is placed in the center along the...Ch. 25 - A charged rod is placed in the center along the...Ch. 25 - A thick spherical conducting shell with an inner...Ch. 25 - A thick spherical conducting shell with an inner...Ch. 25 - A rectangular plate with sides 0.60 m and 0.40 m...Ch. 25 - Prob. 62PQCh. 25 - Prob. 63PQCh. 25 - A uniform spherical charge distribution has a...Ch. 25 - A rectangular surface extends from x = 0 to x =...Ch. 25 - A uniform electric field E = 1.57 104 N/C passes...Ch. 25 - A solid plastic sphere of radius R1 = 8.00 cm is...Ch. 25 - Examine the summary on page 780. Why are...Ch. 25 - Prob. 69PQCh. 25 - Prob. 70PQCh. 25 - Prob. 71PQCh. 25 - A coaxial cable is formed by a long, straight wire...Ch. 25 - Prob. 73PQCh. 25 - Prob. 74PQCh. 25 - A solid sphere of radius R has a spherically...Ch. 25 - A solid sphere of radius R has a spherically...Ch. 25 - A very large, horizontal conducting square plate...Ch. 25 - Prob. 78PQCh. 25 - A particle with charge q = 7.20 C is surrounded by...Ch. 25 - A sphere with radius R has a charge density given...
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
- If the curved rod in Figure P24.32 has a uniformly distributed charge Q = 35.5 nC, radius R = 0.785 m, and = 60.0, what is the magnitude of the electric field at point A?arrow_forwardTwo positively charged spheres are shown in Figure P24.70. Sphere 1 has twice as much charge as sphere 2. If q = 6.55 nC, d = 0.250 m, and y = 1.25 m, what is the electric field at point A?arrow_forwardA very long, thin wire fixed along the x axis has a linear charge density of 3.2 C/m. a. Determine the electric field at point P a distance of 0.50 m from the wire. b. If there is a test charge q0 = 12.0 C at point P, what is the magnitude of the net force on this charge? In which direction will the test charge accelerate?arrow_forward
- A coaxial cable is formed by a long, straight wire and a hollow conducting cylinder with axes that coincide. The wire has charge per unit length = 20, and the hollow cylinder has net charge per unit length = 30. Use Gausss law to answer these questions: What are the charges per unit length on a. the inner surface and b. the outer surface of the hollow cylinder? c. What is the electric field a radial distance d from the axis of the coaxial cable?arrow_forwardA When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Lets see what happens if we break a finite rod up into a small number of finite particles. Figure P24.77 shows a rod of length 2 carrying a uniform charge Q modeled as two particles of charge Q/2. The particles are at the ends of the rod. Find an expression for the electric field at point A located a distance above the midpoint of the rod using each of two methods: a. modeling the rod with just two particles and b. using the exact expression E=kQy12+y2 c. Compare your results to the exact expression for the rod by finding the ratio of the approximate expression to the exact expression. FIGURE P24.77 Problems 77 and 78.arrow_forwardA thin wire with linear charge density =0y0(14+1y) extends from y0 = 1.00 m to infinity. If 0 = 1.45 105 C/m, what is the magnitude of the electric field due to this wire at the origin (y is measured in meters)?arrow_forward
- A solid sphere of radius R has a spherically symmetrical, nonuniform volume charge density given by (r) = A/r, where r is the radial distance from the center of the sphere in meters, and A is a constant such that the density has dimensions M/L3. a. Calculate the total charge in the sphere. b. Using the answer to part (a), write an expression for the magnitude of the electric field outside the spherethat is, for some distance r R. c. Find an expression for the magnitude of the electric field inside the sphere at position r R.arrow_forwardTime left C For which of the following charge distributions would Gauss's law not be useful for calculating the electric field? a spherical shell of radius R with charge uniformly distributed over its surface O a. O b. an infinitely long cylinder of radius R with charge uniformly distributed over its surface Oc. a uniformly charged sphere of radius R an infinite planar sheet having constant surface charge density Oe a cylinder of radius R and height h with charge uniformly distributed over its surface NEXT PAGEarrow_forwardA very long, uniformly charged cylinder has radius R and linear charge density λ. a. Find the cylinder's electric field strength outside the cylinder, r≥R. Give your answer as a multiple of λ/ε0. Express your answer in terms of some or all of the variables R, r, and the constant π. b. Find the cylinder's electric field strength inside the cylinder, r≤R. Give your answer as a multiple of λ/ε0. Express your answer in terms of some or all of the variables R, r, and the constant π.arrow_forward
- Electric Fields 3. A plastic rod is bent into the quarter circle of radius R as shown below. A total positive charge of Q is evenly distributed along the rod. a. In terms of the given quantities, what is the linear charge density A? b. Set up the two integrals you would evaluate to find the components of the electric field. The integrals should be written in terms of the given quantities {Q and R} Ex Ey с. Evaluate your integrals to write down the electric field vector at the origin. y E = -f 10 + +arrow_forward. The space between the plates of a parallel-plate capacitor is filled with two slabs of linear dielectric material. Each slab has thickness 2a, so the total distance between the plates is 4a. Slab 1 has a dielectric constant of 2, and slab 2 has a diclectric constant of 1.5. The free charge density on the top plate is o and on the bottom plate -o. a. Find the electric displacement D in each slab. b. Find the electric field E in each slab. Find the polarization P in each slab. Find the potential difference between the plates. Find the location and amount of all bound charge. f. Now that you know all the charge (free and bound), recalculate the field in each slab, and confirm your answer to (b). 2a Slab | Slab 2 2aarrow_forwarda. Some discussions in the web refer electric field lines as“lines of force”. Discuss the advisability of thisdescription.b. Can an electric field exist in a region of space in whicha electric charge would not experience a force? Explain.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 LearningPrinciples 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