Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 21, Problem 70P
Calculate the electric fields in Example 21.2 directly, using the superposition principle and integration. Consider the shell to be composed of charge elements that are coaxial rings, whose axes pass through the field point, which is a distance r from the center. (Hint: Consult Example 20.6. You'll have to evaluate the cases r < R and r > R separately.)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A slab of insulating material has a uniform positive charge density ρ, as shown in the figure below. The slab is infinite in the y and z directions.
Derive expressions for the field for the following regions. (Use the following as necessary: ε0, ρ, d, and x as necessary.)
(a) the exterior regions (x > d/2)E = _____ in the +x +y +z direction(b) the interior region of the slab (0 < x < d/2)
E = _____ in the +x +y +z directionNote: your answers should be the same when x = d/2
A flat wire of infinite length has width W and charge density sigma. If we align the wire so that it is everywhere at y=0 and extends in x from x=d to x=d+L, then calculate the electric field at x=0. Hint: Treat the wire as an the sum of the contributions of many "long wires" where the linear charge density satisfies: lambda=sigma*L.
s of the 15.13 The Coaxial Cable. A long coaxial cable con-
sists of an inner cylindrical conductor with radius a and
an outer coaxial cylinder with inner radius b and outer
eld also radius c. The outer cylinder is mounted on insulating
supports and has no net charge. The inner cylinder has
a uniform positive charge per unit length A. Calculate
the electric field a) at any point between the cylinders,
a distance r from the axis; b) at any point outside the
outer cylinder. c) Graph the magnitude of the electric
field as a function of the distance r from the axis of the
cable, from r=0 to r = 2c. d) Find the charge per unit
length on the inner surface and on the outer surface of
-ntained
by the
can you
%3D
the outer cylinder.
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
A woman looks at her face in the handheld mirror. Rank the amount of her face she sees in the three situations ...
Conceptual Integrated Science
What force do the blades of a 4300-kg helicopter exert on the air when the helicopter is (a) hovering at consta...
Essential University Physics: Volume 1 (3rd Edition)
An alpha-particle (m=6.641027kg,q=3.21019C) moving with a velocity v=(2.0i4.0k)106m/s enters a region where E=(...
University Physics Volume 2
The force, when you push against a wall with your fingers, they bend.
Conceptual Physics (12th Edition)
32. || 200 J of heat is added to two gases, each in a sealed container. Gas 1 is in a rigid container that does...
College Physics: A Strategic Approach (4th Edition)
An ideal gas is made to undergo the cyclic process shown in Figure 1.10 (a). For each of the steps A, B, and C,...
An Introduction to Thermal Physics
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 long, insulating cylinder with a 33 cm radius has charge distributed uniformly throughout itsvolume. The cylinder has a charge per unit length of 4 uC/m.a) What is the electric field at point P, where r1 = 49 cmb) What is the volume charge density p?c) Now consider the cylinder to rotate about its cylindrical axis with constant angular velocity 77 rad/s. Byconsidering the Amperian loop (shown below), find the value of the magnetic field B at point P, where r2 = 16 cm.arrow_forwardExpress the answer in unit-vector notation by entering symbolic expressions in the boxes below.A rod is infinitely long with uniform linear charge density X along its length, where >> 0. The rod lies in an xy plane and is parallel to the ax axis as shown in Fig. 22.10.5. What is the symbolic expression for the electric field at the point labeled P in the figure, where the coordinates of point P are (a, b)? Give your answer in terms of λ and coordinates/distances displayed in the figure. Express the answer in unit-vector notation by entering symbolic expressions in the boxes below. Note: You might find it useful to refer to Interactive Exercises 22.9. There you will find the derivation for the electric field produced by a uniformly charged rod of infinite length. D Infinitely-long rod with uniform linear charge density > 0 Ē=0✔ i+ P X(a, b) +X Interactive Figure 22.10.5: An infinitely long rod is parallel to the x axis. The field point P is at coordinates x = a, y = b. 2 2л(D - 6) Ĵ+ 0…arrow_forwardCommon data for Q. 7 and Q. 8. Consider two concentric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given Q amount of positive charges. 7. The electric field in different regions are (a) E= 0 for rd CAREER ENDEAVOUR. (b) E= î for rd (c) E =-,i for r a; = 0 for a d In order to have equal surface charge densities on the outer surfaces of both the shells, the following conditions should be satisfied 8. (b) d= 2b and c = 2a (d) d> b and c = 2a (a) d = 4b and c = 2a (c) d = /2b and e>aarrow_forward
- Two 1.20m nonconducting wires form a right angle. One segment has charge q1=4.0 nC uniformly distributed along its length, the other segment has charge q2 = –6.0 nC uniformly distributed along its length. Point P lies on the central axis of each wire and is 60.0 cm apart. a. The horizontal component of the net electric field at point P is:______N/C. in i or -i. b. The vertical component of the net electric field at point P is:______ N/C. in j or -j. c. The magnitude of the net electric field at point P is:______N/C. d.its direction measured with respect to the x-axis is:_____.arrow_forwardConsider the following. (image) (a) Figure (a) shows a nonconducting rod of length L = 9.00 cm and uniform linear charge density λ = +2.16 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 8.00 cm along the rod's perpendicular bisector? ________________mV(b) Figure (b) shows an identical rod, except that one half is now negatively charged. Both halves have a linear charge density of magnitude 2.16 pC/m. With V = 0 at infinity, what is V at P? ________________mVarrow_forward2. (1) A circular ring of radius R has a linear charge density C/m; see Fig. 23.48. (a) What is the field strength along the axis at a distance x from the center? (b) For what value of x is the field a maximum? (c) How should the field strength vary for x > R? Verify that your function meets this crite- rion. (d) Sketch qualitatively the field strength as a function of x. R FIGURE 23.47 Problem 2.arrow_forward
- A thin rod lies along the positivex-axis and has uniform linear charge density λ= +6.0×10−15C/m. Its left end is located at x0= +2.0 m, and its right end extends out to infinity.An electron is placed at the origin and released from rest.Determine the electron’s acceleration immediately after beingreleased. (Hint: this will require building and evaluating anintegral.) In your diagram, make sure to pick out an arbitraryelement of charge along the rod, and indicate the force it exertson the electron. For your limit check, investigate what happensto the electron’s initial acceleration as the left end of the rodis moved closer to the origin (i.e., as x0→0).arrow_forwardGauss's law Formulated by Karl Friedrich Gauss (1777-1855), a German Mathematician. Provide a means in determining the electric field or electric field intensity as produced by charge (point or distributed). Since Coulombs Law is already popular in point charges, Gauss's Law is more useful in distributed charges specially if it is symmetrically distributed in a closed system, such as charges in long wire or in a relatively infinite plane. Electric field E for uniformly distributed system Charge distribution Point of Electric Field Figure interest Charge q distributed on the surface of a conducting with radius R outside sphere; r > R 1 q E = 4T€, r² inside sphere: E = 0 r< R Long wire, with uniform distribution at a distance r from the wire E = charge per unit length A 2nɛ, r Infinite plane sheet, with a charge per at any distance from the plate E = 2πεο unit area o Two conducting plates oppositely charged, with densities o and – o at any point between the E = conducting plate ACTIVITY:…arrow_forwarddo it with electromgnatic , with stepse clear hand write. please do allarrow_forward
- Consider a point charge Q sitting at the center of a spherical, linear dielectric shell with a permittivity of ϵ, and an inner radius a and outer radius b. Where the polarization P = Q/(4*pi*r^2) (1-(e_0/e)) r-hat. part a) Find the the bound volume charge densities in the dielectric as well as thebound surface charge densities at the two surfaces (r = a and r = b). part b) What is the energy of this configuration?arrow_forwardTwo isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density o. The spheres are located far away from each other, and connected by a thin conducting wire. Find the new charge density on the bigger sphere.arrow_forwardWhich of the following charge distributions will generate a uniform electric field at the specified distance? Select all that apply. a) A distance r from the center of a long, thin line of uniform charge with length L where r << L. b)A distance r away from a large disc of uniform charge (with radius R) where r << R (and not near the edge of the disc) c)A distance r away from a sheet of uniform charge (with dimensions a x a) where r << a (and not near the edge of the sheet). d)Any point between two infinitely large sheets of uniform charge, one with total charge +Q and the other with total charge -Q. e)A distance r from the center of a sphere of uniform charge (with radius R) where r >> R. f)Halfway between two infinitely large sheets of uniform charge, each with total charge -Q.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
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher: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
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
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