Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
9th Edition
ISBN: 9781305372337
Author: Raymond A. Serway | John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 24, Problem 58AP
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.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A nonconducting spherical shell of inner radius x and outer radius y has a
positive volume charge density p=A/r, where A is constant and r is the
distance from the center of the shell. A positive charge q is located at the
center of the shell. Find an expression of A if the electric field at x
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?
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?
Chapter 24 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
Ch. 24.1 - Suppose a point charge is located at the center of...Ch. 24.2 - If the net flux through a gaussian surface is...Ch. 24 - Prob. 1OQCh. 24 - Prob. 2OQCh. 24 - Prob. 3OQCh. 24 - Prob. 4OQCh. 24 - Prob. 5OQCh. 24 - Prob. 6OQCh. 24 - Prob. 7OQCh. 24 - Prob. 8OQ
Ch. 24 - Prob. 9OQCh. 24 - Prob. 10OQCh. 24 - Prob. 11OQCh. 24 - Prob. 1CQCh. 24 - Prob. 2CQCh. 24 - Prob. 3CQCh. 24 - Prob. 4CQCh. 24 - Prob. 5CQCh. 24 - Prob. 6CQCh. 24 - Prob. 7CQCh. 24 - Prob. 8CQCh. 24 - Prob. 9CQCh. 24 - Prob. 10CQCh. 24 - Prob. 11CQCh. 24 - A flat surface of area 3.20 m2 is rotated in a...Ch. 24 - A vertical electric field of magnitude 2.00 104...Ch. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - A nonuniform electric field is given by the...Ch. 24 - An uncharged, nonconducting, hollow sphere of...Ch. 24 - Prob. 8PCh. 24 - Prob. 9PCh. 24 - Prob. 10PCh. 24 - Prob. 11PCh. 24 - A charge of 170 C is at the center of a cube of...Ch. 24 - Prob. 13PCh. 24 - A particle with charge of 12.0 C is placed at the...Ch. 24 - Prob. 15PCh. 24 - Prob. 16PCh. 24 - Prob. 17PCh. 24 - Find the net electric flux through (a) the closed...Ch. 24 - Prob. 19PCh. 24 - Prob. 20PCh. 24 - Prob. 21PCh. 24 - Prob. 22PCh. 24 - Prob. 23PCh. 24 - Prob. 24PCh. 24 - Prob. 25PCh. 24 - Determine the magnitude of the electric field at...Ch. 24 - A large, flat, horizontal sheet of charge has a...Ch. 24 - Prob. 28PCh. 24 - Prob. 29PCh. 24 - A nonconducting wall carries charge with a uniform...Ch. 24 - A uniformly charged, straight filament 7.00 m in...Ch. 24 - Prob. 32PCh. 24 - Consider a long, cylindrical charge distribution...Ch. 24 - A cylindrical shell of radius 7.00 cm and length...Ch. 24 - A solid sphere of radius 40.0 cm has a total...Ch. 24 - Prob. 36PCh. 24 - Prob. 37PCh. 24 - Why is the following situation impossible? A solid...Ch. 24 - A solid metallic sphere of radius a carries total...Ch. 24 - Prob. 40PCh. 24 - A very large, thin, flat plate of aluminum of area...Ch. 24 - Prob. 42PCh. 24 - Prob. 43PCh. 24 - Prob. 44PCh. 24 - A long, straight wire is surrounded by a hollow...Ch. 24 - Prob. 46PCh. 24 - Prob. 47PCh. 24 - Prob. 48APCh. 24 - Prob. 49APCh. 24 - Prob. 50APCh. 24 - Prob. 51APCh. 24 - Prob. 52APCh. 24 - Prob. 53APCh. 24 - Prob. 54APCh. 24 - Prob. 55APCh. 24 - Prob. 56APCh. 24 - Prob. 57APCh. 24 - An insulating solid sphere of radius a has a...Ch. 24 - Prob. 59APCh. 24 - Prob. 60APCh. 24 - Prob. 61CPCh. 24 - Prob. 62CPCh. 24 - Prob. 63CPCh. 24 - Prob. 64CPCh. 24 - Prob. 65CPCh. 24 - A solid insulating sphere of radius R has a...Ch. 24 - Prob. 67CPCh. 24 - Prob. 68CPCh. 24 - Prob. 69CP
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 nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r R)?arrow_forwardAn insulating solid sphere of radius a has a uniform bulk density ρ and a total positive charge Q. Calculate the magnitude of the electric field at a point outside the sphere.arrow_forwardA positively charged cylinder has a uniform volume charge density. Height l is larger than its radius a (1»a). a P a. When Point P is very close to the surface of the cylinder (1>r>a), the electric field there can be derived by treating the cylinder as an = Eŝ. infinitely long one. Suppose that we already measure the electric field at P as charge density in terms of E and a (ŝ is the radial unit vector in the cylindrical coordinate system as defined in the Equation: now use the Gauss's law to find the volume cos o â + sin ø ŷ, - sin ø Âx + cos ø ŷ, î. b. Now we move the detector from Point P to Point Q, which is so far away from the cylinder (R>l>a), that the cylinder can be treated as a point. Based on result in Part (a), find out the electric field at Q (Note that OQ is in the x direction.)arrow_forward
- A spherical insulator with radius R is centered at the origin. The volume charge density p of the insulator is non-uniform and varies with position according to p(r) = ar, where a is a constant. Derive an expression for the electric field E(r) for all points outside the sphere (r > R). Hint: finding the total charge of the sphere will require an integral.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_forwardFigure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distancer from the common axis. The vertical axis scale is set by E, -4.5 x 10° N/C. What is the linear charge density of the shell? Number E r(cm) (A) Units 13.8arrow_forward
- Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from the common axis. The vertical axis scale is set by E; = 3.9 x 10° N/C. What is the linear charge density of the shell?arrow_forwarda) Find the surface charge density σ2 of the cylindrical shell of radius R2. (Note the unit in the input box and the sign of charges.) Surface charge density σ2Give your answer up to at least three significance digits. b) Find an expression of electric field at rmm from the center where R1<r<R2. Assume the cylinder has a length L and L is very long so that electric field is uniform. Consider that the insulating material between the cylinders is air. (Hint : use Gauss's law and cylindrical Gaussian surface with radius r.) Magnitude of the electric field at r=0.76mm Give your answer up to at least three significance digits. c) Calculate absolute value of the potential difference between the wire and the cylinder. Absolute value of the potential difference Give your answer up to at least three significance digits. d) Calculate the capacitance C for this cylindrical system. Assume that the length of the cylinder is L=17cm. Capacitance C for this cylindrical system Give your…arrow_forwardAn 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_forward
- Charge density p Figure 2: (True,False) (a) The electric field inside the sphere is given by Ē = (7 – b) An insulating sphere of radius R has a spherical hole of radius a located within its volume and centered a distance b from the center of the sphere where a < b < R(a cross section of the sphere is shown in figure 2). The solid part of the sphere has a uniform volume charge density p: (b) The electric field inside the hole is constant and is given by : (F – 6) = (True, False) -デ+ E = Ësphere + E(-p) 3e0 3e0 3€0 - 2rb cos 0: (c) The electric field inside the sphere of radius R but outside the hole of radius a is not constant and is given by |7–6| = /r2 + b² -pa3 デー5 デ+ (True, False) - 6|3 E = Ësphere + Ē(-P) 3e0 3e0 F –arrow_forwardFigure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from the common axis. The vertical axis scale is set by E, = 3.3 × 10³ N/C. What is the linear charge density of the shell? (a) Number -E₂ r (cm) 6 Units 11.4 >arrow_forwardConsider a cylindrical insulator of radius R and length L. This object has a surface charge density of σ(Φ) = a sin(5Φ) ( sigma(phi) = a sin(5(phi)) ) where a is a constant. If L >> R, determine the electric field inside and outside the cylinder.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author: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
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