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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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Chapter 23 Solutions
PHYSICS FOR SCI.AND ENGR W/WEBASSIGN
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- E7BP4arrow_forward50. 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 P23.50arrow_forwardA 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.…arrow_forward
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