Concept explainers
CALC Self-Energy of a Sphere of Charge. A solid sphere of radius R contains a total charge Q distributed uniformly throughout its volume. Find the energy needed to assemble this charge by bringing infinitesimal charges from far away. This energy is called the “self-energy” of the charge distribution. (Hint: After you have assembled a charge q in a sphere of radius r, how much energy would it take to add a spherical shell of thickness dr having charge dq? Then integrate to get the total energy.)
Want to see the full answer?
Check out a sample textbook solutionChapter 23 Solutions
University Physics (14th Edition)
Additional Science Textbook Solutions
Essential University Physics: Volume 1 (3rd Edition)
Modern Physics
The Cosmic Perspective (8th Edition)
Tutorials in Introductory Physics
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
- a. 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 Two positively charged spheres with charges 4e and e are separated by a distance L and held motionless. A third charged sphere with charge Q is set between the two spheres and along the line joining them. The third sphere is in static equilibrium. What is the distance between the third charged sphere and the sphere that has charge 4e?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_forward
- Calculate the electric field due to a uniformly charged rod of length L, aligned with the x-axis with one end at the origin; at a point P on the z-axis.arrow_forwardProblems 72, 73, and 74 are grouped. 72. A Figure P26.72 shows a source consisting of two identical parallel disks of radius R. The x axis runs through the center of each disk. Each disk carries an excess charge uniformly distributed on its surface. The disk on the left has a total positive charge Q, and the disk on the right has a total negative charge Q. The distance between the disks is 3R, and point A is 2R from the positively charged disk. Find an expression for the electric potential at point A between the disks on the x axis. Approximate any square roots to three significant figures. FIGURE P26.72 Problems 72, 73, and 74.arrow_forwardA particle with charge q on the negative x axis and a second particle with charge 2q on the positive x axis are each a distance d from the origin. Where should a third particle with charge 3q be placed so that the magnitude of the electric field at the origin is zero?arrow_forward
- An insulating sphere of radius a is placed at the center of a spherical conductor whose inner radius is b and outer radius is c (see figure). The +Q charge is uniformly distributed throughout the insulator sphere, while the spherical shell is -Q charged. Find the electric field strength E as a function of the radial distance r, a. inside the insulator ball (r<a) b. in a<r<b c. inside the spherical shell (b<r<c) d. outside the shell (r>c) e. How much charge on the inner surface of the spherical conductor (r= b), and how much on the outer surface of the spherical conductor (r = c)?arrow_forwardA point charge, Q1 = -4.2 μC, is located at the origin. A rod of length L = 0.35 m is located along the x-axis with the near side a distance d = 0.45 m from the origin. A charge Q2 = 10.4 μC is uniformly spread over the length of the rod. Part (a) Consider a thin slice of the rod, of thickness dx, located a distance x away from the origin. What is the direction of the force on the charge located at the origin due to the charge on this thin slice of the rod? Part (b) Write an expression for the magnitude of the force on the point charge, |dF|, due to the thin slice of the rod. Give your answer in terms of the variables Q1, Q2, L, x, dx, and the Coulomb constant, k. Part (c) Integrate the force from each slice over the length of the rod, and write an expression for the magnitude of the electric force on the charge at the origin. Part (d) Calculate the magnitude of the force |F|, in newtons, that the rod exerts on the point charge at the origin.arrow_forwardSuppose that a conducting sphere is charged positively by some method. The charge is initially deposited on the left side of the sphere. Yet because the object is conductive, the charge spreads uniformly throughout the surface of the sphere. The uniform distribution of charge is explained by the fact that ____. a. the charged atoms at the location of charge move throughout the surface of the sphere b. the excess protons move from the location of charge to the rest of the sphere c. excess electrons from the rest of the sphere are attracted towards the excess protonsarrow_forward
- Compute for the work done, in millijoules, in moving a 8-nC charge from A(0, 0, 1) m to B(0, 0, 7) m against the electric field due to a ring charge of radius 9 m on the plane z = 0 centered at the origin. The ring has a total charge of 8 mC.arrow_forwardConsider an infinite line of charge, with linear charge density +3.5 x 10-12 C/m. This line of charge is parallel to the z-axis and intersects the x-y plane on the x axis at x = -6.7 m. Now consider a second infinite line of charge, with linear charge density +2 x 10-12 C/m. This line of charge is also parallel to the z-axis and intersects the x-y plane on the x axis at x = +14.3 m. Calculate the magnitude of electric field, in N/C, at the origin. Use ε 0 = 8.9 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forwardSuppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the functionarrow_forward
- 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