A small metal sphere, carrying a net charge of q1 = -2.90 mu C , is held in a st

Question

A small metal sphere, carrying a net charge of q1 = -2.90 mu C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.80 mu C and mass 1.90 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 (Figure 1). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. Part A What is the speed of q2 when the spheres are 0.450 m apart? Part B How close does q2 get to q1?

Explanation / Answer

A) Initial Kinetic energy(T1)= mv2/2 = 0.4598J

Initial potential energy(V1)= kq1q2/r = 0.2545 J

Take potential energy at r=0.45m as V2.

V2=0.4524J

Apply Conservation of energy

T1+V1=T2+V2;

T2=0.2619J

mv2/2 =0.2619; velocity(v)= 16.6038=16.6 ms-1

B) At the closest approach, particle gets the minimum kinetic energy(which is=0). Take V- potential energy when kinetic energy=0

Apply Conseration of energy

T1+V1= V;

V=0.7143J

k*q1q2/r=V; r= 0.285 m

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