A small metal sphere, carrying a net charge of q1 = 2.80 µC, is held in a statio

Question

A small metal sphere, carrying a net charge of q1 = 2.80 µC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = 3.50 µC and mass 2.10 g, is projected toward q1. When the two spheres are 0.800 m apart, q2 is moving toward q1 with speed 22.0 m/s (see figure below). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

(a) What is the speed of q2 when the spheres are 0.400 m apart? m/s

(b) How close does get q2 to q1? m

Explanation / Answer

Initially the total energy is
E = PE + KE = kQq / d + ½mv²
E = 8.99e9N·m²/C² * 2.8e-6C * 3.5e-6C / 0.8m + ½ * 0.0021kg * (22m/s)²
E = 0.216 J

(a) When d = 0.400 m, PE = 8.99e9N·m²/C² * 2.8e-6C *3. 5e-6C / 0.4m = 0.220 J
so KE = 0.0673J - 0.220J = -0.1527 J = ½ * 0.0021kg * v²
v = 12.05 m/s

(b) When it gets as close as it can, KE = 0, and
PE = 0.0673 J = 8.99e9N·m²/C² * 2.8e-6C *3. 5e-6C / d
d =1.309 m

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