A small metal sphere carrying a net charge of q1 240 C is

A small metal sphere, carrying a net charge of q1 = -2.40 C , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.30 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.

what is the speed of q2 when the spheres are 0.380 m apart?

Solution

Change in PE

                     dU = - kq1q2[1/d2-1/d1]

                        = -9*10⁹*2.40*10^-6*7.30*10^-6[1/0.380 -1/0.800]

                     = - 0.2178473 J

use the law of conservation to find the speed of q2.

                0.5mv² -0.5mv_i² = dU

                0.5*0.0019*(v²-22^2)= -0.2178473

                v = 15.96 m/s