A small metal sphere of mass 1.5 g and charge q₁ = - 2.80 C is held stationary at the origin. A second small metal sphere of mass 1.0 g and charge q₂ = 7.80 C is projected toward q₁. When charge q₂ is at x = 0.800 m, it is moving toward q₁ with speed 22.0 m/s. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

a) Find the electric potential at x = 0.800 m due to charge q₁. b) Find the potential energy for the system of two charges when they are 0.800 m apart. c) Will the potential energy for the pair of charges increase or decrease as charge q₂ moves closer to charge q₁? Will the speed of charge q₂ increase or decrease as it moves closer to charge q₁? Justify your answer. d) Find the potential energy for the pair of charges when they are 0.160 m apart. e) Find the speed of charge q₂ when the two charges are 0.160 m apart.

k = 8.99 10⁹ N.m² /C²