A small metal sphere, carrying a net charge of q_1 = -2.80 mu C, is held in a st

Question

A small metal sphere, carrying a net charge of q_1 = -2.80 mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -3.60 mu C and mass 1.30 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 (see figure below). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. What is the speed of q_2 when the spheres are 0.400 m apart? How close does get q_2 to q_1?

Explanation / Answer

a)By conservation of energy,

KE= EPE

1/2m*(vf^2-vi^2) =- EPEf + EPEi

1/2m*(vf^2-vi^2) =- kq1q2/rf + kq1q2/ri

½*1.30*10^-3*(vf^2 – 22^2) = -(9*10^9*-2.80*10^-6*-3.60*10^-6)/0.4 + (9*10^9*-2.80*10^-6*-3.60*10^-6)/0.8

After calculation we get vf= 17.6m/s

b)

Here vf=0m/s and rf=….?

1/2m*(vf^2-vi^2) = kq1q2/rf - kq1q2/ri

½*1.30*10^-3*(0^2 – 22^2) =- (9*10^9*-2.80*10^-6*-3.60*10^-6)/rf + (9*10^9*-2.80*10^-6*-3.60*10^-6)/0.8

After calculation we get rf= 0.21m

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