SOLUTION The +Fand the –Fforce each cause the rod to rotate in the same sense about the zaxis. Therefore, the torques from these forces reinforce one another. Using the expression (E )(L/2) for the magnitude of each torque, we find that the magnitude of the net torque is ______________________________________________________________________________

Chapter 18 Problems 99968. REASONINGThe magnitude of the electrostatic force that acts on particle 1 is given by Coulomb’s law as . This equation can be used to find the magnitude of the charge. SOLUTIONSolving Coulomb’s law for the magnitude of the charge gives (18.1) Since q1is positive and experiences an attractive force, the charge q2must be . ______________________________________________________________________________ 69. SSMWWWREASONINGEach particle will experience an electrostatic force due to the presence of the other charge. According to Coulomb's law (Equation 18.1), the magnitude of the force felt by each particle can be calculated from , where are the respective charges on particles 1 and 2 and ris the distance between them. According to Newton's second law, the magnitude of the force experienced by each particle is given by , where ais the acceleration of the particle and we have assumed that the electrostatic force is the only force acting. SOLUTION a. Since the two particles have identical positive charges, , and we have, using the data for particle 1, Solving for , we find that b. Since each particle experiences a force of the same magnitude (From Newton's third law), we can write F1= F2, or m1a1= m2a2. Solving this expression for the mass m2of particle 2, we have

1000ELECTRIC FORCES AND ELECTRIC FIELDS ______________________________________________________________________________ 70. REASONING AND SOLUTION The electric field is defined by Equation 18.2: E= F/q0. Thus, the magnitude of the force exerted on a charge q in an electric field of magnitude E is given by (1) The magnitude of the electric field can be determined from its xand ycomponents by using the Pythagorean theorem: a. From Equation (1) above, the magnitude of the force on the charge is b. From the defining equation for the electric field, it follows that the direction of the force on a charge is the same as the direction of the field, provided that the charge is positive. Thus, the angle that the force makes with the xaxis is given by F= (7.50 ×10–6C)(1.00 ×104N/C) = ______________________________________________________________________________ 71. REASONINGThe two charges lying on the xaxis produce no net electric field at the coordinate origin. This is because they have identical charges, are located the same distance from the origin, and produce electric fields that point in opposite directions. The electric field produced by q3at the origin points away from the charge, or along the −ydirection. The electric field produced by q4at the origin points toward the charge, or along the +ydirection. The net electric field is, then, E= –E3+ E4, where E3and E4can be determined by using Equation 18.3.

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