Suppose that we know that the electric field created by an infinitely long charged cylindrical rod is axial. Assume that the rod is an insulator and has a uniform positive interior charge density p0 and has a radius R. a. Find the electric field both inside and outside the rod. b. Explain why the rod's linear charge density (charge per unit length) is lambda = p0 * pi * R2. c. Express the rod's external electric field in terms of lambda.

Suppose that we know that the electric field created by an infinitely long charged cylindrical rod is axial. Assume that the rod is an insulator and has a uniform positive interior charge density p0 and has a radius R. a. Find the electric field both inside and outside the rod. b. Explain why the rod's linear charge density (charge per unit length) is lambda = p0 * pi * R2. c. Express the rod's external electric field in terms of lambda.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 74PQ

See similar textbooks

Similar questions

A charged rod is curved so that it is part of a circle of radius R (Fig. P24.32). The excess positive charge Q is uniformly distributed on the rod. Find an expression for the electric field at point A in the plane of the curved rod in terms of the parameters given in the figure.
A coaxial cable is formed by a long, straight wire and a hollow conducting cylinder with axes that coincide. The wire has charge per unit length = 20, and the hollow cylinder has net charge per unit length = 30. Use Gausss law to answer these questions: What are the charges per unit length on a. the inner surface and b. the outer surface of the hollow cylinder? c. What is the electric field a radial distance d from the axis of the coaxial cable?
A Ping-Pong paddle with surface area 3.80 102 m2 is placed in a uniform electric field of magnitude 1.10 106 N/C. a. What is the magnitude of the electric flux through the paddle when the electric field is parallel to the paddles surface? b. What is the magnitude of the electric flux through the paddle when the electric field is perpendicular to the paddles surface?
A very long, thin wire fixed along the x axis has a linear charge density of 3.2 C/m. a. Determine the electric field at point P a distance of 0.50 m from the wire. b. If there is a test charge q0 = 12.0 C at point P, what is the magnitude of the net force on this charge? In which direction will the test charge accelerate?
A When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Lets see what happens if we break a finite rod up into a small number of finite particles. Figure P24.77 shows a rod of length 2 carrying a uniform charge Q modeled as two particles of charge Q/2. The particles are at the ends of the rod. Find an expression for the electric field at point A located a distance above the midpoint of the rod using each of two methods: a. modeling the rod with just two particles and b. using the exact expression E=kQy12+y2 c. Compare your results to the exact expression for the rod by finding the ratio of the approximate expression to the exact expression. FIGURE P24.77 Problems 77 and 78.
A solid sphere of radius R has a spherically symmetrical, nonuniform volume charge density given by (r) = A/r, where r is the radial distance from the center of the sphere in meters, and A is a constant such that the density has dimensions M/L3. a. Calculate the total charge in the sphere. b. Using the answer to part (a), write an expression for the magnitude of the electric field outside the spherethat is, for some distance r R. c. Find an expression for the magnitude of the electric field inside the sphere at position r R.
Two positively charged spheres are shown in Figure P24.70. Sphere 1 has twice as much charge as sphere 2. If q = 6.55 nC, d = 0.250 m, and y = 1.25 m, what is the electric field at point A?
A sphere with radius R has a charge density given by = cr3. Use Gausss law to find an expression for the magnitude of the electric field at a distance r from the center of the sphere, where a. r R and b. r R.
The electric field at a distance of 0.154 m from the surface of an insulating solid sphere of radius 0.385 m is 1970 N/C. Assuming that the charge on the sphere is uniformly distributed, a) what is the charge density within it? b) Calculate the electric field inside the sphere at a distance of 0.150 m from the center.
A conductive sphere with a cavity has an outer radius of 0.30 m, an inner radius of 0.25 m, and a charge distribution on its surface of +5.80 µC/m2. If a charge of -0.56 µC is placed in the middle of the cavity inside the sphere (ke = 8.99 × 109 Nm2/C2nd)a) What would be the new charge density outside the sphere?b) What is the electric field just outside the sphere?c) What is the electric flux through the spherical surface just inside the inner surface of the sphere?
(a) Find the net electric flux through the cube shown.(b) Can you use Gauss’s law to find the electric field on the surface of this cube? Explain.
n figure (a), a particle of charge +Q produces an electric field of magnitude Epart at point P, at distance R from the particle. In figure (b), that same amount of charge is spread uniformly along a circular arc that has radius R and subtends an angle θ. The charge on the arc produces an electric field of magnitude Earc at its center of curvature P. For what value of θ does Earc = 0.665Epart? (Hint: You will probably resort to a graphical solution.) _________° (please include units so that I can follow it easier)