A small metal sphere, carrying a net charge of q_1 = -2.70 mu C, is held in a st

Question

A small metal sphere, carrying a net charge of q_1 = -2.70 mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -7.20 mu C and mass 1.90 g, is projected toward q_1. When the two spheres are 0.800 m apart, q_2 is moving toward q_1 with speed 22.0 m/s (Figure 1). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. You may want to review (pages 752 - 758). For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Conservation of energy with electric forces. What is the speed of q_2 when the spheres are 0.390 m apart? How dose does q_2 get to q_1 ?

Explanation / Answer

Part A: Conserving the initial energy at the distance of ri = 800m and rf = 390m. Mass of the particle m = 0.0019 kg and k = 8.99 x 109 N m2 C-2.

Ei = Ki + Ui => Ei = 1/2 m vi2 + k q1 q2 / ri = 1/2 x 0.0019 x 222 + k (-2.7x10-6) x (-7.2x10-6) / 0.8 = 0.678 J

Ef = 1/2 m vf2 + k q1 q2 / rf

Equating the two energies, Ef = Ei

=> vf2 = (0.678 - 0.448) x 2 / m = 242.1

=> vf = 15.56 m/s

Part B: Considering head-on collision, at the distance of closest approach, there will be only potential energy

So, Ei = 0.678 J and Ef = k q1 q2 / rm

=> rm = k q1 q2 / Ei = 0.258 m

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