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 = -7.80 mu C and mass 1.90 g, is projected toward q1. When the two spheres are 0.800 m apart, q_2 is moving toward q_1 with speed 22.0 m/s Assume that the two spheres can be treated as point charges. You can ignore the force of gravity What is the speed of q2 when the spheres are 0.410 m apart? How close does q_2 get to q_1?

Explanation / Answer

As we know that

Initially, total energy E = U + KE = kQq / d + ½mv²

E = 8.99e9N·m²/C² * -2.7e-6C * -7.8e-6C / 0.8m + ½ * 0.0019kg * (22m/s)²
E = 0.696725 J
At r = 0.00041 m

U = 0.18954N·m² / 0.00041m = 462.2926829 J.

Maybe you meant r = 0.410 m: there,
U = 0.18954N·m² / 0.410m = 0.462.2926829 J, so the remaining
KE = (0.696725 - 0.462.2926829)J = 0.234432317 J = ½ * 0.0019kg * v²
v = 15.70894204 m/s

(b) U = 0.696725 J = 0.18954N·m² / r
r = 0.272044206 m

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