Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 16 - Electric Charge and Electric Field - General Problems - Page 471: 58

Answer

a. $F_{B\;on\;A}= k\frac{Q^2}{R^2}$ b. $F_{B\;on\;A}= k\frac{Q^2}{2R^2}$ c. $F_{B\;on\;A}=k\frac{3Q^2}{8R^2}$

Work Step by Step

a. Spheres A and B have the same sign of charge, so the force that sphere B exerts on sphere A is directed away from sphere B. Use Coulomb’s law to find the magnitude of the force that B exerts on A. $$F_{B\;on\;A}=k\frac{Q_AQ_B}{R^2}= k\frac{Q^2}{R^2}$$ b. If sphere B touches initially uncharged sphere C, the net charge is equally shared between them. The new charge on B is Q/2. Spheres A and B have the same sign of charge, so the force that sphere B exerts on sphere A is directed away from sphere B. Use Coulomb’s law to find the magnitude of the force that B exerts on A. $$F_{B\;on\;A}=k\frac{Q_AQ_B}{R^2}= k\frac{Q(Q/2)}{R^2}$$ $$F_{B\;on\;A}=k\frac{Q^2}{2R^2}$$ c. If sphere A is now touched to sphere C, again the net charge is equally shared between them. Sphere A had Q, and sphere C had Q/2, so the new charge on each sphere is 3Q/4. Spheres A and B have the same sign of charge, so the force that sphere B exerts on sphere A is directed away from sphere B. Use Coulomb’s law to find the magnitude of the force that B exerts on A. $$F_{B\;on\;A}=k\frac{Q_AQ_B}{R^2}= k\frac{(3Q/4)(Q/2)}{R^2}$$ $$F_{B\;on\;A}=k\frac{3Q^2}{8R^2}$$
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