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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, −Q/4; and sphere C, Q/2, where Q=2.00×10−14C. 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=4.68×10−19N

Step by step solution

01

Given

Sphere A, Q; sphere B, -Q/4; and sphere C, Q/2, whereQ=2.00×10−14C

d = 1.20 m

02

Understanding the concept

UseCoulomb’s 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=4.68×10−19N

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Most popular questions from this chapter

In Fig. 21-27a, particle 1 (of charge q1) and particle 2 (of chargeq2) are fixed in place on an x-axis, 8.00cmapart. Particle 3 (of chargeq3=+8.00×10-19C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force on it. Figure 21-27bgives the xcomponent of that force versus the coordinate xat which particle 3 is placed. The scale of the x-axis is set by xs=8.0 cm. What are (a) the sign of charge q1 and (b) the ratio q2/q1?

Figure 21-11 shows four situations in which five charged particles are evenly spaced along an axis. The charge values are indicated except for the central particle, which has the same charge in all four situations. Rank the situations according to the magnitude of the net electrostatic force on the central particle, greatest first.

Point charges of +6.0μCand −4.0μCare placed on a x-axis, at x=8.0mand x=16m, respectively. What charge must be placed at x=24mso that any charge placed at the origin would experience no electrostatic force?

A particle of charge Qis fixed at the origin of an x-ycoordinate system. Att=0a particle (m=0.800g, q=4.00μC) is located on the xaxis atx=20.0cm, moving with a speed of50.0m/sin the positive ydirection. For what value of Qwill the moving particle execute circular motion? (Neglect the gravitational force onthe particle.)

Question: Figure 21-31 shows an arrangement of four charged particles, with angle θ=30.0°and distance= 2.00 cm. Particle 2 has chargeq2=+8.00×10-19C; particles 3 and 4 have chargesq3=q4=-1.60×1019C. (a) What is distanceDbetween the origin and particle 2 if the net electrostatic force on particle 1 due to the other particles is zero? (b) If particles 3 and 4 were moved closer to thex-axis but maintained their symmetry about that axis, would the required value ofDbe greater than, less than, or the same as in part (a)?
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