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Ch 21 Sol spr 08 - Electric Charge and Electric Field 21.6...

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Electric Charge and Electric Field 21.6. Identify: Apply Coulomb's law and calculate the net charge on each sphere. Set Up: The magnitude of the charge of an electron is Execute: This gives And therefore, the total number of electrons required is Evaluate: Each sphere has 890 excess electrons and each sphere has a net negative charge. The two like charges repel. 21.7. Identify: Apply Coulomb’s law. Set Up: Consider the force on one of the spheres. (a) Execute: so (b) so And then Evaluate: The force on one sphere is the same magnitude as the force on the other sphere, whether the sphere have equal charges or not. 21.9. Identify: Apply , with . Set Up: . An electron has charge Execute: . The spheres have equal charges q , so and . . The charges on the spheres have the same sign so the electrical force is repulsive and the spheres accelerate away from each other. 21
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Evaluate: As the spheres move apart the repulsive force they exert on each other decreases and their acceleration decreases. 21.23. Identify: Apply Coulomb’s law to calculate the force exerted on one of the charges by each of the other three and then add these forces as vectors. (a) Set Up: The charges are placed as shown in Figure 21.23a. Figure 21.23a Consider forces on The free-body diagram is given in Figure 21.23b. Take the y -axis to be parallel to the diagonal between and and let be in the direction away from Then is in the -direction. Execute: Figure 21.23b (b)
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Same for all four charges. Evaluate: In general the resultant force on one of the charges is directed away from the opposite corner. The forces are all repulsive since the charges are all the same. By symmetry the net force on one charge can have no component perpendicular to the diagonal of the square. 21.24. Identify: Apply to find the force of each charge on . The net force is the vector sum of the individual forces. Set Up: Let and . The charge must be to the left of or to the right of in order for the two forces to be in opposite directions. But for the two forces to have equal magnitudes, must be closer to the charge , since this charge has the smaller magnitude. Therefore, the two forces can
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