Concept explainers
CALC A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows:
where ρ0 is a positive constant. (a) Find the total charge contained in the charge distribution. Obtain an expression for the electric field in the region (b) r ≥ R; (c) r ≤ R. (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field.
Learn your wayIncludes step-by-step video
Chapter 22 Solutions
University Physics with Modern Physics (14th Edition)
Additional Science Textbook Solutions
Genetic Analysis: An Integrated Approach (3rd Edition)
Campbell Biology (11th Edition)
Campbell Biology: Concepts & Connections (9th Edition)
Microbiology: An Introduction
Human Physiology: An Integrated Approach (8th Edition)
Chemistry: A Molecular Approach (4th Edition)
- A cylinder of length L=5m has a radius R=2 cm and linear charge density 2=300 µC/m. Although the linear charge density is a constant through the cylinder, the charge density within the cylinder changes with r. Within the cylinder, the charge density of the cylinder varies with radius as a function p( r) =p.r/R. Here R is the radius of the cylinder and R=2 cm and p, is just a constant that you need to determine. b. Find the constant po in terms of R and 2. Then plug in values of R and 1. to find the value for the constant p. c. Assuming that L>>R, use Gauss's law to find out the electric field E inside the cylinder (rR) in terms of 1. and R. d. Based on your result from problem c, find the electric field E at r=1cm and r=4cm.arrow_forwardA charged nonconducting rod has a length L of 2.0 m and a cross-sectional area A of 8.0 cm?; it is placed along the positive side of an x axis with one end at the origin. The volume charge density p is the charge per unit volume, with the units of coulomb per cubic meter. a) How many excess electrons are on the rod if the rod's volume charge density pu is uniform with a value of –10 µC/m³? How does that compare to the total number of electrons you would estimate would be in the rod? (By compare, just a ballpark estimate- to within several orders of magnitude, factors of ten). b) What is an expression for the number of excess electrons on the rod if the rod's volume charge is nonuniform and is given instead by pN=ax³ where a is a constant? c) What value of a is necessary for the rod in part b to have the same number of excess electrons as the rod in part a)?arrow_forwardDon't use chat gpt It plzarrow_forward
- E6P12arrow_forwardA non-uniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−4r/3R) for r≤R ρ(r)=0 for r≥R ρ0 is a positive constant Obtain an expression for the electric field in the region r ≤ Rarrow_forwardAn isolated conductor has a net charge of +12.0 x 10 6 C and a cavity with a particle of chargeq = +3.50 x 10-6 C. What is the charge (a) on the cavity wall and (b) on the outer surface? (a) Number Units (b) Number Unitsarrow_forward
- can you please ans (a) & (b)?arrow_forwardAn 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_forwardIn 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_forward
- = Three uniform charge distributions are present in a region: an infinite sheet of charge, a finite line charge, and a ring of charge. The infinite sheet of charge at (x, -3, z), where x and z spans from negative to positive infinity, has a charge density Ps 5 nC/m². The finite line charge at (0, -1, z), where z ranges from -2 to 2, has a charge density -4 nC/m. Finally, the ring of charge, with a radius of 3m and charge density PL 2 nC/m, is parallel to the xz-plane centered at (0, 4, 0). All coordinates are in meters. Use the value k = 9 x 10⁹ in your solutions and = answers. Question: Determine the magnitude the electric field due to the infinite sheet charge only at (0, 2, 0).arrow_forwardElectric charge is distributed over the disk a2 + y < 20 so that the charge density at (x,y) is o(x, y) = 5 + x² + y² coulombs per square meter. Find the total charge on the disk.arrow_forwardCharge is distributed throughout a spherical volume of radius R with a density ρ = αr2, where α is a constant. Determine the electric field due to the charge at points both inside and outside the sphere.arrow_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 Learning
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning