PHYSICS F/SCI (LL) + MOD MAST ACC >BI<
4th Edition
ISBN: 9780134893365
Author: Knight
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 24, Problem 53EAP
II A long cylinder with radius b and volume charge density p has a spherical hole with radius a < b centered on the axis of the cylinder. What is the electric field strength inside the hole at radial distance r Hint: Can you create this charge distribution as a superposition of charge distributions for which you can use Gauss's law to find the electric field?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
c.
i. Compare the electric flux in a cubical surface of a side 10cm and spherical surface ofradius 10 cm, when a charge of 5µC is enclosed by them.ii. How does the electric field enclosing a given charge vary when the area enclosed bythe charged is doubled. Assuming the electric flux is constant.
a)
A solid sphere, made of an insulating material, has a volume charge density of
? = a/r,
where r is the radius from the center of the sphere, a is constant, and
a > 0.
What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4?r2dr. (Use the following as necessary: a, r, and ?0.)
b.)
What If? What if the charge density as a function of r within the charged solid sphere is given by
? = a/r^2?
Find the new magnitude and direction of the electric field within the sphere at radius r. (Use the following as necessary: a, r, and ?0.)
(a) A solid sphere, made of an insulating material, has a volume charge density of ρ = a/r, where r is the radius from the center of the sphere, a is constant, and a > 0. What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr. (Use the following as necessary: a, r, and ε0.)
magnitude E=________
direction: radially outward, radially inward, or no direction?
(b) What If? What if the charge density as a function of r within the charged solid sphere is given by ρ = a/r2? Find the new magnitude and direction of the electric field within the sphere at radius r. (Use the following as necessary: a, r, and ε0.)
magnitude E=_________
direction: radially outward, radially inward, or no direction?
Chapter 24 Solutions
PHYSICS F/SCI (LL) + MOD MAST ACC >BI<
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
- A sphere with radius R has a charge density given by = cr3. Use Gausss law to find an expression for the magnitude of the electric field at a distance r from the center of the sphere, where a. r R and b. r R.arrow_forwardIf the hemisphere (surface C) in Figure 25.10 (page 760) is tilted so that its disk-shaped cross section makes a 25 angle with the electric field, what is the electric flux through the hemisphere? Use Example 25.1 to check your result.arrow_forwardA 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 of M/L3. Sketch a graph of the magnitude of the electric field as a function of distance for 0 r 3R.arrow_forward
- (a) Calculate the electric flux through the open hemispherical surface due to the electric field E =E0k (see below). (b) If the hemisphere is rotated by 90( around the what is the flux through it?arrow_forwardA cylinder with radius r = 0.75m and length l = 0.6m that has an infinite line of positive charge running along its axis. The charge per unit length in the line is 7µc/m. i. What is the electric flux through the cylinder due to this line of charge? ii. What is the flux through the cylinder if its radius increased to r = 0.32m? iii. What is the electric field intensity at radius r = 0.32m and l = 0.6m? iv. What is the flux through the cylinder if its length increased to l=0.8m? v. What is the electric field intensity at radius r= 0.32 and l=0.8m? vi. Briefly explain the effect of an increase or decrease of radius and length on the electric field intensity.arrow_forward(a) A cubic shape conductor with edge length 2m has 16C charge (i) What will be the electric flux? (ii) What will be the flux if the cube edge length increases to 4m? (ii) Calculate the flux density for a casearrow_forward
- The electric field at point P just outside the outer surface of a hollow spherical conductor of inner radius 10 cm and outer radius 20 cm has magnitude 450 N/C and is directed outward. When a particle of unknown charge Q is introduced into the center of the sphere, the electric field at P is still directed outward but is now 180 N/C. (a) What was the net charge enclosed by the outer surface before Q was introduced? (b)What is charge Q? After Q is introduced, what is the charge on the (c) inner and (d) outer surface of the conductor?arrow_forwardIn Figure 1, a non-conducting rod of length L = 10.0 cm has a charge –q = -3.0 fCuniformly distributed along its length.a) What is the linear charge density of the rod?b) What are the magnitude and direction of the electric field produced at point P, atdistance of a = 6.00 cm from the rod?c) What is the electric field magnitude produced at distance a=50m by the rod?arrow_forwardConsider a uniform electric field of E = ⟨E cos θ, E sin θ, 0⟩ and a flat disk of radius R. a) What is the electric flux through the disk if it sits in the xy-plane? b) What is the electric flux through the disk if it sits in the xz-plane?arrow_forward
- The electric field everywhere on the surface of a thin spherical shell of radius 0.750 m is measured to be equal to 890 N/C and point radially toward the center of the sphere. (a) What is the net charge within the sphere's surface? (b) What can you conclude about the nature and distribution of the charge inside the spherical shell?arrow_forward(a) An insulating sphere has radius R and uniform volume charge density ρ.Calculate the electric field at the point P which is inside (r < R) andoutside (r > R) of the sphere by using Gauss’s law. Here r is the distancebetween the center of the sphere and the point P.(b) Discuss the possibility of choosing Gaussian surface other than the sphere.For instance what if you choose the cylindrical surface as a Gaussian surface, is it possible to use Gauss’s law in order to calculate the electric fieldof a charged sphere? Explain your answer in detail.arrow_forward1) Consider a line charge of infinite extent in the Z direction with charge densityλ =λ0/(1 + ( Z/a)2) where λ0 is a positive constant • a) What is the total charge Q enclosed by an imaginary Gaussian surface of radius r? • b) What is the electric flux through this surface due to the line charge?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 Learning
Physics 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