Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 24, Problem 61EAP
II A spherical ball of charge has radius R and total charge Q. Theelectric field strength inside the ball (r < R) is E(r) = r4Emax /R4.
- What is E in terms of Q and R?
- Find an expression for the volume charge density p(r) inside the ball as a function of r.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
H
A very long line of a thin conducting wire produces a radial outward
electric field of magnitude 2.24 kN/C at a radial distance of 45.1 cm.
How much charge (in nC) is contained in a 5.52-m long length of this
wire?
A thick insulating cylindircal shell of inner radius a=2.8R and outer radius b=5.3R has a uniform
charge density p.
b
What is the magnitude of the electric field at r=9 R ? Express your answer using one decimal place in units of
pR
:?
€0
Two small insulating spheres with radius 6.50×10−2 m are separated by a large center-to-center distance of 0.600 m . One sphere is negatively charged, with net charge -2.40 μC , and the other sphere is positively charged, with net charge 3.95 μC . The charge is uniformly distributed within the volume of each sphere.
a.
What is the magnitude E of the electric field midway between the spheres?
Take the permittivity of free space to be ϵ0 = 8.85×10−12 C2/(N⋅m2) .
Chapter 24 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 24 - Suppose you have the uniformly charged cube in...Ch. 24 - FIGURE Q24.2 shows cross sections of...Ch. 24 - The square and circle in FIGURE Q24.3 are in the...Ch. 24 - Prob. 4CQCh. 24 - Prob. 5CQCh. 24 - What is the electric flux through each of the...Ch. 24 - Prob. 7CQCh. 24 - The two spheres in FIGURE Q24.8 on the next page...Ch. 24 - The sphere and ellipsoid in FIGURE Q24.9 surround...Ch. 24 - A small, metal sphere hangs by an insulating...
Ch. 24 - l. FIGURE EX24.1 shows two cross sections of two...Ch. 24 - FIGURE EX24.2 shows a cross section of two...Ch. 24 - FIGURE EX24.3 shows a cross section of two...Ch. 24 - The electric field is constant over each face of...Ch. 24 - The electric field is constant over each face of...Ch. 24 - The cube in FIGURE EX24.6 contains negative...Ch. 24 - The cube in FIGURE EX24.7 contains negative...Ch. 24 - The cube in FIGURE EX24.8 contains no net charge....Ch. 24 - What is the electric flux through the surface...Ch. 24 - What is the electric flux through the surface...Ch. 24 - II The electric flux through the surface shown in...Ch. 24 - ]12. A 2.0cm3.0cm rectangle lies in the xy-plane....Ch. 24 - A 2.0cm3.0cm rectangle lies in the xz-plane. What...Ch. 24 - Prob. 14EAPCh. 24 - 15. A box with its edges aligned with
the...Ch. 24 - What is the net electric flux through the two...Ch. 24 - FIGURE EX24.17 shows three charges. Draw these...Ch. 24 - Prob. 18EAPCh. 24 - FIGURE EX24.19 shows three Gaussian surfaces and...Ch. 24 - What is the net electric flux through the torus...Ch. 24 - What is the net electric flux through the cylinder...Ch. 24 - Prob. 22EAPCh. 24 - Prob. 23EAPCh. 24 - A spark occurs at the tip of a metal needle if the...Ch. 24 - The electric field strength just above one face of...Ch. 24 - The conducting box in FIGURE EX24.26 has been...Ch. 24 - FIGURE EX24.27 shows a hollow cavity within a...Ch. 24 - A thin, horizontal, 10-cm-diameter copper plate is...Ch. 24 - Prob. 29EAPCh. 24 - Prob. 30EAPCh. 24 - II A tetrahedron has an equilateral triangle base...Ch. 24 - Charges q1= —4Q and q2= +2Q are located at x = —a...Ch. 24 - Prob. 33EAPCh. 24 - A spherically symmetric charge distribution...Ch. 24 - A neutral conductor contains a hollow cavity in...Ch. 24 - Prob. 36EAPCh. 24 - 37. A 20-cm-radius ball is uniformly charged to 80...Ch. 24 - Prob. 38EAPCh. 24 - Prob. 39EAPCh. 24 - Prob. 40EAPCh. 24 - A hollow metal sphere has 6 cm and 10 cm inner and...Ch. 24 - Prob. 42EAPCh. 24 - Find the electric field inside and outside a...Ch. 24 - Prob. 44EAPCh. 24 - Prob. 45EAPCh. 24 - Prob. 46EAPCh. 24 - FIGURE P24.47 shows an infinitely wide conductor...Ch. 24 - FIGURE P24.48 shows two very large slabs of metal...Ch. 24 - Prob. 49EAPCh. 24 - A very long, uniformly charged cylinder has radius...Ch. 24 - Prob. 51EAPCh. 24 - Prob. 52EAPCh. 24 - II A long cylinder with radius b and volume charge...Ch. 24 - A spherical shell has inner radius Rin, and outer...Ch. 24 - Prob. 55EAPCh. 24 - Newton's law of gravity and Coulomb's law are both...Ch. 24 - Prob. 57EAPCh. 24 - An infinite cylinder of radius R has a linear...Ch. 24 - Prob. 59EAPCh. 24 - A sphere of radius R has total charge Q. The...Ch. 24 - II A spherical ball of charge has radius R and...
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
- HW1: Region y 0 is a dielectric medium (€,-1 = 2). If there is a surface charge of p, = 2 n on the conductor, determine E and D at (a) A (3,-2,2) (b) B (-4,1,5)arrow_forwardA wire with a negligible diameter is coaxial with a very thin cylindrical shell of radius R=4.79cm. Both are composed of an insulating material, and for practical purposes, they are infinitely long. The wire has a uniform linear charge density, λ1=−112pC/m, and the cylinder has a linear charge density, λ2=+531pC/m, that is uniformly distributed around its circumference. a. If r is the distance from the wire, then what is the magnitude, in newtons per coulomb, of the electric field at r=3.08cm. b. If r is the distance from the wire, then what is the magnitude, in newtons per coulomb, of the electric field at r=8.81cm.arrow_forwardQ. 30: A hollow spherical conductor of radius R has a charge Q on it. A small dent on the surface decreases the volume of the spherical conductor by 2%. Assume that the charge density on the surface does not change due to the dent and the electric field in the dent region remains same as other points on the surface. (a) AE is the electrostatic energy stored in the electric field in the shallow dent region and E is the total electrostatic energy of the spherical shell. Find the ΔΕ ratio E (b) Using the ratio obtained in part (a) calculate the percentage change in capacitance of the sphere due to the dent.arrow_forward
- A(i.) Sketch a graph showing how the electric field strength E varies with distance r from the center of a uniform solid metal sphere of radius ro, which is positively charged. (ii.) Explain the shape of your graph for r ro.arrow_forwardHuman nerve cells have a net negative charge and the material in the interior of the cell is a good conductor. If a cell has a net charge of -7.52 pC, a. what are the magnitude and direction (inward or outward) of the net flux through the cell boundary? b. what is the volume charge density passing through the cell? Assume that the portion of the cell in question is spherical with radius r 1.2 × 10¯6m.arrow_forwardA conducting sphere of radius r1 = 0.27 m has a total charge of Q = 2.6 μC. A second uncharged conducting sphere of radius r2 = 0.34 m connects to the first by a thin conducting wire. The spheres are separated by a very large distance compared to their size. a. What is the total charge on sphere two Q2 after they are connected, in coulombs? b. What is the surface charge density of the second sphere, σ2, after they are connected in coulombs per square meter?arrow_forward
- A 5 cm radius ball is charged to 190 nC. The charge is uniformly distributed throughout the volume of the ball. a. What is the charge density for this ball? ANS. 3.628733×10-4 C/m^3 b. How much charge is enclosed by a sphere of radius 1 cm concentric with the ball??arrow_forwarda. Figure 24.22A shows a rod of length L and radius R with excess positive charge Q. The excess charge is uniformly distributed over the entire outside surface of the rod. Write an expression for the surface charge density . Write an expression in terms of for the amount of charge dq contained in a small segment of the rod of length dx. b. Figure 24.22B shows a very narrow rod of length L with excess positive charge Q. The rod is so narrow compared to its length that its radius is negligible and the rod is essentially one-dimensional. The excess charge is uniformly distributed over the length of the rod. Write an expression for the linear charge density . Write an expression in terms of for the amount of charge dq contained in a small segment of the rod of length dx. Compare your answers with those for part (a). Explain the similarities and differences.arrow_forwardA thin, semicircular wire of radius R is uniformly charged with total positive charge Q (Fig. P24.63). Determine the electric field at the midpoint O of the diameter.arrow_forward
- Often we have distributions of charge for which integrating to find the electric field may not be possible in practice. In such cases, we may be able to get a good approximate solution by dividing the distribution into small but finite particles and taking the vector sum of the contributions of each. To see how this might work, consider a very thin rod of length L = 16 cm with uniform linear charge density = 50.0 nC/m. Estimate the magnitude of the electric field at a point P a distance d = 8.0 cm from the end of the rod by dividing it into n segments of equal length as illustrated in Figure P24.21 for n = 4. Treat each segment as a particle whose distance from point P is measured from its center. Find estimates of EP for n = 1, 2, 4, and 8 segments. FIGURE P24.21arrow_forward(a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 10.0 g. Silver has 47 electrons per atom, and its molar mass is 107.87 g/mol. (b) Imagine adding electrons to the pin until the negative charge has the very large value 1.00 mC. How many electrons are added for every 109 electrons already present?arrow_forwardA very large disk lies horizontally and has surface charge density = 2.3 nC/m2. An electron is released at the surface. (It begins from rest and moves vertically upward.) Ignoring gravity, find the speed of the electron when it is 1.0 mm above the disk.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 LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher: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
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY