Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 23, Problem 35P
You are working for the summer at a research laboratory. Your research director has devised a scheme for holding small charged particles at fixed positions. The scheme is shown in Figure P23.35. A large insulating sphere of radius a carries a total positive charge Q with a uniform volume charge density. A very thin tunnel is drilled through a diameter of the sphere and two small spheres with charge q are placed in the tunnel. These spheres are represented by the blue dots in the figure. They find equilibrium positions at a distance of r on either side of the center of the sphere. Your research director has had great success with this scheme. (a) Determine the specific value of r at which equilibrium exists. (b) Your research director asks you to see if he can extend the system as follows. Determine if it is possible to add transparent plastic tubes as extensions of the tunnel and have the small spheres be in equilibrium at a position for which r > a.
Figure P23.35
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Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconducting walls, the beads move, and at equilibrium, they are a distance d apart (Fig. P22.44).
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50. Two small spherical conductors are suspended from light-
weight vertical insulating threads. The conductors are brought
into contact (Fig. P23.50. left) and released. Afterward, the
conductors and threads stand apart as shown at right.
a. C What can you say about the charge of each sphere?
b. N Use the data given in Figure P23.50 to find the tension in
each thread.
c. N Find the magnitude of the charge on each sphere.
0.500 m
( = 0.750 m
e3 0.750 m
23.4° 23.4°
0.350 g
0.350 g
FIGURE P23.50
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 E23.1. 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.…
Chapter 23 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 23.2 - Suppose a point charge is located at the center of...Ch. 23.3 - If the net flux through a gaussian surface is...Ch. 23 - A negatively charged rod of finite length carries...Ch. 23 - A positively charged disk has a uniform charge per...Ch. 23 - A uniformly charged ring of radius 10.0 cm has a...Ch. 23 - The electric field along the axis of a uniformly...Ch. 23 - Example 23.3 derives the exact expression for the...Ch. 23 - A uniformly charged rod of length L and total...Ch. 23 - A continuous line of charge lies along the x axis,...Ch. 23 - A thin rod of length and uniform charge per unit...
Ch. 23 - (a) Consider a uniformly charged, thin-walled,...Ch. 23 - A vertical electric field of magnitude 2.00 104...Ch. 23 - A flat surface of area 3.20 m2 is rotated in a...Ch. 23 - A nonuniform electric field is given by the...Ch. 23 - An uncharged, nonconducting, hollow sphere of...Ch. 23 - Find the net electric flux through the spherical...Ch. 23 - Four closed surfaces, S1 through S4 together with...Ch. 23 - A charge of 170 C is at the center of a cube of...Ch. 23 - (a) Find the net electric flux through the cube...Ch. 23 - A particle with charge of 12.0 C is placed at the...Ch. 23 - A particle with charge Q = 5.00 C is located at...Ch. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Find the net electric flux through (a) the closed...Ch. 23 - Figure P23.23 represents the top view of a cubic...Ch. 23 - Determine the magnitude of the electric field at...Ch. 23 - Prob. 25PCh. 23 - Prob. 26PCh. 23 - A large, flat, horizontal sheet of charge has a...Ch. 23 - A nonconducting wall carries charge with a uniform...Ch. 23 - A uniformly charged, straight filament 7.00 m in...Ch. 23 - You are working on a laboratory device that...Ch. 23 - Consider a long, cylindrical charge distribution...Ch. 23 - Assume the magnitude of the electric field on each...Ch. 23 - A solid sphere of radius 40.0 cm has a total...Ch. 23 - A cylindrical shell of radius 7.00 cm and length...Ch. 23 - You are working for the summer at a research...Ch. 23 - You are working for the summer at a research...Ch. 23 - Find the electric flux through the plane surface...Ch. 23 - Prob. 38APCh. 23 - Prob. 39APCh. 23 - Show that the maximum magnitude Emax of the...Ch. 23 - A line of positive charge is formed into a...Ch. 23 - Prob. 42APCh. 23 - A sphere of radius R = 1.00 m surrounds a particle...Ch. 23 - A sphere of radius R surrounds a particle with...Ch. 23 - A slab of insulating material has a nonuniform...Ch. 23 - A sphere of radius 2a is made of a nonconducting...Ch. 23 - Prob. 47CPCh. 23 - Prob. 48CPCh. 23 - Review. A slab of insulating material (infinite in...Ch. 23 - Identical thin rods of length 2a carry equal...Ch. 23 - A solid insulating sphere of radius R has a...
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