Two identical particles of charge 6 μμC and mass 3 μμg are initially at rest and held 3 cm apart. How fast will the particles move when they are allowed to repel and separate to very large (essentially infinite) distance? Now suppose that the two particles have the same charges from the previous problem, but their masses are different. One particle has mass 3 μμg as before, but the other one is heavier, with a mass of 30 μμg. Their initial separation is the same as before. How fast are the particles moving when they are very far apart?

The charges will repel each other and go away with increasing velocity, their kinetic energy coming from their potential energy.

Their potential energy at distance d

= kq₁q₂ / d

= 9 x 10⁹ x 36 x 10⁻¹² / 2 x 10⁻² J

= 16.2 J

Their total kinetic energy will be equal to this potential energy.

2 x 1/2 x mv² = 16.2

= 3 x 10⁻⁶ v² = 16.2

v = 5.4 x 10⁶

v = 2.32 x 10³ m/s

When masses are different, total P. E, will be divided between them as follows

K E of 3 μ = (16.2 / 30+3) x 30

= 14.73 J

1/2 X 3 X 10⁻⁶ v₁² = 14.73

v₁ = 3.13 x 10³

K E of 30 μ = (16.2 / 30+3) x 3

= 1.47 J

1/2 x 30 x 10⁻⁶ x v₂² = 1.47

v₂ =.313 x 10³ m/s