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Chapter 21: Q65P (page 629)

The initial charges on the three identical metal spheres in Fig. 21-24 are the following: sphere A, Q; sphere B, 鈭�Q/4; and sphere C, Q/2, where Q=2.00脳10鈭�14C. Spheres Aand Bare fixed in place, with a center-to-center separation of d=1.20m, which is much larger than the spheres. Sphere Cis touched first to sphere Aand then to sphere Band is then removed. What then is the magnitude of the electrostatic force between spheres Aand B?

Short Answer

Expert verified

F=4.68脳10鈭�19N

Step by step solution

01

Given

Sphere A, Q; sphere B, -Q/4; and sphere C, Q/2, whereQ=2.00脳10鈭�14C

d = 1.20 m

02

Understanding the concept

UseCoulomb鈥檚 law to solve the problem.

03

Calculate the magnitude of the electrostatic force between spheres A and B

When sphere C touches sphere A, they divide up their total charge (Q/2 + Q) equally between them. Thus, sphere A now has charge 3Q/4, and the magnitude of the force of attraction between A and B becomes

F=k(3Q/4)(Q/4)d2=4.68脳10鈭�19N

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Most popular questions from this chapter

Earth鈥檚 atmosphere is constantly bombarded by cosmic ray protonsthat originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth鈥檚 surface would intercept protons at the average rate of1500 protons per second. What would be the electric current intercepted by the total surface area of the planet?

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Fig. 21-22a). The electrostatic force acting on sphere 2 due to sphere 1 isF鈫�.Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Fig. 21-22b), then to sphere 2 (Fig. 21-22c), and finally removed (Fig. 21-22d). The electrostatic force that now acts on sphere 2 has magnitudeF'. What is the ratioF'/F?

Figure 21-14 shows two charged particles on an axis. The charges are free to move. However, a third charged particle can be placed at a certain point such that all three particles are then in equilibrium. (a) Is that point to the left of the first two particles, to their right, or between them? (b) Should the third particle be positively or negatively charged? (c) Is the equilibrium stable or unstable?

Figure 21-18 shows four situations in which particles of charge +qor -qare fixed in place. In each situation, the particles on the xaxis are equidistant from the yaxis. First, consider the middle particle in situation 1; the middle particle experiences an electrostatic force from each of the other two particles. (a) Are the magnitudes Fof those forces the same or different? (b) Is the magnitude of the net force on the middle particle equal to, greater than, or less than 2F? (c) Do the xcomponents of the two forces add or cancel? (d) Do their ycomponents add or cancel? (e) Is the direction of the net force on the middle particle that of the canceling components or the adding components? (f) What is the direction of that net force? Now consider the remaining situations: What is the direction of the net force on the middle particle in (g) situation 2, (h) situation 3, and (i) situation 4? (In each situation, consider the symmetry of the charge distribution and determine the canceling components and the adding components.)

Question: What would be the magnitude of the electrostatic force between two 1.00Cpoint charges separated by a distance of (a) 1 .00 mand (b) 1.00 kmif such point charges existed (they do not) and this configuration could be set up?
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