Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 25, Problem 34PQ
A very long line of charge with a linear charge density, λ, is parallel to another very long line of charge with a linear charge density, −2λ. Both lines are parallel to the y-axis, and are the same distance r from the y-axis, where the first wire is to the left of the origin and the second is to the right. Use Gauss’s law and the principle of superposition to find an expression for the magnitude of the electric field at the origin.
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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...
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- A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of , and the cylinder has a net charge per unit length of 2. From this information, use Gausss law to find (a) the charge per unit length on the inner surface of the cylinder, (b) the charge per unit length on the outer surface of the cylinder, and (c) the electric field outside the cylinder a distance r from the axis.arrow_forwardA solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown in Figure P19.75. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r a. (b) From this value, find the magnitude of the electric field for r a. (c) What charge is contained within a sphere of radius r when a r b? (d) From this value, find the magnitude of the electric field for r when a r b. (e) Now consider r when b r c. What is the magnitude of the electric field for this range of values of r? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density?arrow_forwardA circular ring of charge with radius b has total charge q uniformly distributed around it. What is the magnitude of the electric field at the center of the ring? (a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) none of those answersarrow_forward
- In which of the following contexts can Gausss law not be readily applied to find the electric field? (a) near a long, uniformly charged wire (b) above a large, uniformly charged plane (c) inside a uniformly charged ball (d) outside a uniformly charged sphere (e) Gausss law can be readily applied to find the electric field in all these contexts.arrow_forwardConsider a thin, spherical shell of radius 14.0 cm with a total charge of 32.0 C distributed uniformly on its surface. Find the electric field (a) 10.0 cm and (b) 20.0 cm from the center of the charge distribution.arrow_forwardFind an expression for the magnitude of the electric field at point A mid-way between the two rings of radius R shown in Figure P24.30. The ring on the left has a uniform charge q1 and the ring on the right has a uniform charge q2. The rings are separated by distance d. Assume the positive x axis points to the right, through the center of the rings. FIGURE P24.30 Problems 30 and 31.arrow_forward
- Consider the charge distribution shown in Figure P19.74. (a) Show that the magnitude of the electric field at the center of any face of the cube has a value of 2.18 keq/s2. (b) What is the direction of the electric field at the center of the top face of the cube?arrow_forwardTwo solid spheres, both of radius 5 cm, carry identical total charges of 2 C. Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume. (i) How do the magnitudes of the electric fields they separately create at a radial distance of 6 cm compare? (a) EA EB = 0 (b) EA EB 0 (c) EA = EB 0 (d) 0 EA EB (e) 0 = EA EB (ii) How do the magnitudes of the electric fields they separately create at radius 4 cm compare? Choose from the same possibilities as in part (i).arrow_forwardFigure P15.49 shows a closed cylinder with cross-sectional area A = 2.00 m2. The constant electric field E has magnitude 3.50 103 N/C and is directed vertically upward, perpendicular to the cylinder's top and bottom surfaces so that no field lines paw through the curved surface. Calculate the electric flux through the cylinder's (a) lop and (b) bottom surface, (c) Determine the amount of charge inside the cylinder. Figure P15.49arrow_forward
- The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?arrow_forwardTwo infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .arrow_forwardTwo very long, thin, charged rods lie in the same plane (Fig. P25.30). One rod is positively charged with charge per unit length +, and the other is negatively charged with charge per unit length . The perpendicular distance between the rods is R. Using the coordinate system shown in the figure, sketch the electric field as a function of r from R to +2R. FIGURE P25.30arrow_forward
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Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY