A small metal sphere, carrying a net charge of q 1 = -2.60 C , is held in a stat

Question

A small metal sphere, carrying a net charge of q1 = -2.60 C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.20 C and mass 1.80 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.

What is the speed of q2 when the spheres are 0.450 m apart?

How close does q2 get to q1?

Explanation / Answer

PE of a point charge in the influence of other charge = kq1q2/d

initial :

PEi = (9 x10^9 x 2.60 x 10^-6 x 7.20x 10^-6) / 0.800

PEi = 0.211 J

KEi = mv^2 /2 =(1.80 x 10^-3 ) (22^2 / 2) = 0.436 J

finally:

PEf = (9 x10^9 x 2.60 x 10^-6 x 7.20x 10^-6) / 0.450

PEf =0.374 J

KEf = mv^2 /2

using energy conservation,

0.211 + 0.436 = 0.374 + (0.0018 v^2 /2 )

v = 17.40 m/s .....Ans

it can go towards q1 upto its KE becomes zero.

0.211 + 0.436 = (9 x10^9 x 2.60 x 10^-6 x 7.20x 10^-6) /d + 0

d = 0.26 m

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