1.A long silver rod of radius 3.5 cm has a charge of -3.9исon its surface. Here ŕ is a unit vectorстdirected perpendicularly away from the axis of the rod as shown in the figure.(a) Find the electric field at a point 5 cm from the center of the rod (an outside point).E =NC(b) Find the electric field at a point 1.8 cm from the center of the rod (an inside point)E=0Think & PrepareNC1. Is there a symmetry in the charge distribution? What kind of symmetry?2. The problem gives the charge per unit length 1. How do you figure out the surface charge density σfrom a?

Answered: Image /qna-images/answer/07faa63c-abbd-49aa-8cc8-d8b95d5a560d.jpg

Answered: 1. A long silver rod of radius 3.5 cm…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 55P: The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the...

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A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. You may assume the charge density is uniform.
A long, straight metal rod has a radius of 5.00 cm and a charge per unit length of 30.0 nC/m. Find the electric field (a) 3.00 cm, (b) 10.0 cm. and (c) 100 cm from the axis of the rod, where distances are measured perpendicular to the rods axis.
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.
A total charge Q is distributed uniformly on a metal ring of radius R. a. What is the magnitude of the electric field in the center of the ring at point O (Fig. P24.61)? b. What is the magnitude of the electric field at the point A lying on the axis of the ring a distance R from the center O (same length as the radius of the ring)? FIGURE P24.61
A charge of q = 2.00 109 G is spread evenly on a thin metal disk of radius 0.200 m. (a) Calculate the charge density on the disk. (b) Find the magnitude of the electric field just above the center of the disk, neglecting edge effects and assuming a uniform distribution of charge.
The surface charge density on a long straight metallic pipe is . What is the electric field outside and inside the pipe? Assume the pipe has a diameter of 2a.
A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. You may assume the charge density is uniform.
A 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?
Two 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 P25.30
Three identical charges (q = 5.0 C.) lie along a circle of radius 2.0 m at angles of 30, 150, and 270, as shown in Figure P15.33 (page 524). What is the resultant electric field at the center of the circle? Figure P15.33
Assume the magnitude of the electric field on each face of the cube of edge L = 1.00 m in Figure P23.32 is uniform and the directions of the fields on each face are as indicated. Find (a) the net electric flux through the cube and (b) the net charge inside the cube. (c) Could the net charge he a single point charge? Figure P23.32
Two 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 .

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