Concept explainers
(a) In a certain region of space, the volume charge density ρ has a uniform positive value. Can
Want to see the full answer?
Check out a sample textbook solutionChapter 22 Solutions
Student's Solution Manual for University Physics with Modern Physics Volumes 2 and 3 (Chs. 21-44)
Additional Science Textbook Solutions
Essential University Physics: Volume 1 (3rd Edition)
Physics (5th Edition)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Conceptual Physical Science (6th Edition)
The Cosmic Perspective
Essential University Physics: Volume 2 (3rd Edition)
- An infinitely long cylinder in free space is concentric with the z-axis and has radius a. The net charge density p in this cylinder is given in cylindrical coordinates by, 1 a² +r² where A is a constant. (a) Show that the total charge per unit length, λ in the cylinder is λ = πA ln 2. p(r) = A- Hint: you may find the following integral useful. 1 2 J for r a) and inside the cylinder (r< a). (d) The cylinder is composed of a material in which the polarisation P is given by P = P₁² in (1 +5²) e₁₁ er, r where Po is a constant. Determine the bound charge density pb in the cylinder. Hence, or otherwise, determine a relation between A and Po such that the free charge density of in the cylinder vanishes.arrow_forwardAn infinitely long, solid insulating cylinder with radius Ra is placed concentric within a conducting cylindrical shell of inner radius R, and outer radius Re. The inner cylinder has a uniform volume charge density +[pl, and the outer cylinder has a net linear charge density of -3121. Assume Ip Rål> 132 for all parts. a. Sketch the scenario, indicating how much charge is in each region/surface. What are the charge densities on the inner and outer surfaces of the conducting cylinder? Part a. may be made easier by providing your answer in terms A' = pRa (the 'linear charge density' of the inner cylinder), instead of p.arrow_forwardA 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_forward
- In free space, a linear charge density > is on the z axis. Get the electric force over a unit charge "q" located at P (1, 2, 3) m if the linear charge density is in -4 m < z < 4m = 2μC m Give the answer in unit vectors terms.arrow_forwardQUESTION 1 Problem: An infinitely long cylindrical conductor has radius R and uniform surface charge density o. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forwardA very long line charge having a charge density A is surrounded by a conducting cylindrical shell with inner radius r, = 4.87 cm and outer radius r = 7cm as shown in the figure. System is in electrostatic equilibrium condition. What would be the electric difference AV = V(r=0.55 cm) - V(r= 6.4 cm) ? Provide your answer in terms of Ak with 2 significant figures. potential 6 P Answer:arrow_forward
- As seen in Figure-3, there are loads with a volumetric charge density of pa=(3P)C/m^3 in the region with pε(0,a) of the coaxial cylinders nested in empty space.Radius p ε (b,c) in the region with a volumetric charge density pbc=(5/p^4)C/m^3, the cylinder surface with radius p=d It is very thin and on this surface σd=2C/m^2 density superficial charge. What is the electric field in each divided region? (a=2mm, b=4mm, c=6mm, d=8mm)arrow_forwardA surface of revolution is formed by rotating the function y = – about the x axis. Suppose you were to take the portion of this surface that is in the domain that goes from x=a to x=+∞ and turn it into an electrical conductor, and then place a finite charge +Q onto it. Once the conductor attains electrostatic equilibrium, how would its final surface charge density vary as Q is varied? O The surface charge density is always undefined, independently of how Q is varied O It varies in direct proportion to Q in the region where xarrow_forwardYou are calculating the electric field in all space given the above infinite slab of charge in the x-y plane, centered on z=0. The slab has an inhomogeneous charge density given by p = 6.5|2| in units of C/m³. The slab has a thickness of 7.8m in the z direction. 1) What is the magnitude of the electric field as a function of z inside the slab? Give your answers in terms of [z], and epsilon. E(|z| 3.9m) = = 0 |z|> 3.9m , for Instructionsarrow_forwardA spherical conducting shell with outer radius 3 meters carries total charge Q2 of -9 Coulombs. Inside the shell cavity is an object carrying total charge Q1 of -3 Coulombs. What is the total charge on the inner surface of the conducting shell? Make sure to give the proper sign.(Note that you are not being asked the total charge of the entire shell.)arrow_forwardFind the ratio of q/Q for the E-field to be zero at adistance of z = 3.52R for the charge distributionand geometry of problem #30 of the text. a isthe charge on the LARGER ring. Q is the chargeon the SMALLER ring.arrow_forwardAssume you have a proton in an atom, and that proton is surrounded by an electron shell where the charge is evenly distributed across the entire surface of the shellI. The proton would feel O a large repulsive net force. O no net electrostatic force. O force direction cannot be determined. O a large attractive net force.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON